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HYDRAULIC MANUAL

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WORKS BY THE 8AUB AUTHOR, 1

MODERN METROLOGY. A Manual of the Mciiical Units

Surbi:!, CuUc Cipuily. >nd Wtith< Uniu. Pabt H.-Mcuiol
SytlcmL Tibls al europEUi, Onenul, ud Pigu Symmt:

Unio baied on SyiMmi: Coqiumi ; AUowsnct AprimDIi.—
FropoKil £i>El»h UkuuJ StiUib ; PmpoKd G^O£h Tempentun.

AID TO SURVEY PRACTICE. 38S PP- L«ge crown,

RnuU Suiveyi, ti pp.^ Fidd Kecordi, is pp.

CANAL AND CULVERT TABLES. 400 pp. Royjl, aSi.

(Alkn, .878.1 Tuil. 48 pp. ; TbUb. 3»» PP.; K«mpl«, .. pp,

TRANSLATION OF KUTTER'S -NEW FORMULA

FOR VELOCITV.' jj. pp D.im. i«. W. (Sp<.n. .IjS.) Tut

POCKET LOGARITHMS, AND OTHER TABLES.

ijopp. iBimi, V- (AUcn. iMd.) Tut ud Kumplcs, !> pp.

ACCENTED FOUR-FIGURE LOGARITHMS. JSo pp.

ACCENTED FIVE-FIGURE LOGARITHMS. 300 pp.

Super roYal. i&i. (Allen, iBIi.) Foi Ni.mberj, Kopp. F«Tri*ai».

■Ktncil kuim u Ihe Ccntaimil lJi>»u>ii of tbe De(nt, «» pp.

Tnil ac, lo pp.

Re>dr (or Pr«..
AID TO ENGINEERING SOLUTION. Engineering

THE CALCULUS FOR PURPOSES OF ENGINEERS.

P«T L— Analjucal Fronam. Puii 11, -Applied Citailiu.

L

^^^

1

HYDRAULIC MANUAL"^'

CONSISTING OP

WORKING TABLES AND EXPLANATORY TEXT

INTENDED AS

0

A GUIDE IN HYDRAULIC CALCULATIONS AND FIELD OPERATIONS

BY

LOWIS D'A.^JACKSON

AVTMOS or 'canal and CULVBVT TA9LBS' * AID TO SUSTBV PKACTICB*
' ACCINTBO nVS-PICUSB LOGARITHMS ' ' MODBRN MBTKOl OCV ' *

AND OTHBR WORKS

FOURTH EDITION.

REWRITTEN AND ENLARGED

QirKk

1 M. DE VAPONA A
LONDON

CROSBY LOCKWOOD AND CO.

7 STATIONERS'HALL COURT. LUDGATE HILL

l883^N

— y ■ . —

[Ail rights reserved]

f

LOMOON : pmnrrn) bt

SrOTTISWOODB AND Ca, NBW-STKBBT SQUAkS
AND PAKLIAMBNT STSBBT

PREFACE

THE FOURTH EDITION.

* this edition, some alterations and extensive additions

have been made. Chapter I. remains generally as before,

the alterations being comparatively small ; in the portion

licvoted to Sections of Flow, the quotation from Neville's

work has been expunged, and that subject has been

neu'ly treated ; in the portion devoted to Distribution of

Velocity in Section, full advantage has been taken of

the deductions made by Major Allan Cunningham, and

^^Jhcsehave been inserted with his consent, but also with

^^Knae modification for which he is not responsible ; the

^^Hfercnces to Box's work and to Stoddard and Dwyer's

^^fcrks have been entirely expunged ; and the whole

chapter has been revised.

In Chapter II., a summary of the methods of
gauging and of the operations of Major Allan Cunning-
ham in his recent experiments on the Ganges Canal, has

betn added. This has been reprinted from 'Engineering'

HLwith the consent of the editor, and with that of Major
^Kpinningham. This chapter has also undergone revision.

SUMMARY.

-•o»i

TEXT.

CHAPTER L

Explanation of Prhiciplis and Formuub adoftkd in Cav
cmjkTiON— 12 Sectjoiis.

CHAPTER IL

On Fisld Operations and Gauging, with buep Accounts
OF Modes adopted— 12 Sections.

CHAPTER HI.

Miscellaneous Paragraphs on various Subjects connected
WITH Hydrauucs — 10 Sections.

WORKING TABLES.

I. Gravity— I part.

II. Catchment— 4 parts.

III. Storage and Supply— 3 parts.

IV. Flood Discharge— 3 parts.
V. Hydrauuc Sections— 4 parts.

VI. Hydraulic Slopes— 3 parts.

VII. Channels and Canals— 3 parts,
VIII. Pipes and Culverts— 5 parts.
IX. Bends and Obstructions— 3 parts,
X. Sluices and Weirs— i part.
XI. Maximum Velocities— 2 parts.
XII. Hydraulic Coefficients— 5 partj

MISCELLANEOUS TABLES AND DATA.

I, M. DE VARONA «

CONTENTS

»

CHAPTER L

pwnc:pi.es ;

ll7<liad]miaiiui: Theories. ». Notnlion and Symbofs. 3. Rain-
ItO, Sapylf, and Flood DLwharEE. 4. Slorage. 5. Dischargti
of Open ChutneU laJ Pipts. 6. The Hydniuiic Section of
OuumcUmd Pip«. 7. The Hydraulic Slope. 8. Velociiie»
IB S«<t>oi>. 9, Dischiign o( Rivers. lo. Bends and Ob^lnac-
Tioiu. II. DiHhurgei of Sluices &iid Weirs, li. Discharge
from Bauni, Lodu, and Retervoin .... 1-

CHAPTER 11.

OH HELD OPESATWKS AND GAUOINC.

r DiKharge. 1. Gauging by Reclangulai
A|ip[iince9 and Inilrunienis for Observaiion ;
the Mcuurrmmi o( Vclociiies. 4. Gauging by means of Sur-
lace Velodlies. 5. Caugiog Canals aiid Slieanu with Loaded
TnbcL 6. The Miaisiippi Field Opei»tiiwii for Ganging very
imifc Riven. J. Field Operations in Gauging Crevasses. S.
Capuia Humphreys' System of Gauging Rivers, and Genend
AbboCi Mode of Deiwroining Discharges. 9. The Enpetiinenis
of d'Arcy and Buin on the Rigoles de Chaiilly et GrDsbois.
lo. Tile GsDgin]; of Tida! Riven in South America, by
J. J. K&rj. II. Laplaiu Cunningham's Experiments on ihe
(lanse* Canal. 13. General remsibs on Systems of Gauging.

CHAPTER HL

FASAGKAPHS 09 TAUOOS KXI»JUXXIC SUHJlCia^.

I. On Modules, x The Contxal of FkxxfaL ^ Tofwap^ 4. Ob
Varioos HjdRxijDaiiuc Fammlae. 5.. Tbe Watexingr of Land.
6w GmalFalli. 7. TbeTIndaiaiaf Fipo. S. Field Dcauu^e.
9^ TheRnmofCouIii la OnWater-Mdea . 211-307

WORKING TABLES.

I. GitAvrnr ;

Valoei of the Ibfoe of gnmtj in feet at <liflciffiit lafifcialet

kvd • • • 4

n. Catchment :

Part f . Total qnaotities of water lesohiiig finom a grreo efiective

rainfa]! ran off from aoj anit of catchment area 8

fart a. Supply in cubic feet per lecood thronghont the jear,
fcaulting from a given effective iain£dl nm off from
one square statute mile of catchment area . . 9

fart 3. Supply in cubic feet per second, resulting from an effec-
tive rlaily rainfall for 24 hours over catchment areas 10

fart 4. F/i divalent supply 12

rif. SfdftAur. ANfi SuffLY I

Vm\ f. (npftdty of fMervoIrs and supply from catchment • 16
f'fiff f. t^titiMtinti tif a continuous supply of water ... 20
f^fift t Kr)HivntHit (if ofrtitlnuous supply 22

^vnrtiptf** • • . 24

fV t^lHMli fit«»MIA»«« I

t'itt t. t nlit^ Mf flMtiil tllAcliarges In cubic feet per second, due

tti mtrltttiftil Hti*N» In stiuare miles ... 28

1*n»t ^. t'Idiul (tl«(t-tmt||M Iti nililo feet per second, due to catch-

\\\^w\ fttM« 30

l*ltl \ l^tMhit firKlHWrty fill ltil(l|{t o|)enlngs • . . 34

co.vrems.

^ 8ktk»»al Data :

hit 1. Fm rvcUngulM coiui'MCtioiis

hil a. Fur tnpeiuidAl Mnd-wclioA!) tuving sidc-tlopes of one

Put ^ Diioauiimi orchannel-icctioiu of equal diiclurgc

^P■n 4. Va]»«$ ol J «nd for S cyliadrioil and ovoidal pipa
and culveTis
Hvl>«Altt.tC StOPM AND GBAOIETfTS :

Pul f. ftedoclioEi of faydnulic slopes and inclinilions
Pin a. Keduclion of uiguiar declivities and grwlienli
Ful 3. Limiting IncUnaLioDS, md uigles of Repose

PCa^iau ash Ckaknels :
Put I. When the bydnalic ilope is lepiescnlcd by a ratio in
llw old form of x foil of unily in a cenain length
Put a. When the hy dtuilic slope is teprestntcd bj S, ihe sine
nf the ilopc

Pin 3. CoadlliODianddimeniians of equal'dischnr^ngchannels

of Inpciaidol i«clioD, with side slopes of one to one

^^Eiampk.

^^^UL P)rES AKD CutVUI^, JDST njiJ. :

^^^K Pan I. Appioniinate velocities io feet per second
^^^V Put 3; Appniumitc dischaiges in cubic leei per lecoad .

^^~ Part 3. Approiimate diBmnera in feel

^ Put 4. Approximate heads in fcei for n length of I poo feet

hn {. Condiliotuofequal-discharEioficulverts and drain-pipes,
mnning juat iidl .......

Eumplei

. BSXCS AStt OasTRUCTtONS :
Put I. Civine loss of head in feet due to bends of 90° in pipes
corresponding to certain discharges
I Part t. Giving loss of head due !□ bends in channels corre-
sponding to certain velocities ....
' Pan 3. GlTing approximite rise of water in feet due to obstruc-
tions, biidges, weirs, &c

Eaanpla

i OunCU AXO OvtftrAI-lS :

I VelAcilia of diicbarge uf orifices, also for deducing mean vclo-
eitin at overfalU

xiv CONTENTS.

FAGS

XI. Maximum Velocitibs:

Part I. Mean velocities of discharge corresponding to observed

maximum velocities and coefficients • • • 126
Part 2. Various limiting velocities •190

XII. Hydraulic Coefficients:

Parti. Coefficients of flood-discharge from catchment areas . 132
Part 2. Formula connecting the co-efficients of velocity with

those of roughness 133

Part 3. 3eneral values of coefficients of roughness (if) for

channels and culverts .134

Local values of n for various canals and rivers . • 136

Part 4. Velocity coefficients (r) for channels, culverts, and pipes. 138
Under grouped values of n for two fixed extreme values

oia 140

Under separate values of n, in separate tables . . 146

Part 5. Co-efficients of discharge for orifices and outlets . . 151

Part 6. Coefficients of dij»charge for overfalls .... 183

MISCELLANEOUS TABLES AND DATA.

Dimensions of trapezoidal masonry dams, for heights up to 40 fiset ;

and sections of lofty dams ....... 156

Formulae and data for retaining walls ...... 158

Table of weight of materials, and pressures on foundations . . 160

Sections of ovoid culverts, compared 161

Cast-iron waterpipes adopted at Rio de Janeiro and at Glasgow . 162
Absorption and strength of cylindrical stoneware pipes • • • 163
Arcs and sectors of circles ••••••••164

Powers, roots and reciprocals . •••••• t$6

Hydraulic machines : return of motive power . • • • • 171

Memoranda for conversion of quantities .172

Constants of labour ••174

CarU^etAble 179

INDEX 181

HYDRAULIC MANUAL.

CHAPTER I.

EXPLANATION OF THE PRINCIPLES AND PORMULiE
ADOPTED IN CALCULATION AND APPLIED IN
THE WORKING TABLES.

Hyilto^Tnamic Theoiiet, 3, Nolstion and Symbols. 3. Rain&ll.
Supply, tnd Fluoi] Dischaige. 4. Storage, j. Diicbaiges of Open
tad Pipes, 6. Th* Hydraulic Section of ChanneU and
Pipes. 7. The Hydraulic Slope. 8. Distribution of Velocily in
9. Discharge* of Rivers. 10. Ekndi and Obitructions.
-II. Discharges of Oiifices, Sluicci, oitd Wcin. 11. Diichuge iiom
Basim, Locks, aiul Reservoirs.

T. HVDRODYNAMIC THEORIES.

The science of hydraulics, yet in its infancy, may be

1 to depend, as far as its practical application by the

'draulic engineer is concerned, on a combination 6f

lin tcnoMTi laws with the empirical results of obser-

I and experiment ; the former few in number, and

miaatcd principally by the philosophers and mathe-

Iftttcians of the past ; the latter also few, and, if we

: the old observations which were carried out on

I veiy petty and limited scale, exceedingly modern.

I to the experiments of d'Arcy in 1856, little

I. H

I

2 PRINCIPLES AND FOSMUl.-E. CHAt- I.

was known about the ^■elodties and discharges ihroii^ .
pipes ; until the operations of Captains Humphre>
and Abbot on the Mississippi rn 1858, the dischai^c 1 .
large rivers was a coroparati\'e]y unexplored subject ; ■;
1865 the experiments of Bazin led the way to a mur.
accurate knowledge of the discharges and velocities ol
water in small channels and culverts, and the eflects of
roughness of surface and variety of material on these
velodties. In 1 870 Kutter and Ganguillet, from obi
vations on Swiss hill -streams, deduced a more exact ti
for effect of declivity on discharge, and Ix^sidcs adi
greatly to the knowledge of effect of roughness. ]
iSSo the extensive experiments of Captain Allan (
ningham on the Ganges Canal had substantiated \
truth of Kutter's laws when applied to very large cai
and dealt the final blow to the velocity-formulae kIC-A
the older hydraulicians.

Before 1856 the less important subjects nione I
been investigated to any practical purpose, such as t
vena contracta, the discharges through small orifices, a
certain forms of overfall, and through short and sd
pipes, the discharges from reservoirs, and the v
in troughs 18 inches wide. There was, however, pM
of theory, and a large number of formula, some of tl
exceedingly complicated in form, mostly resulting I
a number of superimposed theories, the more andetit I
which were based on very limited experiments: m I
the mode often adopted seems to have been to :
a new form of formula, and to prove it by a few pu
experiments, a principle worthy of ancient soothsay)
and which, had it been further supported by traditioi
and name-reverencing hydraulic schools of belies
could only have resulted in prolonged and permai

UYDRODYNAMIC THEORIES. 3

Even now a reference to some works com-
iBti^'cl)' recently published in England wilt show
cnultc to be supported by a most heterogeneous col-
ion of experimental data ; discharges of pipes irre-
Klivc of their material or internal surface, of targe and
small rivers irrespective of the quality of their beds and
the bends in their courses, of canals in any material,
down to wooden troughs, all seem to prove the correct-
ness of a fixed formula having an unvarying constant
cocfficieuL Other works again, having greater accuracy
of result in view, go to the opposite extreme in method
and recommend tlie adoption of two distinct formula: fur
cA.tes in which the principles involved do not varj- in the
^ Jeast, as for instance, in discharges through pipes with low
HjM^ocitics, a formula distinct from that for those with
fHigb velocities is often adopted ; this, amounting to a
^tnethod of successive approximation imperfectly worked
out, Ls almost as unfortunate as the other. From a con-
tinuance of this, however, the modern experiments have
idy saved us to a great extent, and further and more
Ended experiment will probably relieve us from it

ToScen generally, the mass of hydraulic science and
C hydraulic data bearing on the flow of water under
s conditions, prior to about 1856, may be con-
lered superannuated, defective, and often excessively
■leading. Old hydraulic data, such as discharges of
trs, canals, and pipes, seldom can afford the means of
ring near the truth, unless accompanied both by the
mulx used by the observer, and by a large number of
tditions of the case, then mostly neglected.
At present the hydraulic engineer is still quite as
dependent for correclneis of calculated result on the so-

PRINCIPLES AND FORMULAE. CBAF. <•

called empirical data, obtained by experiment and put
into convenient form, as on purely abstract theories ot
laws. The correct application of all known mechanical
laws cannot, however, fail to be valuable in cases admit*
ting of them ; those relating purely to hydrodynamics
are comparatively few, and the most important and best
known of them are the four following : —

First, uniform motion, — If fluid run through any tube
of variable section kept constantly full, the velocities at
the different sections will be inversely as the areas, or

A r=A' r.

This theory of uniformity of motion is also sup-
posed to hold generally with reference to mean velocities
of discharge in open channels under constant supply.
This is actually little more than assuming a theoretical
velocity that will fulfil the conditions of the law, in order
to render calculation convenient, for there is no reason
to believe that actual velocities in a tube of variable sec-
tion would all vary inversely with the area of cross
section.

Second, velocity of issue, — The velocity of a fluid
issuing from an orifice in the bottom of a vessel kept
constantly full, is equal to that which a heavy body would
acquire in falling through a space equal to the depth of
the orifice below the surface of the fluid, which is called
the head on the orifice ; or by way of formula

F=(2flrjy)l

where 5"= the head and gf= force of gravity. The
quantity g represents the accelerating force of gravity,
which varies at different places on the earth's surface and
elevations above the mean sea level, and is also affected

\

llYDnODYNAmC TimORlES.

fc»the spherical eccentricity of the earth at the place, a
inlity that again varies with the latitude ; above the
's surface 3 varies inversely with the square of the
ancc from the earth's centre, below the earth's sur-
e dinxt with the distance from the earth's centre ; to
hill the exact value of g, d'Aubuisson's formula
pplied to English feet are—

T= 20 887 540 ( 1 + 0-001 64 COS 2 V)

ff=32-1696(l +000284 cos 2 0 (l-^*).

I The values of this formula for different latitudes and
' tlCTitions are given in Working Table No. I„ and the
.3iu«s of (?, obtained from observation at different lati-
■ MC9, arc given in Table No I. of the Hydraulic
•iritistics. For purposes of ordinary calculation in
rin^land. and hence throughout these tables, </ is gene-
rally tskcn as 32'2 feet per second ; in India, however,
it would be more correct to use 321 , but the con-
\tnience of using English data will probably outweigh
the need of this exactness until the science of hydraulics
can arrive at higher accuracy.

The above theory supposes that the orifice is inde-
Gnitcly small, and neglects the conditions and size of
Hs sectional area, friction, the pressure of the atmosphere,
and the resistance of Uie air to motion (which increases
with the square of the velocity of the issuing fluid) ; the
practical application of it that shows its discrepancies
most strongly is the fact that the height of a jet is never
equal to the head of pressure on it

K Third, general theory of ftozu. — This is a combina-
of the two previous theories in a modified form,
miDg both uniform motion and the principle of

6 PRINCIPLES AND FORMULjE. chap, l

gravitation, and is best expressed in the form of a
formula —

where V = the mean velocity generated,

R = the mean hydraulic radius of the water-
section,
/S = the hydraulic slope or sine of the slope of the
water-surface.

This formula is a simple equation of the accelerating
force of gravity down an incline with the retarding force
of friction at any section at right angles to the course of
flow, namely :—

«=Q

since, for uniform motion, the total accelerating force is
equal to the total resistance.

This theory is the basis of calculation of flow in full
tubes, and in open channels and unfilled pipes, where
the principle still holds, but / then becomes a sym-
bolic representation of retardation due to a combina-
tion of various causes, including direct friction on the
general incline at the given section.

Fourth^ Vie principle of retardation, — This is repre-
sented by a collection of various small formulae and
methods of making allowance for loss of velocity under
different conditions by a calculated head. These retard-
ations may be introduced into any general formulae,
or may be treated separately. The ordinary sources of
retardation are : —

I. Roughness of surface, varying from that of polished
glass to rock-strewn or deeply-incised rocky torrent-
beds ; also surface-adhesion of liquids.

.t:t. I HYDftODVlfAmC THEORIES. f

z. Irregularity of form, varying from that of a re-
cently made and trimmed rectilinear canal of one single
umfoTin inciination and direction down to that of a river
bed consisting of an infinity of heterogeneous planes
And curbed surfaces. Any departure from uniformity,
lateral and Vertical deviations and bends.

3- Varying head, inconstant pressure, diminution of
^■.lpply, toss of effective head from excess of withdrawal.
4. Contraction at exit, want of perfect freedom of
1 j!I, backwater, contraction of passage, obstacles,

5. Air resistances and effect of wind ; atmospheric

aire ; differential liquid pressure internally.

6. how specific gravity of the liquid in motion, tur-
iity, viscosity, and variation in weight

7. The effect of variation of heat inducing motion
I the liquid, and thus producing perturbation, and the

[nute effects of local change of temperature generally.
I 8. Absorption of velocity by yielding material,
may imperfectly deflect velocity, and partly
absorb direct action.

However rigid these theories may appear in neglect-
ing important points, they are yet generally true in the
abstract, and no substitutes for them have yet been
discovered ; the consequence is that all hydraulic calcu-
lations arc made to depend on them, their defects being
mpenKitcd by using experimental coefficients. It
, therefore, one of the important duties of a
raulic engineer to apply these principles with care
1 circumspection, especially guarding against taking
\ granted ihc formula; and tabular results of different
xilaion. which vary in form and in result to a very
I extent ; some authors even giving a half more
c tban others as due to the same data. During

i

8 PRINCIPLES AND FORMVLiE. CHAr, :

practical work, time forbids a lengthy examination of
principles ; for thisreason, therefore, this short chapter
is given as an easy guide to the proper management
and application to every-day wants of the Working

Tables that follow.

ne can

:ssio^H
: sani^

2. Notation, SyMBOLS, and Units of Measuri

To ensure clearness and rapidity of application of
these theories, it is absolutely necessary that the nomen-
clature should be neither doubtful nor inconvenient,
that the symbols be free from confusion, and the units
of time, weight, and measurement, once adopted, gene-
rally adhered to as much as possible; this alone can
cause the form of a formula to give at a glai
definite idea of the values of its terms and expressiM
Decimalised measures are also necessary for the i
purpose.

The English foot has been generally, though not
quite exclusively, adopted in this work as the unit of
length, surface, and capacity, being the measure onii
narily used for heights and depths, as well as distanci
in survey work, and being now more capable of c.\-
tended application than either the yard, link, or iad
The footweight, or weight of a cubic foot of water *t H
utmost density (the English talent), has been takeni
the unit of weight, being now a recognised legal sts
dard unit. The whole system of decimal mes
founded on these are on the scientific scale at 32"^
Fahrenheit, so as to afford exact correspondence be-
tween cubicity and weight, and to admit of facile con-
version to metric values. The second has been |
rally taken as the unit of time, so that the numbl

IfOTATWN A}^D U.VITS.

jvessing discharges and velocities, which ofVcn are
[ ob numbers, may be as small as possible. This has
been found to be perfectly manageable in practice. In
Ihc can^ departments of Northern India the engineers
have succeeded in abolishing poles, yards, and inches
(rum tfacir plans, estimates, and calculations, and in ad-
hering generally to the second as a unit of time ; they
have also, on the Bari Doab Canal, adopted the old
London mile of $ ooo feet to the exclusion of the statute
mile of 5 2S0. The league of two such miles, or 10 000
feet, being a decimal unit, is now far preferable. The
acre, pole, and old Gunterian chain of 4 poles being
highly inconvenient, the substitutes for these are the
rod of 10 feet ; the chain of 100 feet (Ramsden's) ; the
square chain of locxx) feet, nearly a rood ; the century,
or square cable, of 100 square chains ; and the square
league of 100 centuries. This decimal system of mea-
sures, though retaining the use of a familiar unit, and
iving much needless labour in calculation, at the same
It has some difficulties to contend with, the principal
which are the old habits of measuring water-supply
town5 in gallons instead of cubic feet, and of using
dimension-s of pipes in inches, instead of tithes or tenths
of a foot, estimating pressure on the square inch instead
of on the square foot and square tithe ; these obstacles
will probably gradually disappear.

As regards the French metric system, although it is
DOW adopted for external commerce in most civilised
lines in Europe, there seenns little chance of its en-
rcplacing our own measures, English scientific
ires are naturally more convenient for an English-
to think and calculate in, and are in closer accord-
with English commercial units adopted in trade.

Hit.

W-

to PRl\ClPl£S A.VD FOK.WLyE. CM*P. t

manufactures, and contractors' plant and appliances;
besides, natural units are preferable to artificial ones.

The hydraulic engineer more especially can adopt
the decimal system of measures based on the English
foot with extreme convenience ; nor apparently are
there any very good reasons why the railway engineer
should not do so also, except perhaps the Iradii
loving habits of the multitude, and the meddlesoi
legislation in social matters under which we sufTcr,
which enforces on him the adoption in Parliamentary
plans of the whole of the o!d measures, with the alter-
native of using foreign measures. ITiis difficulty will
perhaps be eventually removed by permissive legisla-
tion, allowing the use of the complete English decimal
series for all technical, engineering, and scientific pur-
poses, apirt from ordinary trade, and fixing the standanJff,
finally on the principles proposed and long advocated by
the author, — namely, at a single normal temperature
in vacuo, the single temperature both for material and
for water being that of the maximum density of dis-
tilled water.— a method far superior to the dual tem]
ature of the French system. In the meantime it may
remembered that decimalisation on any English uni(
is permissive under the Act of 1 878, thus actually ii
eluding tlic whole of the English decimal scien
system ; while there exists no legal prohibition of
ad interim temperatures 32° and 39° in vacuo used
French measure.

The advantage of adhering to one set of symbols
hydraulic formulae, which sometimes appear vcrj- coi
plicated, is sufficiently evident; with this view, thi
fore, the following general notation is drawn up.
velocity notation of the Mississippi survey isalsoattaci
for purposes of reference;

ineer «

itioifci^l
sonwr^

I

General I^otatton.
T-Htit alnGkl) npiirswd in depih.

t-d

I'^astitT nf v-i(c( •liscliar^cd in cubic feet pet stcon<].
• •Ban irln-cily of ttischii^ in feet pet Kcuod.
r, - ntmcouling maiiinum velocity in the ume KCllon.
r-TOticaUc velocily, o( velocity past a Ten ical line oi mi
r - tMBiTOsdic Telocity, or relodly posl a Iransverml. oi
J =-icaMMftl Mca ; a. e„ d^ sabudiary areas.
P—wmitA leclioiuJ perimeter, eKcIutiie of the sarbce-widlb, W,
Afltltc n»i ■» hyiLnuIic rsJim^ ^.

Jl,— diminklied bydnulic radiui? _ — —
hydnalic radius- ^
itnialic slope or padimt in terms of itt «ine'> Z;
t= J— 0-00aforaslopeof1 in .WO.
ludinil length taken in the direction of flow.

. any roth length t or > vertical hcid of pteisure.
of (cTel of the water mrface at the two ends of;.
■ IjOtlie pad of i consumed in overcoming longitudinal channel
kn a iliaighl, legolar course.
- the pari of A coniiuned in overcoming transvetse channel

tM littguiatilies.
' ■ tranoecie width at water surface acros* the direction of flow.
■ votica] depth from suiface leiel.
B brd-widlh or boltoni-widlh of a section.

iX lime ol discharge ; (, f„ 1„ MibsiUinry timei.

IrDt of roogbnesB and irregularity combined.
(41-64^0-C»381 X i), a combined variable.

iml for supply from catchments,
lent iot mean velocity in channel di^chsrgci.
i«nt (or orifice and overlkll discharga and velocities.
Ily acqiured by gravity in oneiecotid^'SJ-a feel agipiojimately.

f, y, z, aie rectangubr co-otdioales taken with reference to
mler, the following conventional arrangement is uiunl,
t taken in the direction of flow, or longitodinally ;

II ia liJtefi acrms the Bow. or transveisdy (

I ia taken veiiically, ot petpendiculai to i.

AD dinwiuioiu are generally in feet and decimals, nnd velocities and
'lucharja arc in feet and ca)iic Feet per second. The foot-weight or
laWnl - 1 ooa cmnca, \t the unit of wdght ; its multiple is the rod-weight
• I 000 fai. fat ilceimi] multiples and submulliplcs see page 14.

^£IS€IKjeS AXD FOMMCLM, ClIAP. L

TAsdj XitaSim ^&€ Mhsissiffi Smroiy,

panDd to die cuncnt

of 100 feet

£r»velodiT M any pone is tike Meai of aD verticil planes paxmnel to the

cmcsL
r^«rgEaad moBk of the Mei teliArtifS is all Temol fdanes pandlel to

tbecsmL
Cr^stlie Bean of tbe bottOB Tdodties IB aD sadi pfames.
^ FsireSodtj at any depdi belov tbe sazfKe at a perpendicular distance

ir^ from the base line.
F^s Telodtj at the sarfux in any vertical plane paiaDel to the current
V^ and y^ - Tclocities at mid-depth and at the bottom in any such plane.
\\ and Fa. = the maximnm and the mean vdocities in any such plane.
YFs riTcr width at any given place.
ir s perpendicolar distance firom the base line to any point of the water

sur^&ce.
K, *■ perpendicular distance from the base line to the snriace fillet moving

with the maximnm vdodty.
/>« total depth of river at any given point <A snrfiioe.
^^sdepth of any given point below the surface.
d, a depth from the surface of the fillet moving with the maximum velocity

in the assumed vertical plane parallel to the current,
fpi as depth from the sur£ux of the fillet moving with a velocity equal to the

mean of the velocities of all fillets in the assumed vertical plane

parallel to the current.
L m maximum or mid-channel depth.

'.I

N^OTATION AND UNITS.

n

As it may be convenient to the reader to have con-
voskn tables at hand for reducing the quantities of water,
ftc, given in foreign works on hydraulics into English
fflcasnre, and the converse, the following two pages are
given to answer this purpose, as far as r^;ards the English
decimal system.

For other corresponding purposes, see 'Modem
Metrology,' London, 1882, Lockwood, and 'Pocket
Logarithms and other Tables,' London, 1880, Allen.

PRINCIPLES AND FORMULjE, a

COMPARISON OF FRENCH AND ENGLISH DEC

EnCiish Scientific Uaits In Ensfish F,«eli

Commercial Units g._.. .5'\i*^.

Lci«tk at e»- Fahrcnbext ^^""^"^ ^^^'P^

foort -10 tithes (or tenths) » 1-00029 feet « 0-301 TSmto

Rod -lOfeet « 3<M796mtoi

C»aui -lOrods -»0479Sdecai

Cable -lOchains .... - 30l79Sb€Cto

League » 10 cables .... » 3i)l79SkikMD

Sur&ce

.Square Foot »100 sq. tithes » 1^00057 sq. ft » ^289 97 d^

Square rod »100sq. feet. . » 9*289 97 m^

Square chain » 100 sq. rods » 9^89 97 ares

Sq. cable or century » 100 sq. chains . « ^289 97 hecti

Square league »100centrs. . . « 9-289 97 kiL i

Capticity

Fluid mil = 1000 fl. doits . . . »28-31S31 milL

Fluid ounce » 1000 fl. mils » i cub. tithe = 28-315 31 cent

CuBicFooT«1000fl.ozs. = 1000 cub. tithes =1-00086 cub. ft. =28-31531 dec \
Cubic rod =1000 cubic feet . . =28-315 31 met.

WeiKht

Mil = 1000 doits - 28*315 31 milgr

Ounce (millesimal) =1000 mils . = 28*315 31 grami

Foot weight or talent = 1000 ors. = 62 '42454 lbs. = 28*315 31 kilog,

Rod weight =1000 fwL . = 28-315 31 millic

COMPOUND UNITS.

Pressure.

I talent (or foot- weight) per sq. foot . =304-7q4 5 kilog. per m^t. ca

„ „ „ . . = 0-03047945 kilog. per cei

I talent (or foot weight) per square tithe » 30 "479 45 milliers per m^t. >

I rod- weight per square foot . . = 304*794 5 milliers per meL c

Irrigation.

I cubic foot per square chain . . = 0*304 794 5 met. cub. perl
I cubic foot per century . . . -• 0*003 047 9 met. cub. per!
I cubic rod per century . . . « 3*047945 m^i. cub. perl

Power and Work.

I foot-talent = 8*630 354 2 kilogramm^tr

I h.-p. = 528 foot-talents per minute . = i*oi2 63 c.-v. force de ch«

Heat and Electro-magnetism.
I foot-mil = o*oo8 630 35 metre-gramr

Simple and Compound Units of Reduction.

English into French

Simple . . . 0*304 794 494 Cubic . . . 0*028 3
Square . • . 0*092899683 Fourth power . . 0008 c

NOTATION AND UNITS.

- SYSTEMS AT 32* AKD 39° FAIiR. IN VACUO,

'T - lO dfauBittc* .

rn Engli-h

Conimercinl I' nils

Bl es- Fahrenliell

- 3-181 S3 feet

Sckalilic EquinlEal

■ »280 90 reet
= 3'eSO 90 rotts

■ 3'380 90 cbnins

iCjujit.nOdkfan. CXI. .
— ttOucs

-lOliim ,

• tOhccioUlm

= 10770 43 sq. ft. = 10'76* 30 srjuare feel
^ W'TSl 30 square rodi
-10-764 30 sq. ebains
>c 0' 107 64 K|. leugvcsi

-3£'3tG68e<i[d, ois,

- 0'3&3 17 cubic feet

- 3-631 66 cubic feet
- 3S-346 83 cuK ft. =35316 58 cubic feet

= 35-316 58 doiu

- 3-331 658 mils
-21046: lbs. -35-316 68 ouncfs

= 3-S3I 66 foolweigbt

- 36-316 58 footweiEhl

^H COMPOL'ND UNITS.

nauH per mkre ami . . ^ 0-003 280 9 tiil«nls per sq. fool

nmmc per cenlimitiE eani . — D'328 039 9 lalenl; )>« eq. lithe

ir p«f piHit ant . . . ^ 3-280 899 laicnls per sq. fool

w pa caUnttic aari . . - 31-808 990 cod-weighi p«[ sq. foot

3'280 899 cubic feet persq, cbun

3!8'0e9 9 cubic feet pef century

0-328 090 cubic todi per century

^I.^'Z.IIVLES AXD FO^MUUE. OUP. L

5- F^Ajn^f ". SiTFiT, AXD Flood-Discharge.

. hyoTEzliz works of inigatian, diaxnage. storage^
tier supply, rh-er iziprDvczDCsi, asul land reclamation,
are zirjrt. dt kss a'rerrftc Inr i3)e amount and periodicity
of ibc Ta£n:2ll : fee xnam- of than caxcfbl and trust-
Tonihy rcinfoll sraiisdcs and data are absolutely requi-
site ; but ibe rarure and amount of detafl required vary
n-iih the nature of :be work ; works of storage being
those that, perhaps, require the greatest amount of
accurate informataon. In order that these local records
should be suiBdent to form a correct basis for the en-
gineering cata of these laner works, thc\" should com-
prise obsenatior.s extenclr.g o\-er a period of ten years,
or of the local period comprehending a cjxle of rainfall
from one season of maximum rainfall to another, in-
cluding years of extreme drought ; from these the
following results can be deduced : —

1. The mean, maximum, and minimum monthly rain-
fall, from which the mean and extreme falls for each
natural local season, wet, cold, and hot, can be obtained.

2. The mean and maximum daily falls in twenty-
four hours, for each month in the rainy season.

3. Mean and maximum hourly falls, longest con-
tinuous falls and droughts, and special occurrences.

These, arranged in a convenient tabular form, are
all the rainfall data that the engineer will generally
require.

In most cases, also, and especially in hot climates,
evaporation records are also necessary ; and sometimes,
too, it is advisable to possess other meteorological data,
such as those of humidity, temperature, atmospheric

SUPPLY AXD FLOOD DISCHAKGE. ij

TTissure, and wind ; and, what is often difficult to pro-
Li:re, sonne data of absorption and percolation that
would be applicable to the soils of the district under
conudcration.

On many of the works before mentioned, the first
duty of the engineer is to account for the whole of the
downfall, or to discover what becomes of it all, under
both ordinary and unusual circumstances, so that he
may be able to deal with more certainty of knowledge
with that portion of it that more intimately affects his
u-orks; as, for instance, the bridge- builder with the
floods, the engineer of storage works with the drought,
«nd those of canals and river-improvement with both.
\ geographical and geological knowledge of the catch-
' nt afca, whose rainfall alTects the works, is hence also
; the boundaries of this area, its lines of watcr-
[ and drainage, its disposition as regards prevailing
ids, the nature and porosity of its soil, and the
■ount of vegetation or cultivation on it, as well as any
BJlablc records from whlcli the quantities of water
lally run off by its streams and rivers in various
loris may be arrived at, arc all data necessary for
bblishing satisfactorily a perfect knowledge of the
1 of the whole of the rainfall under any circum-

[ In many instances it is, from want of sufficient in-
mation. utterly impossible to obtain this perfect
bwlcdge : in others, the deficient dau may be siiip-
d by approximative deduction from the data of other
*», so that a tolerably correct approximate balance
f be struck between the downfall and the amount
rated, absorbed, and run o(T: in any case, how
, the engineer may, with time and means at his

iS mmCJFLSS AXD formula. ckap.I-

dtsposai, gauge the streams and rivers affecting his
works, and make correct records of the amount of wat«
ran off in them at different seasons of the year, and in
exceptional floods. Failing, howev-er, both time and
o|)portun)t}'. such data ha^'e to be observed in a rapid
tnknmr that will enable him to determine this approxi-
tltdy ; such as the section and fall of the i

s at various stages, floodmarks, and a few \-eloc
r\'ations.

The results principally required are the flood i
maximum discharge, in cubic feet per second, of t
nvcr or stream draining the catchment area ; its mei
dischai]ge throughout the year ; and its minim
discharge in seasons of extreme drought, as well a
its ordinar>' low stage . dividing each of these by |
catchment area, similar results per unit of catchm^
arc obtained, to obtain the depth in feet of i
run off under each of those conditions. The relatlj
between these quantities and iJie probable or apprq
mate downpour over the catchment area can thet
comi>ared with those known to exist in other i
sponding cases, and a valuable check on these import
results thus obtained.

Flood discAarge. — The determination of the quantH
of water discharged from a catchment area in a river c
.stream at a time of extreme flood is a matter that I
\'er>- often of the highest im|x>rtance. Costly bridge
have continually been sacrificed, and long tcngdis ofu
damaged for want of sufficient attention having been p
to this subject.

When the data mentioned in the foregoing paq
graphs can be obtained, and are properly handled, thei
is lillle difficulty in arriving at a generally correct r

SUPt*t,V AND FLOOD DISCHARGE.

•c- in many cases only some of these are forthcom-
'.he bases of calculation are considerably narrowed,
■: '.iic various and partial modes that have to be adopted
-ssarily vary with the available data,
firj/,— If the catchment area is not very large — that
-jot exceeding 400 square miles, or 100 square leagues
It may sometimes be assumed tliat the whole of it is
;.ultancou5ly subject to the same amount of maximum
iTipour, and that the loss by absorption and evapora-
i j:i is also tolerably uniform over the whole ; if then
soroc tnistworthy data for this loss should be available,
the flood discharge can be computed direct ; thus :

Let F, the actual downpour in 24 hours, be 0'8 feet, and the
loM by absorption and evaporation one fourth ; then the effective
laioUl /=0-8— 0-2=0-6 ; and the corresponding flood dis-
e per second, Q, from a catchtneni {K) of 4 square leagues,

M>b

=2718 cubic feet per second.

■tloel

If the rainfall or the loss vary over portions of the

catchment, the parts may be treated in the same way,

[la obtain a total value of Q through summation. For

purpose Table 1 1., Part 3, can be used.

Seiotut. — If the catchment area under consideration

happen to form part of some large region, whose rainfall

has been thoroughly investigated, and in which numer-

mis flood discharges have been arrived at through

:tt^- observations and compulation, some general

ienl of drainage (t) may have been determined

that region. In that case the computation for flood

;c from any portion of it can be computed by

Jb

a.. I^KIA CIFLES AND FORMULM. chap. L

"Htt tiuce best-knoirn fonnnbe for this purpose are

,2 e=rI^100(iL)i.

,3; Q=ii 1300 !:(£)"*.

In oil these JT is the catchment in square statute
xnilefv, V the dcod discharge in cubic feet per second ;
in the third L is the length of the m^n river or stream
under consideration, in statute miles ; while the coeffi-
cients Iv. i%. h^ are the local drainage coefficients suit-
able to each formula respecti\"el>-.

Fonnula J]^ requires a \'er\' wide range of values of
t., and is hence inconvenient, though simple in form.

Formula ^2 is preferable; it is a modification of
Coionei Dickens's formula, Q=825 (iH^ suited to Bengal
proper and Bahar : though it aften^ards appeared that
Formula ^2) with coefficients near to t=8-25 was suited
to large tracts of Indian plains having an annual rainfall
of from 24 to 50 inches.

It seems, however, more rational to use a coefficient
more closely dependent on a similarit>' of general con-
ditions, of which the maximum day's downpour is perhaps
the most important In Northern India where this latter
is about 1*5 feet in or near hills, and ix) foot in the plains,
the flood waterway allowed for bridges has generally
been based on the assumption that the rainfall run off
would amount to vo foot in depth over the whole ; and
allowance has been made with these data for the flood
waterway of the streams and rivers crossing both the
Ganges Canal and the Sarhind Canal ; in other cases,
also, in Northern India, two-thirds of the depth of
downpour is assumed to pass off in flood. It is hence

: IQ aae a coeffident suitable to similar conditions
..iiihmcnt area, within narrower range.
Vtic values of k\ for India generally lie between i
' n : sec coefficients in the Working Tables at Table
'■'... Part J ; — some further values of it, applicable
vuiuus fiver basins in India, are also given in
i- lable of flood discharges at page [S] of the Hydraulic
Sutislics in the second part of this Manual. The
valiKS of the general expression, for a value of i',= r,
art given for catchment areas of various sizes in the
^nVing Tables, at Table IV,. Part i, and the local
it can be readily applied to these quantities.
Formula (:i) was deduced by Mr. Burge, of the
Madras RaiU-ay, from observations in the tract through
which that line pa^ws ; and is suited to it, with a value
of l:,= l J the conditions being that the maximum down-
pour in 12 hours was 6 inches, and the area elevated
from 500 to 1 300 feet above mean sea level, consisting
principally of unstratified rocks. It was deduced from
' •-■ervations on 27 bridges, of above 80 feet span, on the
i.uiras Railway, and its results correspond closely with
;!itseof recorded flood sections ; the errors lying between
464 feet too high and 340 too low in height of section.
Mr. Barge argued justly that the length of the river neces-
ly extends the time of the discharge, and hence
lishcs the quantity passing off within a certain
and that al.so the functions of discharge, the
Iraultc slope, the cross section, and the head affected
' . the sinuosities in greater length, are reduced by iL
. imitting this, the same principle would apply not
i^-nly to the main ri\*er, but also to its tributaries ; the
number and conditions of the tributaries would pro-
bably be a more important consideration. Again, there

PRINCIPLES AND FORMULA.

is much difficulty in saying where a main river b
so much so, that in the first place the introduction offl
index of f against a coefficient of 1 300 would appeafT
be a needless attempt at exactitude ; and in the seca
place the introduction of the length of the river at alll
an equation of this sort is a matter incapable of 1
extended application ; although in the instances fro
which this formula was laid down it has been very 1
cessfuliy introduced.

A better mode of introducing a function somei
similar to this would be to apply the ratio of extrfl
breadth to extreme length of catchment area; and I
troduce it in formula (a), the range of whose coefficiel
(i^j) for India seem to be between I and 24— an impj
tant step already gained. It then takes the form,

(4) (2 = i, I 100 (K)',

where B=extreme breadth of catchment area.

and i = extreme length of catchment area,

and tj=a new coefficient,
obtaining a more tangible improvement, capable of j
tended application. It is unfortunate, however, that f!
this formula a sufficient number of values of the new
coefficient are not yet forthcoming; although in the
instances in which it has been applied the improvement
seems clearly manifested in reducing tlie range, so th.i'
for the present it is generally better to use formula {2
while in special cases the ratio can be easily introdlH
to obtain values of k^.

Third. — When coefficients of the class^,,it^i^tJ
not available, and the conditions of rainfall and off
sorption and evaporation arc so defective as to be inl

fiocnt, direct observation of each single river or stream
within the catchment becomes the sole guide. It then
mcs necessary to fall back entirely on recorded flood-
irks, as a means of approximating to the flood dis-
rge ; and, after gauging the discharges of the channels
ii their ordinary stages, to assume the flood discharges to
pproportional to them according to the ordinary formula.

: A is the sectional area up to flood-tnark, B its
■draulic mean radius, and a and r are similar quan-
: ies corresponding to the discharge (q) determined under
!.■ conditions of observation in each separate channel.

damage
Mob of
^uschiiM

■tthev mi

■P 4. Storage.

Reservoirs generally have for their object either
the detention of flood water that might otherwise cause
damage, as in works of river improvement, or the utilisa-
B of it in canals, of navigation, irrigation, or driving
Kincry, or for town supply. For the first purpose
Kthey must, to effect their purpose, be very extensive, and
strongly aided by tlie natural formation of the country ;
fof the last purpose they are, in one respect, excepting
tinder vcrj' favourable conditions, particularly ill-fitted.

The collection of drinking-water from the surface of
. ind necdH, in the first place, a clean, uncultivated and un-
Uiliabitcd tract of land as a catchment area ; and in the
xatd place, the water stored in the reservoir, which is
ibic to become putrescent, or seriously affected by the
I, plants, and animalculae that inhabit stagnant
, requires a %-cry perfect and careful filtration, of

»4 FRIXC/i'LES AND FOKMUL.S. awi

a sort beyond the ordinary' economic powers of muoi
pa.litie5 or pubitc companies. Indeed, it is now assen
to be an incontrovertible Tact, that it is to the taini
water of rivers and reservoirs that one-half of most p
ventible diseases are due, the other half being caused
want of ventilation, faulty drainage, and mistaken aio<
of managing sewage, or, in other words, that impure
and tainted water are the chief enemies of human liJi
and there is, therefore, every reason to belie%-e that
the future, when the general public become awake tothi
and acquire enough energy to throw off the incubus
vested interests in the form of water-companies, be
tainted rivers and open reservoirs will be i
condemned as sources of drinking-water supply, and tt
the water filtered, stored, and preserved against impuri
by nature in the permeable and unvitiated strata of t
earth, will be considered, as it justly is, a neccssar)-
life and health, and be drawn on in a more scientific a,
enlightened way than is at present usual. Anoth
quarter of a century may show us scientific men objci
ing, on sanitary grounds, to the watering of our stre<
with such water as is now habitually and unconcemedl
used in preparing our food.

It will therefore be only under conditions very &i
able for clean collection and storage, or under cin
stances that admit of no better alternative, that the wati
of storage reservoirs will be used for drinking purposi
Such water will, however, still remain valuable under on
nary circum-stanccs, for extinguishing fires, waterin
streets, and many other purposes, in which it is not habiti
ally brought into contact with the human body, an
where its impurities are of little avail.

The determination of the size and dimensions of

t-r. 4 STORAGE. 15

storage resen'oir is a matter erdrely governed by local
citcumstances and requirements. The assumptions that
the area covered by it should bear a certain proportion
to tlial of the catchment area, or that the amount of
water stored should be as nearly as possible one-third of
the available supply, are not by any means rules to be
applied without a very large discretionary power, al-
though there are rules laid down in various forms by dif-
ferent hydraulic engineers that very much resemble these.
The object being the collection and retention of a cer-
tain amount of water for a definite purpose, and the
■ circumstances being the local formation of the ground
dthc amount of available downpour on the catchment
, all the economic considerations depend on these
bts.

■"The Intention may either be to store as much water
tossible within a certain amount of expenditure of
t, or only a definite amount sufficient for a certain
K)se, or to store all that can possibly be obtained
1 a knowledge that the extreme amount would not
^enough. Again.in some cases thequality of the water
I the convenience of proximity, or of cleanliness of
; may be considerations outweighing all others. If,
rcfore, the latter is the case, there are generally not
local conditions answering the purpose within
■litch any choice can be made ; the same may be gene-
rally said to be true with reference to the second case in
which a definite amount is required. It is only therefore
^uder special circumstances, when the object is to store
^Hl utilise as much water as possible, that much choice
^^pft to the engineer.

^V'^Large artificial reservoirs being generally made on
^K natural surface of the ground, and bounded in one

26 PRI.VCirLES AND FOUMUI.^.

direction only by an embankment of earth or a dam •
masonry or brickwork, the first object is to choose a
or sites where the greatest amount of water can best' ir-
with the shortest and least amount and length of em-
bankment; for this purpose a river go i^e, narrow and
precipitous, terminating a great length of country, having
a gradual fall towards it, offers the best ordinarily natural
cdnditions ; if, in addition, the lateral or transverse slope
of the country is also very gradual, it becomes a large
natural basin, with one narrow outlet ; and if this admits
of being easily dammed, an extraordinary advantage
not often available presents itself.

The economy of constructing one lai^e reservoir
ia preference to two or more small ones to hold the
same amount would, perhaps, be evident at first sight
to most people. The author has, however, met so large
a number of persons that believe the contrary, that he is
constrained to give the following mathematical ]
of it by Graeff.

Let a single reservoir, or rather its contents \
full, be .supposed to consist of a number of I
layers of water, the sum of which will equal the t
content, and let

£r=the height of any one layer ;

P and iS=the perimeter and surface of its l<v
side;.

P" and i? = the perimeter and surface of its up
aide ; then the volume of this layer will be

=ttff+

bB* ,cH*

Hence the above expression becomes

In the case where the lateral and longitudinal slopes
• ■f the ground are uniform, we can imagine the reservoir
to consist of one only of these layers ; and its contents
rUt then represent that of the whole reservoir. In this
the height of the layer will be the extreme depth of
water stored, and the quantities i9 and P will become
indefinitely small in comparison with S' and /*■, and
may hence be neglected : hence the total volume of
iter stored = i HS", and this is the volume of a reversed
ic having 3' for its base ; a demonstration that proves
rapidly the amount of storage increases with the
of water, or with the height of the embankment
To the height of dams, again, there is a practical
t ; earthen dams of great height require an enormous
section, being consequently very costly as well as
dangerous, and are in themselves difficult to manage as
regards escape ; masonry dams have a Umit to their
height, due to the pressure per unit of surface on the
foundation ; the highest yet built that is still standing
not exceed 164 feet, and it is very improbable that
it height will be greatly exceeded for some time to
unless iron is made to enter largely into their con-
'9tniction.

After choosing a site for a proposed reservoir, one of
the first points requiring attention is the determination
of its storage capacity up to different proposed levels of
e«cape. For this purpose, marks are fixed at differences

^ floes n
Kdinth
Hbome,
^'fltnicti

I

18 rRtNClPLES AND FORMULA. citAi-.^

of level of about S or 10 feet, on any convenient short
line of section ; and the contours of these levels are
marked out and surveyed all around the basin, in order
to obtain the perimeters and areas at each contour ; from
these, as before shown, tlie contents of each lamina can
be calculated, and the content up to any other contour.
If, however, it be preferred to obtain this by means of a
series of longitudinal and transverse sections taken up to
the heights of the various contour levels, it is perhaps best
to direct tlic former in conformity with the axis or axes
of figure of the basin, and the transverse sections at right
angles to them, and, as far as possible, at equal distances
along them ; although In some instances, unequal dis-
tances and inclined directions, more suited to the form
and disposition of the ground, would give more correct
results; the true values of the corresponding rectangular
transverse sections can then be obtained from the oblique
sectional areas by multiplying them by the cosines of
their angles of obliquity. Should a winding river chan-
nel or depression form part of the basin, it is often more
convenient and correct to estimate its content indepen-
dently, and add it in afterwards.

The following are the three formula most used
obtaining the contents from the sectional areas : —

1. If there be only two sectional areas, .<l,,.^j,
at a time, at a common distance, (/,

the contents = ^d (.rf,+^0,or=gd(^,.^J,+ v'27^,)J

2. If there be three equidistant sections, ^,,^,,^|
taken at a time, and their common distance is <Z,thco

tents=''?(-), + 4 J,-l-J,).

I

1. 4 STORAGE. ay

3. If there be any even aumbcr (m) of eqaidtstant
ioM, Ay,A^, Suc^ up to ^„ at a conttnon distance, ^
the contcnts=d(i<l, + vl,+4c. + vi^, + |<<,).
I '-.c accuracy of result will of course depend on tbe
tiineness of the sections, and the suttabiliQ' of thcif

Ritions to the genera! form of the reservoir.
The capacity of the reservoir being obtained, the
)unt of supply that can be expected annually from
, uw catchment area may be obtained, either in total
quantities or in continuous quantities as cubic iect per
second, by the aid of Parts t and z of Table II. of the
^Vuflcing Tables ; in these calculations much labotf jB
ived b>' deducting, in the first place, the allowance d^H
\'< evaporation and absorption on the catdUDcnt vein
from the rainfall given, and making use of the aTailaUe
or cfTcclive rainfall or rainfall run off as the basis of cal-
culation for supply.

If a small supply alone be involved, the use of Part

I. Table III. of the Working Tables wll enable the

^^pntents of the reservoir, and extent of catchment area

^Hhsssary to afford the supply, to be rapidly determined.

^^■^ 1, Table III., may also be occanonally useful,

^^merc the supply is limited by the needs of an extent

rif land to be irrigated, or the population of a town

ret {ui ring water for public purposes.

The section of waterway of escape has next to be
determined ; tliis depending on the flood discharge and
the maximum downpour in twenty-four hours. In these
[:3lcuIations. Part 3, Tabic IT. of the Working Tables is
useful : so also are Parts I and 2. of Table IV., in con-
nrrtion with the formula already given for flood dis-
■-harec

AU thc5C arc of course simply modes of calcubtJng,

3"

Pifl.VCrPLES AND FORMULAE.

CHAfS

or of shortening, the calculation of the quantities \
water ; the determination of them has to be left to 1
discretion of the engineer and the requirements of t
case. Should the supply be required to maintain j
certain depth of water for navigation in a canal,
seasons, the supply deficient, the loss in the canals
evaporation and filtration, and all such data, will deter-
mine the amount ;— if for irrigation, the amount of land,
its quality of soil, and probable water duty ;
latter subject information is given in Chapter III,
in the Hydraulic Statistics, where data of the watering
and water duty usual in France, Spain, Italy, i
Northern and Southern India, are given. Or if the
supply is required either for motive power or the public
purposes of town supply, the amount and height
delivery require determining with reference to local conj
ditions ; in such matters, therefore, no guide would I
of use. Lastly, if the object is the control of floods,
the whole of the physical conditions of the river and
its banks, from its highest watershed down to its mouth
or embouchure in the sea, will be matters affecting I
amount, and the management and regulation of I
storage : on this subject sec the paragraph in ChaptC
HI.

land, I

'.4

:ring^^
, and 1

the

lb lie ■

ods, I

S- Discharges of straight, uniform REAaiEsl
OF Open Channels, and of Pipes.

The various modes of gauging velocities and <
charges are described in Chapter 1 1, on field operatiot
and gauging. The calculation of velocity or of did
charges, under different conditions and for diffcre
data, may be considered independently of gauging.

OP£Jf CffAXNEU AND P/r£S.

iTiportant to the engineer that he should at any time

^blc to calculate, in a few moments, the discharge

\ny pipe, channel, or canal, fronri such suflicicnt data

!ic may possess, or obtain readily.

The number of calculated velocity formula, their

ir-cty, arid the wonderful amount of complication in

r-in, as well as the want of exactitude of result they

. '.«, is inily astonishing ; and when, on the other hand,

It: obsen'cs some engineers adhering slavishly to the

allies and data of one hydraulician. others to those of

other, and others again going through the conscien-

■us. but very lengthy, course of examining everything

, Al cvcr>' hydraulician has said or done in the matter

ol calculation of mean velocity of discharge, one cannot

but feel pained as well as surprised.

It would be quite out of place in this portion of a
Manual of this description, which has for its object the
npplying the engineer with information and tables for
calculating hts quantities and data in as rapid a way as
practical correctness will allow, to enter into a detailed
inrestigation of all these formula, and the reasons for
setting them all aside and adhering to that adopted in
prtfercnce and to the exclusion of all others ; it will,
ihcrcforc, suffice for the author here to mention the
reason for adopting any one formula or conclusion as
ii is brought forward. A comparison of the results of
various hydrodynamic formula will be given in Chapter
ltl„ among tlie miscellaneous detached paragraphs.

The general formula for dischai^e, based on the
theories mentioned in the section t of this chapter, is

the terms of which are given in the general notation,

3*

PSl.VCIPl.ES AND FOkMUL.€.

page II.; the mean velocity of discharge being the
smaller and more convenient quantity to deal w-ilh, for
open channels and canals, and the discharge itseir being
the quantity more often lequired for pipes, sewers, and
closed tubes, syphons, or tunnels of all sorts.

Taking, however, the expression for mean velocity
of discharge, obtained by equating the accelerating
effect of gravity down an inclined plane with the retard-
ing effect of friction, it can be put into the form mofttB
convenient for English measures —

r=cxlOO(BS)',
where c is a variable experimental coefficient, dependifl
on the surface, the conditions, the diroeniiions, and t
hydraulic slope of the channel or pipe, and hence i
on a further experimental coefficient n of roughness an
irregularity combined, which again involves both
functions R and S : its value under extreme conditicH
varies from 0*25 to about 200.

A correct formulated determination of the value d
the coefficient, c, for all conditions, is a matter that can
only be said to have been even approximately arrived
at in the last few years, from an examination of the
experimental results of d'Arcy and Bazin on tlic dL^J
charges of pipes, open channels and ordinary rivers, Slldfl
those of Humphreys and Abbot on the discharges ofl
very large rivers, and on his own obsenations on Swll^|
hill-streams and channels, by Hcrr W. R. Katter, ^|
Bern.

The determination of coefficients of this type fr:
which we are indebted to him, and tables rendering .;
easily found for open channels and rivers of any sort ci
dimensions in metric measures, arc gt\'cn in his valuabli

'SCiTjt/taSS OF OPE.V CHANNELS. 33

the • Cultur-Ingcnieur' for the year 1870.
mparison of these coefficients of Herr Kutter with
ndetl results, principally Indian, made, collected, and
lUed by the author between 1S60 and 1873, con-
<med to the belief that the formula of Kutter was the
bcrt extant ; but that the classification of coefficients was
defective !LS applied to canals and straight, uniform
mer-reaches.

The v-alues of tlie coefficients var>'ing so greatly in
the vanoua classes, it became necessary to reinvestigate
the subject. This was done, and eventually an extension
and an alteration of the classes was made by the author ;
the foimula was freshly worked out for English units,
and the whole was set forth in detail in the author's
work, • Canal and Culvert Tables ' (London, 1 878, Allen).
Under this new arrangement, the values of c, the
coefficient of mean velocitj-, are also given in this edi-
tion of this book in Part 4, Table Xlt.

With the aid, therefore, of these tables of coefficients

H^9 and the values of the expression tOO {R Sy, given in

^Bkble VII., the values of V, the mean velocity of dis-

^foar^ of straight and uniform reaches of canals and

open channels can be rapidly determined in a few

raontcnts, according to the most improved and correct

method yet known.

With the aid of the same tables of coefficients {c) and
the values of the expression,

q=c K 3927 (Sd')'' whenc= 1,
given in Table VII!,, the discharge of any full cylindrical
pipe, sewer, or tunnel, may also be determined by apply-
ing auhabte values of c

These tables, to which explanatory examples are

PRINCIPLES AND FORMULA.

; purpose ?
slope or hydraulic

I pipes j

attached, can also be used for the c<
obtaining the head, diameter, hydraulii
radius, due to given discharges of channels and
it will, however, be necessary for the calculator to
member that all dimensions, even diameters of pipes,
best invariably kept in feet, and that all slopes are k<
in the form known as the sine of the slope, mentioned
the general notation, given in section 2 of tliis chapti
Should it be necessary to reduce these from grad;
given in other forms, such as in feet per English i
or as a fall of unity to a certain length. Table VI.
be used to save calculation.

Tfie Derivation of the Coefficients. — So far for the
velocity formula actually adopted, and the mode of
working it in calculating results. As regards the for-
mula itself, independently of the determination of
variable coefficient, it is none other but the Kytclweii
formula, or Chezy formula, in a very much improvi
form, having the results of modern experiment
rated with it. An examination of the old hydrai
formulae for mean velocity shows that most, in fs
almost all of them, were modifications of the Chi
formula, some of them adding an additional term
function, and altering the value of the experimental co-
efficient, but still asserting its fixity.

In the earlier editions of this Manual, written before
Kerr Kutter had published his valuable improvement, all
the formulae having fixed coefficients were rejected
the author, who at the same time asserted the princi|
that no fixed coefficient was suit.ible to all circumstances,
and that the engineer should choose for himself a cocfn
cient most .suitable to the special circumstances, dimei'
sions, and condition of the pipe, channel, or river, with

DISCITAPGES OF OPEN CHANNELS.

discharge he was dealing ; and that the recorded
nsults of experiment should be always consulted for the
purpose of approximating as closely as possible to th^
special circumstances of the case under consideration.
In addition to that recommendation, a mode of arriving
at values of c, in cases of canals in earth, in good order,
ander \"ery limited conditions, was also then mentioned.

consisted in a method of successive approximation ;
to assuming c= 1 ; and then from the mean velocity

resulting, assuming a second value of c, according to
the following table, was calculated, or a second true
vclodty of discharge, V.

viKie

1-0 -910

1-2 -930

II -940

M -950

le -968

rt ■!»»

Ir A lew values of c, suitable to pipes under various
vdocities, were also given ; but they were detached, and,
from want of experiment, very insufficient Yet the
tnic state of the case, and the mode most advisable for
adoption until investigations on a larger scale threw
more l^ht on the matter, was then clearly set forth.

Now that the experiments of d'Arcy and Bazin, of
Humphreys and Abbot, and of Ganguillct and Kuttcr,
have been reduced to one formulated expression, the
labour of choosing a coefficient from general experi-
mental records is rendered needless as far as regards
tMdiiiary canals and culverts ; although it would be ad-
vantageous to experimentalise on the actual case.

As regards natural channels of rivers otherwise than
those whose conditions approximate to those of canals,

36 PRINCIPLES AND FORMVLM.

the necessity of rererring to records of experiment still
remains, although the Kutter coefficients may be of great
assistance even in this branch of the subject

The determination and tabulation of the coefficients
(c) has gone through three stages of development, i. The
first was that made by Bazin, based on the experiments
conducted by d'Arcy, by Bazin himself, and by various
engineers of the French Fonts et Chauss^es. The
principles asserted were that the coefficient depended on
two quantities or qualities only, namely, the condition ol
surface of the bed and banks touched by the water, and
the hydraulic mean radius of the section of discharge.
Four categories of coefficients were adopted.

I St. For very smooth surfaces, well -plastered surfac
in cement, and well-planed plank.

2nd. For even surfaces, ashlar, brickwork, and ordJ*|
nary planking.

3rd. For rough surfaces, as rubble.

4th, For earthen channels generally

The values of an intermediate coefficient c for Fren<^
measures in these four categories were —

(2)c, = 0-O0019(l + ~^-)
(4)c,=0-00028(l + 13-)

The corresponding values of the final coefficient c fortfae
English formula in feet may be obtained ffx>m the above
viilues of c, by the formula

JIGSS OF OPEff CHANNELS.

^™ 100(0 100 (ft S)'

under an arrangement that keeps the values of c within
A limited range approximating to unity, and throws ico
into the old general expression for the Cheiy formula.

The values of these coefficients (c), adapted to the
corresponding formula in English feet, are generally as
follow, in tfaeir respective categones : —

I

I 57

1%

■ '■8

R

^

l-M

1

0

l»4

3

1-26

4

lib

5

l»7

6

J '38

1

1-38

8

I 39

3

r»9

10

IJ9

It

1-29

14

fJO

1&

130

IB

"■31

M

■87

0-98

These coefficients are not correct for canals in earth
generally, and are notoriously incorrect for large canals ;
ihcy are useless to English engineers, excepting in so far
as they afford them a laiowledge of the velocities and
discharges that French engineers would assume to hold
with certain known conditions. In the matter of dog-
nutic prejudice, and mutual international recrimination,
llie balance between the French and the English is
tolerably even : if the English are insular and coldly im-

Eiblc, the French are bureaucratic and healed with
ly ; yet science will progress in spite of all petty
et, both individual and national.

''".Ode™.... ."^""^

""«> certain";; b" ;°" J^ ".= P-'nc/pf *'"'^J '" Zy

cor

pen
Kle

^ secboj)

*«d con.

[tj £t/ISC0AJftiSS OF OPEIV ClfANXBLS.

m ot roughness and irregularity. At present the
nciplc is useful to hydraulicians in relative application.
ptwil be further referred to in Section 8 of this Chapter
(n Vttocitics.

I Tif second stage of development was effected by
HIte and Ganguillet Their own experiments on tor-
»iti Slid streams in Switzerland, combined with the
suits of Humphreys and Abbot on very large rivers,
li Ihcm to believe that the coefficient should not be
1 within so small a number of categories, and
'bl the coefficient was a function of the hydraulic
■iope, besides being a function of the roughness of sur-
'w ictcd on by the water, and of the hydraulic mean
radiuit of the section. They therefore extended the
'iit^fwies of coefficients for artificial open channels
"I earthen beds from one to four distinct classes, and
'^tcreascd the other categories adopted by Bazin from
i'cc to ux ; these new ten classes being arranged in
■ rrordancc with the following coefficients (a) of rough-
ens and irregularity adopted as suitable to the surface
onder consideration.

Genera/ values.
OB— W«U-(iUneI plink.
■OS— Verj sncDtb Eiufaccs, plastrn in cement,
illl— PUiIrr ia CKtacai, with oDe'lhird ssod.
O! — I'npLinoi plunk.
'DO — BiickiMMk and cut dose.

-'W— C«iudi wiili l«d and bnnki of verj finr gravel, well punned.
Vi—Ri^vn hH Cknalii In Eaith. in perTecI older 2nd regimen, and ptr-

faetty iicc Uora ilonea anil weeda.
.^>— Rinnanil Canali in Blanh, in modeiately good order anii regimen,

tanng Hone* ind veelt ucosionally.
.^— Klfon and CanaU in E*nh, In bad oider and iegitn«n, having stone*
sad trcni* in grtal qoaolity.

40 PRINCIPLES Aim POMtmJL

I

The values of the coefficients of discharge (ejj A

on the value of (ti), as well as on the hydraulic slope and

hydraulic radius of the open channel under consideration,

in accordance with the following formula for French

measures.

9« . 1 ^000155

..(.,.«J!|«)_^

which IS also given in the following form :—

z

u oo . 1 . OOOl 55 , /^„ , 0-001 56\
where 0=23+ - + g — ; anda;— nf 23 + &— )•

The values of c, for French measures are tabulated
in Herr Kutter's book * Die neuen Formeln fur die
Bestimmung der mittlem Geschwindigkeit des Wassers
etc/ pages 336, 386, and 436, for the three classes in
which 71=0025, 0*030 and 0*035 respectively, and a dia-
gram there given enables c^ to be roughly read off for
any conditions. The same data with complete tables of
velocities and discharges suited to French measures are
reprinted with the consent of Herr Kutter and attached
to a translation entitled * The New Formula for Mean
Velocity of Discharge * (London, 1876, Spon).

The values of c, a corresponding coefficient suited to

English feet, may at any time be easily derived from any

value of c, calculated or given for French metres by the

formula

• cssO-0181 c^

It is, however, preferable to obtain English data in a

iL

DISCNAJICKS OF OF£.N CBASS£tt.

more direct manner from qccnl EngtiA tsUcKas "^
be bercaAer explained.

3. Tlu third stage of dcvdopment «f these oriifaAe
coefficients was carried out by tfie aotbor of tbb boob at
the rc<)ue»t of the Indian Govcntment ia 1S77 sad i^&
The general truth of the rotmola cf Hen J
previously been accefded by him, after a kaj^dqf a
ti^tion of the principles and the rcconkd baaic c
ments ; the formula itself had abo already boa
ployed by him in the calcoIsCions for foaie e
designs for Mr. John Fowler. The riaoiffcy of the
formula, however, acted both as an iidiantjge. ia eeaeal
applicability and as a disadvantage in Aoice of categwy
or class ; almos^t e\-erythiog centred itKlf 10 the dwice
BU' the v-alne of n, the coefficient of roij^wwii aad ifrqn*'
^■tri^ ; for the effect of various valoes of K had been
Ignstly met in the formnla, and that of varioos values of
8 had been perhaps too cautiously allowed, yet was
approximately and substantially correct. A fresh inde-
pendent determination of a set of value* of a was there-
fore neccsiary.

The author having been for many yean and in many
places a persistent observer and coilector of data of
hydraulic experiment, having bad nnosualty numerous
opportunities since 1859 on works of iirigatioa, on river
imprm-cmcnt works, on canals, and on waterworks both
in South America and in Northern, and Southern India,
of obtaining such information, and also ha^-ir^ been
f^rmitted both at Calcutta, Madras, Bombay, and in
! :)ndon to search among oflicia] records of such works,
' : is-as hoped tliat enough would be fortbcoming to gi%-c
•omc limiu to the application of the formula for canals
f fixed values of r of independent determinatiorL

42 PRIXCIPLES A.VD FOR3iUI.jC. CHAP. I.

The result of these labours and collections was suc-
cessful so far as it affected canals in earth, within the
range of the records, of cases that had fallen under his
personal obser\'ation, and that thus admitted of little
doubt as to condition.

Briefly, the results were, that none of the cases in
canals in earth were below ii=0*017, that the cases in
which n=(H)25 was approximately applicable were not
canals in by any means perfect order, that any channels
of a condition suited to ns50'035 were from irr^^larity
beyond the scope of anything but excessively coarse and
almost useless determination ; and that a large number
of cases of canals in good order happen to give a value
of n not far from ox)225.

Fi\-e fixed classes were therefore assigned to canals
in earth of \'anous soils, and in various conditions.

1st 71=0-020 for very firm, regular, well-trimmed soil.
2nd « =0*0225 for firm earth, in condition above the

average.
3rd 71=0*0250 for ordinary earth in avenge condition.
4th 71=00275 for rather soft friable soil in condition

below the average.
5th 71=0*030 for rather damaged canals in a defective

condition.

The attempts of the author to determine indepen-
dently values of n suited to canals in artificial materials,
plank, rubble, ashlar, and cement, were ineffectual from
want of sufficient mention of age, quality, and condition
of surface of these materials in recorded cases of experi-
ment then forthcoming. For the special material rubble
these latter did not afford quite sufficient reason for

-ting to HeiT Kutter's value of n^Ofll? for that
iLKLUrrial in a norma] condition, but they did indicate a
wide range of values ; as to other materials, nothing re-
Hiltcd on account of the reason before given ; the general
conclusion was that each material should have a wider
rmge of values of n suited to various conditions.
Accenting, therefore, the normal values given by Herr
"_:tcr as correct, the extension of their range was
:led by the following arrangement.

= ■'■01(1 Smooth cement, worked plaster, planed wood,

and glazed surfaces in perfect order.
= <I0!3 The materials mentioned under O'Oio when in

imperfect or inferior condition. Also brickwork,

ashlar, and unglazed stoneware in a good condition.
-0-017 Brickwork, ashlar, and stoneware in an inferior

condition. Rubble in cement or plaster in good

.:0<B0 Rubble in cement in an inferior condition.

Coarse rubble rough-set in a normal condition,
=^^225 Coarse dry-set rubble in bad condition.

It may be noticed that it might be considered prefer-
I'rtogive more simple values to ti, as i, r3. 17, 2, 2 J,
'-.and to modify the general formula to suit them ;
1: as there is yet some doubt on this point, and as
Ublbhcd custom must be considered also, the values
>t: for the present been allowed to retain their original

Application 0/ the cotffictcnts. — Coefficients, velocities,
d discharges suited to canals of practical dimensions

Idaia, were worked out and tabulated in accordance
•-'i\ these results; they will be found in 'Canal and
"h-crt Tables' (London. i8;8, Allen). Tables of

44 PKIXCIPLES AND FOSMUI.^.

the coefficients are also given in the Working T^!
of this book {see Table XII.) ; these can be appln'l
the tabulated values of 100 \' HS, given in Table \ i :
thus obtaining for any case the value of a mean vclo..

from the formula

F=c. 100 WiS.

Also to obtain Q, the corresponding quantity of i
chaise, the values of ji, the section of flow, or hydrau.,,
sectional area, may be taken from Table IV., thus com-
pleting the data for the formula

Q=AV=A.c. \m>/lis.

A value of c may, however, be occasionaliy, thoi.
rarely, required for some intermediate value of n ; in '.:
case it may be interpolated without important erroi, ■
if accuracy be required, it should be calculated from !
formula. This, after reduction of terms for direct a].':
cation to English feet, has been altered into the follow ;
more convenient form : —

^/R

(-1-8H\

where

"I00n\.m4
»i-TiAl-6-

vkJ

0-00281 \

For the converse process of determining a vali
from given data, which is more complicated, see
ample at pages 376-377 of ' Canal and Culvert T(
before mentioned.

As it is of interest to notice the effect of the
of n on the coefficient c, under ordinary hydraulic :
of from I in 1000 to i in loooo, the two folt'
pages of tabulated values are here given
that c varies there from 0'329 to 2-I70, the exti

; VaiDcf

DISCaA/tGBS OF OPEX CHAN.VEU.

45

mcticable being about 0*25 and 2*50. From this it is

'tvX that if. from unwillingness to turn over the pages

: ihular quantities in this book or in the ' Canal and

: L;rt Tables,' it be preferred to use a fixed coefficient

unity, c=l, for every case of velocity in canals, the

■>:;iic error naay be thrice in excess, or more than a

'1 in diminution, while the calculated probability of

- being right approximates to zero.

The above-mentioned mode of calculating mean

kiiies and discharges is intended to apply generally

■traight, uniform reaches of open channels. For ordi-

;r.' natural channels, as of streams and rivers, it affords

--■Ay a coarse approximation, as such discharges can-

'! be accurately ascertained without some velocity-

' rt-r.-wion.

!i will, howe%-er, be perfectly evident that the general

■hod does not by any means preclude the application

jn aDowance or deduction for special circumstances.

! 1 .laual fact, few channels are either perfectly straight,

fc^cliy regular, or free from easily estimated lateral

ind longitudinal irregularities ; variety in this particular

iilone may affect the amount of discharge by as much

nvmty per cent,, even after making allowance for loss

:i--ad by bends and obstructions. The local conditions

: 1 channel, Uic wind, the amount of silt in suspension,

■ motion of its shoals, the change of the set of its

TTTita, all seriously afTect a discharge calculated from

■1 that make no allowance for these circumstances.

■ -m; causes of retardation are enumerated in section i

■ii:i chapter.

V>K canals and regular rectangular and trapezoidal
nucis in earth in good order, the calculated discharges
be more correct than those for deteriorated and

PRINCIPI£S AND FORMULA.

CoefficimU pf mean velocity suiUd to various tKoUriali, eaicuUut
for afixtd -value of S=l>OOL

^

v.,„

J of*

iofMI

■010

■018

•017

-oao

-0338

■03S0

•0976

■MOO

(l>

(t)

m

0)

ri.)

on.)

(IT.)

(V.)

0-6

1-385

l-Oll

0730

0598

0518

0-4SS

0-404

0-363

1-

.■S6a

1-6.5

0-860

0-715

0-6*5

0-5S4

0-496

0-449

rzs

Km

i-iii

0-901

o-75i

0-660

0-586

0-517

O-47I

l-S

I-6SS

1-349

0-933

0-783

0-688

0-613

0-S5I

OfK

1'7S

1-688

1-279

0-96.

o-8o8

0712

0-635

0-573

0-5U

2-

1716

I -305

0-984

0-829

0-732

0655

OS93

0-450

2'25

1740

13*7

1004

0-84S

0750

o-67»

0-60S

0-5SS

2-6

1-761

1-346

l-Oil

0-864

0-765

0-6S7

0-633

0-S69

27S

1779

1-363

'■037

DS79

0-779

700

0-635

o-sSi

»

'755

■ ■378

1-031

0-892

0-791

0

712

0-647

0-59J

Hlh

1-809

I-39J

1-063

0-904

0-804

«

7*3

0-657

0-603

3-6

i-8«3

1-404

ro7S

0-915

0-8U

0

733

0-667

0-6II

4-

.■84s

1-426

'■09s

0-93S

0-833

0

75'

0-685

0-639

4-S

I -865

I '444

1113

0-95'

0-849

0

767

0700

0-644

B-

1-881

1-460

I'lxS

0-966

0-863

0

78,

0713

0-6S7

5>6

.-896

1'474

1-141

0-979

0-876

0

793

0725

0-668

6-

1-909

■■487

'■'53

o-ggi

0-887

0

804

0-736

0679

frS

1-921

1-498

.164

l-ooi

0-897

0

814

0-746

06SS

7-

'■93'

1-S08

1174

1-010

0-907

0

8J3

0754

0697

75

1-940

I -517

1-183

i-019

0-915

0

83'

0-763

070s

S'

1-949

rS»6

1191

loa?

0-923

0

839

0770

0712

85

1-957

■534

1-198

1-034

0-930

0

S46

0-777

o7'9

9

■ -964

'■54'

1-205

1-041

0-937

0

853

0-7S4

0736

10

1-977

■■554

1-21S

1-054

0-949

°

865

0-795

0737

1S

Z-OJ3

I 599

.■163

i-ogS

0-993

0

908

0-838

0-7S0

20

1-051

1-627

1-291

1126

.021

0

^If'

0-866

0807

■

■

■

■

1

if^l

■

■

■

^B D/SCJUKGES

Of QPEH CIIA.VSBLS,

1

'^ ^eigmis of

tutan

tioafy snitei to various maUrialt, eakitUiUd ^H

/,.r » A"'

■aiueti/S=Q-(j(Kl\.

v^«gr.

■010

■013

-017

030 ■0S26

■0330

-0375

-0900

(■)

m

O)

(It 01.)

PU-,

CT)

(T.l

.163

0916

0-6S8

0539 0-4*7

O-4IO

0-J6S

O-JJJ

'■4?8

1-097

0806

0^ 0-S8S

0-SI8

04*i

e-4Ji

:■;.

" S4S

1-155

o-Bss

0713? o-6iS

05S«

0499

o

453

■ 558

i-wi

0-89S

07SO? o-«i9

O-S87

0-SJ9

0

480

:-■

■643

1-140

0-919

0-780 0-6S7

0-6.J

OSS4

0

SO*

>68o

1-274

0-9S9

0-807 07«l

0-637

o-i:6

0

PS

i7tJ

1-30J

0984

0-83. 07J4

0-658

0-S9S

0

H3

«74"

1-339

1007

0851 0754

o67«

o«.3

0

5*0

.■;i

«:66

I-3S»

itnS

0871 077a

0693

0^

575

.788

t-37>

1046

O'SSS 0-788

0709

oii«j

os»»

.809

1-39'

1063

0-904 0-803

0-733

0-6i7

<r6ta

, i

.Si7

1-40S

1-079

09:8 0-8.7

0736

0*70

0<I4

i860

i--(3«

t-.o6

0-944 o-S4i

0760

o^t

0-636

iSM

i-,6i

r .30

0967 o-«4

07S0

07 ■*

0-6SS

I-9H

1-JS7

I -153

0-987 0-883

0-799

0730

0671

'«J

1-S08

i-i;o

I -COS 0-900

o-Si6

0746

0-688

>-?s»

1-S.6

1187

.■021 0-916

0-83.

0760

0-7«

1^5

• 557

1-317

0050 0-943

0-8S7

0-786

0717

11I.I

.■S«3

1-I4»

.i>73 0-966

o-SSo

0808

0748

i-ojs

ifcS

I-J63

1094 0986

0-899

0-8*7

0-767

t«5S

1-6JS

I-2S1

l-IIJ IXm*

0-916

0S44

0-783

»i>n

i-di

i-a98

.■118 i-oao

0-932

0-859

0-798

IS

aoM

i-«S7

1313

1143 I-OJ4

o-94fi

0-873

o'8ii

^^L

I' 103

i«7»

vyA

1 .S* 1-047

0-95B

0-885

0-81J

^^1

3-1 M

I«l3

I-3J*

.-■68 i-os»

0970

0-896

o-83i

■

3'tl6

i-69t

1 .M9

1 178 I-069

0-9S0

0-907

0-845

■

a-i7o

1758

'393

"" '■'"

t-oii

0-949

0-886

1

I

k

■

■

■

■

1

48 PRINCIPLES AND FORMULA. cha?. t

irregular channels ; the errors due to various irregulari-'
ties in the former case forming a smaller percentage. For* '
mulae for velocity and for discharge are, however, almost
as frequently used in determining a section of canal
intended to convey a certain discharge, as to obtain a
discharge from data of an actual canaL

In these cases, a consideration of the various forms of
section, suitable to different purposes, is also necessary.
This matter has been treated and repeated in nearly the
same terms in all works on hydraulics published in the
last half-century ; the ideas were perhaps due to laborious
hydraulicians now forgotten, as they cannot be clearly
traced ; and little can be now added to them ; but as
the entire omission of the subject in this Manual might
cause disappointment, section 6 will be devoted to that
special subject, though its treatment will be slightly
modified to suit modem notions of discharge.

The discharge of pipes.

The calculation of the discharge of pipes may be
conducted either on the same principle as that of arti-
ficial channels or on that of orifices. It is extremely un-
fortunate that the investigations of Ganguillet and Kutter
were limited to open channels, and hence the application
of their principles to pipes, though rationally superior to
any other mode previously adopted, cannot be conducted
with the same amount of experimental record in support

Assuming then the general formula for mean velocity
of discharge —

F=cxlOO(i^S)^
and adapting it to terms of the diameter of a pipe In

=0-23(

: . it becomes for lull cylindrical pipes and tubes of

-i^rts, where R=^ and d U the internal diameter,

V=cx 50 (dS)K

.1 as the actual discharge U the quantity more usually

uLrcd direct in the case of pipes, this is —

Q=AV=c X O-rsSid' X 50(dS)\

-0x39-27(5^";*,

(or discharges in cubic feet per second.

The converse forms of this expression bdng —

\c*SJ '

i?-lx00648§.*
c* a"

ifhefc It is the head in feet for a length of 100 feet, or
i qual to 100 5.

The s-alucs of these quantities are given in Parts I,
■' 3. and 4, of Tabic VIII., for a value of c— 1, and the
uluei of c given in the table of coefficients of discharge.
Tabic Xil., can be applied ; the powers and roots of c
an be lakcn from the Miscellaneous Tables.

With regard to these coefficients, it will be noticed
that for want of sufficient experimental data, a coeffi-
cient of roughness n = 0-010 has been assumed as appH-
nble to glaxcd or enamelled metal pipes, and one of

13 for ordinary metal and earthenware or stoneware
;■« under ordinary conditions, but not new ; and there

rttiy reason to believe that these assumptions are

wially correct, if we compare the smoothness of sur-
jCi- of a glazed pipe with that of very smooth plaster in

-icnt. and that of an ordinary pipe, in average condi-
' n, with that of ashlar or good brickwork ; in addition

nne» "

Jo FR/NCrrlES AND FORMVLM, cU*''

to th[s, such few partial and limited experimental t^^^
as are available support this assumption.

In applying, however, to pipes the coefficients "
discharge resulting from the foregoing formula, o^"-"
would naturally be unwilling to push to extremes *
principle derived from observation on open channe'^
and would prefer stopping at a point where the i
pcrimenlal data now forthcoming leave us. It woul
tlierefore, seem imprudent at present to assume that t
asserted law of coefficients holds good for an hydraulE^
radius R less than 01 foot. This limiting hydrauli*?
radius of 01 foot or of i tithe or tenth is that of a 5-inct«
pipe, or a pipe having a diameter of 0'4 foot ; and in case^
of falls steeper than 0-001 the corresponding coefficient for
glazed pipes is 084, and for ordinary pipes 0-61. Hence
for the present, and until further experiments have
thrown more light on the subject, it may also be as-
sumed that the coefficient of discharge for all full cylitt;
drical pipes, having a diameter less than 0-4 feci, wJll \
the same as for those of that diameter.

Reverting to the original formulae for mean velcx
and for discharge in pipes of all sorts.

= C.100s/flS

= v^^=vl.c.lOO^

RS

it must be borne in mind that, though with open chaniM
and unfilled culverts 5 represents the sine of the slope d
the water surface, with filled pipes under low heads dl^
to their inclinations S represents the sine of a i
hydraulic slope that is not necessarily identical with tllc-
inclination of any part of the pipes; while if ihcr
should, in addition, be any permanent statical head . ;
pressure on the upper entrance of the pipe, the conditions

BVDRAUUC SECTION.

n changed by this further complication, and the
e principle is then only partially applicable.
Wth siphons also that ha\x been exhausted of air. a
Liira] pressure of one atmosphere is added to the effec-
li« differential head.

■pwsc matters will be further explained in Section 7,
ptcd to the hydraulic slope.
It nust also be noticed that it is merely with filled
"■'indrical pipes that the mean hydraulic radius is ecjual
■ ane-fourth their diameter. In all other cases the value
Bmust be determined from the section of flow, what-
I it may be, by dividing that sectional area by the
erimcter of the bottom and sides up to water surface

This subject will be treated in Section 6,
earing in mind the liabilities under these two special
pdiarities, it yet remains that both S and R have
Un values in connexion Vk'ith pipe discharge that
OUf be applied in the general formulx originally given.

lU

^B The H\-draulic Section or Section of

1' On examining the equations representing the prin-
ciple of flow and of discharge (Section i, Chapter I.),
fc will be noticed that the sectional area of flow, and
inctioo tile hydraulic mean radius, are both involved.
s may still remain considerable doubt whether
I cases the mean hydraulic radius, R^-=,\% the

ea« term for correct introduction into any general
Ulla of the type,

g=.lV=.4.c. 100^:55.

SI FRLVCIPLES AND FORMULM.

In excessive))' wide and comparatively shallow sections
of (low the resistance of the air on the water surface be-
comes BD important function, and in that case, the prime

hydraulic radius ii,=-p — ^ might, as adopted by Cu;'

tain Humphrcj-s and Abbot on the Mississippi, be tncif
suitably introduced, with a corresponding new set of c<j-
efficients c, in place of c In the converse case of vcrj'
narrow and very deep sections of flow, an augmented

h>-dniulic radius fl,=

night be a convenient means

of modification for obtaining the augmented discharges
actually resulting in such sections, that are physical
due to diminished total friction on the perimeter t
mostly consists of the two sides.

There is, however, much doubt as to the mode i
limits within which these functions could be correctly il
Iroduccd ; while the two extremes of excessive width a
of very great depth of section are of comparatively r
practical occurrence. A general adherence to the u
U. the mean hydraulic radius in al! ordinary cases, »■
hence advisable, and will for purposes of convenience be
assunied in this book, except where otherwise mentioned.

The relative dimensions of the hydraulic section (
section of flow become important principally from t
points of view ; first, when the maximum discliarge p
sibte through the section has to be considered,
draini^e-culs, flood-escapes, and such channels whei
erosion from high velocity might not be a serious defefl
secondly, when in design tliere is sufficient scope ]
various forms of section that would have equal discbd
ing powers, and among which a choice has to be ma^l

77H? RyDKAmrC SSCTlOff.

r

Tkt efifdithns of the eanal section of maximum
discharge.

• From the functions involved in the general formula
■ diicliuge

Q=Ac. IQO^tiV,

iitvident that though the conditions of a complete
limum cannot be determined, those of a partial and
iy complete maximum admit of reduction in known
Assuming that the side slopes of the section are

by practical considerations of soil, &c., that the
,ulic slope is constant, and the coefficient of rough-
s itlso ; and using the following symbols :

Let ( to 1 be the given ratio of the side slope.

b and d the bed width and depth of the water

R the mean hydraulic radius.
/* the wet perimeter.
S the hydraulic slope.
Now with a trapezoidal section of any proportions,

'l(h+ld)

R=^=-

^H ' -P "6+2d(l+i')'

^^* Under the condition of maximum discharge, A will
be a maximum, so also will R ; and when these are
temporarily constant, P will be a minimum.
hxxittfA=d.Sb4-b.Sd + 2td.H^Q (i)
>P= Sb + 2M(\^e)^ -0 (2)
Subtracting (i) from (2).

2Aifci + (')*-fti j- +ih(,\-d)-hSd=0;

54 PRINCIPLES AND MtUmtJk.

substituting for ^6 its value, —29d (1 +t^) ,
2c^d { i (1 -h t^)^-td 1 -6^(i=0 ;

dividing by ?d and reducing,
6 = 2d|(l+t»)*-^}

substituting this value ofb, in A=d (•ft + fd),
il=(i«|2(l +<»)*-« I

and -B=

b-^2d{l+fi)i

Then for any given value of t, the quantities d and 6

may be expressed in terms of VA with numerical coeffi-
cients ; according to the following table.

The above results may also be reduced to another
form of expression.

If a the angle of inclination with the horizon of the
side slope be given, it is evident from the above that
t = cotg a, and A may be also expressed in the old
form, d^ (cosec a + tan ^ a) ; whence also corresponding
values of d and 6 may be reduced from given values of
a ; this form is, however, not practically as convenient
as the former.

The geometrical figure obtained by this process is a
trapezoid touching a semicircle ; it has the least perimeter
for a given area, and has greatest values of R, F, Q, and
approximately of c. It cannot be drawn or determined

-T i TSE HYDRAVUC SECTION. sj

:;irtncaUy under ordinary practical conditions, but
'j: algebraic determination it may be verified by dia-

.';/ (/ rilathe Trap^zcUal Sections of maximum discharge
htaHg ii given area A, and ^tn side slopes t to 1,

NoTOCTioil feictoti to be malliplied by ./A

■■■■'

(ovJdcI-t.

loi A bed width

rDr/il>ydi;ii.Lic

,:i„,

o-;o7.

1-4143

°JS36

arf"

0-743Q

.■.60.

0-3715

i-8ii6rf'

,ii.1

O7S''0

0'93SJ

0-379S

1-7361^

07587

o-MiJi

0'3794

17370 rf'

075S9

075S9

0-37&)

I75rf'

07 'SS

o-6jj6

0-3745

|>S384^'

■|to)

O'so»i

0'3S79

1-9516*

■..(,1

07071

0-4714

0-3536

arf"

00S91

o-4'74

0-3445

2-1056 i'

o«6ii

0-3517

0-3310

i-rftarf'

0-6414
o-sSSj

0-3003

0-3180

=■47"'''

0-3268

o-a944

2-8851 rf-

". :.. 1

o-S4«4

0-I7S0

0-2743

3-3H6rf'

i^

o-tasj

o-i.ps

01426

4-2461 J=

s general trapezoid comprises also the rectangular
Fflic square sections ; these including most ordinary
fcrms of canal and channel section. Sections with
carved side-walls may be dealt with by an approximative
correspondtog process. The theory applied in the fore-
goii^ reduction is not complete nor rigidly correct,
Ifaoagb nearly so ; its application to deep sections in
which the depth exceeds the width in moderation will
be less accurate, and it probably would not hold at all
■cdlose in which the depth exceeds double the width.

56 PRINCIPI£S AifD FORMULM.

The condition of equal-discharging canal sectiohs.

In navigable canals, and canals of supply and of irri^
gation, high velocities and great fluctuation of draught
under variation of supply are generally inadmissible^
thus precluding the use of sections of absolute maximuni
discharge. An economic section will then not allow of^
any waste of sectional area, or of depth which is more
expensive than width, but will have the highest maximum
discharge that the limiting predetermined velocity and
other fixed local circumstances admit. These circum-
stances are, the nature of the soil in the bed and banks,
their liability to damage from erosion, and the side slope
that can be practically maintained in it ; the hydraulic
slope and the inclination of bed that are locally practi-
cable ; and in some cases the navigable depth to be
maintained during conditions of lowest supply. The
mean width of section therefore generally remains the
only important function of discharge that can be much
varied in designing the section ; hence, if a predetermined
depth has to be approximately maintained, the usual
practice is, to assume originally some fixed convenient
ratio of mean width to depth, such as lo to i, 14 to i, or
16 to I, and after calculating the velocity due to this as
well as the other predetermined conditions, to reduce or
increase the assumed mean width by two or three feet at
a time by repeated trial until a safe bottom velocity is
attained in the form of section.

Such a final section being, then, safe as regards limit-
ing velocity and sufficient for the required discharge, is
then perhaps only one out of a number of equal-dis-
charging sections that might be devised ; and some
other one of these might be preferable for any special

THE HYDHAUUC SECT1^:V.

n

It may Uicreforc be necessary to know the
lations bctu-een mean width and depth in such a
s of sections, when the side slope* hat-e been finally
mined.
In order to discover the relation between mean width
and depth, giving various sections that will discharge
the same quantity of fluid, when the hydraulic slope is
a constant quantity, we must use the condition that the
areas of all such sections are inversely as the square
roots of their hydraulic radii ; that is,

WD
A ■>/lt=a,A constant; and as A = WD; R= y . an?

ir'/>» _,

this becomes

H'+2/>

hidi may be reduced to either of the followfag fonns
i.k terms of the modified section according as either d
or w is the new quantity soi^t.

d*

2a''

=0

or vr — sW — =-=0.

In the first case, let W= 100, D= 1, 2, 3. 4, 5, 6. suc-
T.-ssively, then the values of a are thus in each of the
•mx cases,

Z> . . 1 2 3 4 5 6

d . . 99-01 277-3 504-7 769-9 1066 1389

and for a fixed \'alue 1^=90, the corresponding values
. of ff are

. 1-074 2-151 3-232 4-312 j-391 6-483
I for a fixed value of <i=2*5,the corresponding values

I

27-25 72-53 1301 1972 372-1 353-8

r»— T"

TT 3?

F"^- ■■f?r:i

Hiimiie

nsczssc^

xsicr zr

111

pOF-

^; but in

i'j* 21=1 3*5ii£i lix safx. wjoL

l.ur^rrr3imr 1,rmnnr. li**:: ALsl

3Cie£ "nl ir

ir xmr 5r=r2s irEth the

««*iii

- le nm :c i^ltt ' r snrrirc :c i

IP

rsr-rcpe admits
and

^"^^r.tlv r^ izrrir --.srhirrs. frr ti-; r*sicc that a drcular
z'^zl'.n pfsrftCLy f^lfli :!•* c:r.d:t::c5 «* a ciaximum-
cl-^ih-^r^ir.- sen::-, ii :: Lis th-e >.i5t Ti-ened perimeter
f'.r a ^-fvet: sectfir-il ansa. Ar. cr>er 5^~c£rcle has the
virr.c ^e'.rr.etrlcal priDcrr.-. ari al>? has its hvdrauh'c
rr.'An radfiis equal to half its ir-iddle ceoth. but this is
not the ca.sc with a closed semicircle. The relative
flimfmhtrjn<i of such sections in terms of the square root
of the area arc thus : —

» T«lil« of kinet to seconds for the first thirty rainntes hare been added
III thnt lMi<;k for thi* ti^ecial purpoie.

THE HYDRAUUC SECTION.

L 1

SS.

„H-^:id,h

wi"-.,.

■iiiuiiljide

0-7979

0-37*9

15958

i-Sooa

0-2821

0-3990

0564^

0-7854 rf-
1-5708 .P

0-9155 jf

In old water-pipes the section may be much dimi-
ni'fwi by incrustation and deposit ; when this is the
'i*c the reduced section should be employed in calcu-
i iting itf discharge ; but in most cases of old pipes the
:ji«c of decreased velocity and discharge is not merely
the [iiminution of section, but the higher friction due to
'ulness and roughness of the interior surface, so that
''"■''- (bnner mode of making allowance is grossly insuffi-
' tnt The correct method is to use a modified coefii-
ivni of roughness (71), and the corresponding velocity

cocfScicnt (f) due to the conditions of the case in tlie

general formula

Q=^.c.lOO ViiS

See coefficients suited to old metal, and damaged
materials in bad condition, in Working Table, No. XII.

A still better method is to keep the water-pipes free
and clean, and apply some enamelling process as that of
Dr. Angus Smith, so that the full dischai^e due to new

terial in goc»d order may be always maintained.

Sections of Flow in Culverts and Drain-pipes.

; ordinary conditions and purposes of a culvert,
, or drain-pipe are, that it shall carry away the

A

- _ . - jr. -.J- - - . ru- vn: i r-.iii :: rrefourc

. r^ r- :r-.:^=- r^-rv: l ztt^^it ssrrinr j>£S20t com-

n- v-r^rc- r^. — *j rrrv-;^ inz r-'zr:^. r: ^f metrically
rrr.scr-;*-;-.- *.- : irriirr.:. •■ rur-.r rnl? ^ni ellipses.
T-V -.1.7^-: :■' vi riT;-: — >i*j ir i f*r:r::r.v of con-

?<?rr:rL. . ~t .* .irrr risyorr? ru: T.-hcr. :h:s is not
the 13.^; !.-£ r- :L.f ^--z irrr.x ~i:; rvils rristftute the
re?: r.7ie ::" r_ ir: >?rr.:- fr.-r*. thrrruin'.'.y s-'^swering
^- j'-irr^rse^ r.r*: nf^n-.-r^d Thefr crr'AT.s are nearly
5c=i;r:rr^l=r. :h.i5 prssjes?:::^ srr^rc:! : :he:r ir.verts are
sharply ci:r\-ed thus |::-.-:r.s hi^iher nu^h when very
partia.ly nlled : their sides are of fiat curvature or nearly
straight thus preventing lodgment. It may perhaps be
urged that they have the defect of weakness at the sides
under lateral pressure of earth ; this would doubtless be
a sub«tantial objection in loose soil or under some
ftl>ccjal circumstances, but in firm soil and in ordinary

THE fiYDKAVllC SECTION.

% a comparatively trivial one, ad* the blows and
ts received in laying are far more destructive than
Uiniry lateral pressure ; besides this, it must be
juiced that the excavation for placing an ovoid culvert
■Rcungular, slightly exceeding the external width of
pe culvert, and necessitates packing or backing ; thus a
lit incteasc of strength is afforded by the additional
■etc filling. The buiging-in of sides of culverts has
a to be provided against under many circumstances,
ri delicate refinement on this point is impracticable in
' nrdiQaiy cases, while the necessity for avoiding internal
■'-dgmc-nt is peremptory'. For the same reason straight
'ides iloping from the springing of the crown to the
jpfinging of the invert are generally both unobjectionable
Ki advantageous.

The conditions of culverts and drain-pipes, as well as
B anal custom and pracUce, impose limits on their sizes and
^■ttlDensions in section. Cylindrical culverts and drain-
^Rl^es arc now seldom made with diameters exceeding
£'S foot ; when used in larger sizes it is in cases where
tbey can be kept steadily well supplied, and not allowed
to run \-er>' low, a condition that occurs infrequently with
diameters exceeding 5 feet. Ovoidal sewers of various
patterns are generally adopted in a series of regular sizes
from I by 1'5 feet up to G by 9 feet. The two types of
oval moM commonly used are Hawksley's and the Metro-
politan pattern, originally, it is believed, designed by
Phillips ; botli of these, as well as the following type, are
circular-headed. The tendency of engineers up till now
having continually been to adopt culvert sections that
altow of higher Rushing with the same amount of supply,
■ principle i« carried out to the full in thel'cgtop form
tdvert section designed by the autlior, where the in-

PJtWClPlES AND FORMULA. CHutL

I made small to produce greater scour, and tin
sides, being straight, possess die great advantage of p»>
venting the lodgment of sediment These three typel
of ovoid, together with the cylinder, include all that
commonly necessary : their sectional data given
Table V, are arranged for cases where they are eithd
quite full, two-thirds full — that is, filled to two-thirds a
their vertical depths, or one-third full. For any otho
special depths of flow, which arc not frequently wanted, th<
sectional data must be calculated n-ith the help of a tabl
of circular arcs and sectors (see Miscellaneous Tables)
examples of such calculations will be hereafter givea

Culverts and drain-pipes are generally treated
falling in some one of three classes as regards size, th
small, the intermediate, and the large ; there are ala
usual practical limits to their inclinations. As regard
material, they are made in plain earthenware and glazo
stoneware up to dimensions of 2 by 3 feet, rardy aboV
that, and brickwork and concrete, cither plain or coate
with cement, is used in larger dimensions. Iron of a!
sorts, cither plain, painted, or enamelled, may of coura
be used in any dimensions, the adoption of wrought iro
beginning where cast iron becomes inapplicable from th
size of the casting being inconvenient in transport, c
from other reasons.

Proceeding to the calculation of hydraulic data
culvert sections.

Tlu eaUulathn of hydraulic radii and stctienal A
partly-filled culverts.

The determination of values of K, the hydra
1, and A, the sectional area for culverts wh(itl:B

^

THE HYDRAVL/C SECT/OX.

►"t"

Riled, being sometimes rather troublesome, a few ex-
itnpics of such cases may be of use as a guide ; the
cases selected being those of various sections, filled to
one-third and two-thirds their depth adopted in Table
V- In such cases fractions of areas and of perimeters
of circles are frequently used ; and for such purposes
the table of arcs and sectors in the Miscellaneous Tables
b»a been specially constructed.

Taking the Pcgtop section, the geometrical construe
H of which is as follows : —

Taking the transverse diametcr=2; the long dia-
" meter, or total v-ertical depth = 3; the radius of the
upper circle is 10, the radius of the invert is one-eighth
the total depth = 0'375; and the straight sides, which
are tangential to both upper and lower circles, are each
equal to one-half the tota! depth=l-5. For the com-
plete section of the culvert, the sector of the upper circle
extends beyond the semicircle to nearly 20° on each
side ; while the sector of the lower circle extends corre-
spondingly to 20° less than the semicircle on each side ;
tJ. these two sectors are 220" and 140° respectively.
Tbe full sectional area —
^^,=Scctor of 320* to radius l-+Sector of 140° to radius 0-375
^L -t-t«ice hair depth x mean radius ;

^P (Using the table of arcs and sectors),

= 1-91987 xIHl-22173x (0375)' -1-3 x0'6876=4-15418.
And the complete perimeter —
i, Pj^Aic of 320'* to diameter 2-f arc of 140° to diameter 075 +
twice half deptK
=1-91987 X 2-1- 1-22173 x 0-75 -|-3-0=7-7S604.
i if, the hydraulic radius of the AiU section =0-536.
a of B, tor any other diameter are proportional

64 PRMCJPLRS AND FORMULA. CRAl

For the same culvert-section when filled to two-dii:
its depth.

iis=4'15418— area of semidxde to radius 1

=415418-1*57080x1* asSI^SSSS

Ps=7*75604— arc of semicircle to diameter 2

s:7*75604-l-57080x2 »4-6l444

And R^ the required hydraulic radius =20*560

The values of H^ for any other diameter are proportional

For the same culvert-section when filled to one-th
the depth.

^3=sector of 140*» to radius 0-376+} depth x^?±^

=1-22173 X (0-375)«+075xl:ty^ =0-96868

/^3=arc of 140** to diameter 0*75 +i| of the total depth

=1-22173 X 0-75+il x 3 «:2-54130

And 2?3, the required hydraulic radius =0*381

The values of -ff 3 for any other diameter are proportional

Checking the above by calculating for the mid<
portion of the section.

Area=2 sectors of 20° to radius 1+} depth x?^tr«

4

0-34907 + 0-75x5^ =1-61470

and above, 2-58338 -0*96868= 1-61470

Perimeter =2 arcs of 20° to diameter 2+^ total depth.

=0-34907 x 2 + ii - 3 =2-07314

and above, 4-61444 - 2'54130=2-07314

TITE HYDRAULIC SECT10!f.

6S

I DtaUng in the same manner with Hawksiey's Ovoid
lion.lhc geometrical construction of which is thus, —
T»king the transverse diameter=2, and the radius

cf Ilictopscmicircle= 1 ; the radius of each curved side
ris=2. the radius of the invert of 90° is=0-5858.
Id the total vertical depth is 2-5856. The sectors cut
ff liy Ihe triscction of the depth are 164° 12' and 21°.
The lespective areas are —

'*j=lS7I)8xl'+0-7S54x2*-i2+O-7854s(O-5858)»=3-982O

-t»=fr!S8xlB9+ft-7854x2«-i2+07854x-3432=2-6858.

The middle area being more convenient to calculate, this is
0 IMxl 99+-S6652 x 2*--38386 x S+-34 x ■88578=1-6580
««! J.lhearea of bottom potlion=2-6858-l-6580=l-027fl

The conesjxjnding perimeters arc —
/*i=IS7080x 2+0-7854 x4+0-8B4x 1-1716 =720357
/"is-lSrSSx 2+0-7824 x 4+07854 x 11716 =4-33753
"A the feriincter of the middle third is
= 13788x2+ -30652x4 -1-74184

' ^j=W575$-l-74184 =2-59589

^^hBoicc the three corresponding hydraulic radii arc
^H £,-0'fi&3, ^,=0-620, A,=0-3S6.

Chcclcing the above by the top area and perimeter to two-
die depth,

l»+-36652x2»--38986+-34x 88578=2-9542
and 39820- 1 -0278 =2-9642

perinwta=l-57080 x 2 +-36C&2 x 4 =4-60768

and 7 20337 -3-59669

66 PJ^rNClPLES A.VD FORMULA.

In the same way with Phillips' Metropolitan <
of which the geometrical construction is thus : —

Taking the transverse diameter = 2, and the ra
the top scmicircle= 1, the extreme vertical depth
the radius of the curved side = 3 ; the radius of the
is (one-sixth the depth, or) 0-5 ; and the depth
springing to bottom = 2 ; the curved side has an
36° 52' 14", and the invert an arc of 106° 16'. A
tion of the depth cuts off 19° 28' of the side arc
middle portion.

The respective areas, when full, two-thirds full, an
third full, are

J,=l-5708xI» + -64352x3» + -92735x(0-6)»-2xl-54
J,=4'59i3 - 1-5708 =3023

and the area of the middle portion is

•33975 X 3»-2 x J x 2 X -TOesS + 'SOSOr x -82914=1-881

Jj=30234-1-8868=1136 =MS<

The respective perimeters are
/'i=l-57080x 2-h -64352 x6+-92735xl =7-83(

/*,= -64353 «6+-92r36 =4-78*

Mid-portion perimeter=-33975 x 6=3'038
7*4, of lower third =2-76

Hence the hydraulic ladii corresponding are

/i,=0-579, ^,=0-631, and £,=0-413.

For similar culverts of other dimensions thfe
can be reduced in the ratios of the squares of these
meters and tlie hydraulic radii in direct proportj^
the diameters themselves.

The above cases show the utility of the Table o!

TUB HrDRAUUC SECTION.

bSectois given in the additional Tables, which can
■applied to all similar purposes.

TThesc three types of culvert-section, as well as the
r, are illustrated in the Frontispiece of Canal and
Cilven Tables by figures of equal sectional area ; whose

rditive diameters arc thus,

Cylindrical Section
Rinksley's Ovoid
Mciropolitan Ovoid ,
Peglop Section .

M286

r0002 and 1-293
09331 and r3996
0 9813 and 1-4720.

The)' are dix-ided to thirds of their actual longer dia-
frn;lefs,and the dotted line on the Pegtop Section shows
'lie gain in height of flushing that this has in comparison
"i'& the Metropolitan pattern, of equal full sectional
^'''3- Us form is effective in preventing lodgment, and
Iff)' convenient in calculations for intermediate depths.

For the converse process of finding the height to
'lich a certain quantity of liquid, or a fixed sectional
'-.1 will fill a cylindrical culvert, there are two practical
;rji»je3: —
fvnL Let a be the area of the wet segment,

( its perimeter, or arc of the wet segment,
^^_ r the radius of the circle,

^^H n the angle of the sector,

^^H - A the required height or depth,

1^^ Then h.=T-k^T (l-cos'i); (I.)

For example— Let a=0-229 ; t=\\ i = l-231 ;
Then by Tabic of Arcs and Sectors. n= 14X' 0' 22"
and k=\ (l-0-3337) = U-333.

PJimCIPLES AND FORUUt.jS.
Second metfiod. Without using cosines

Applying this to the same example.

. (H.)

i:' = 0125+ ^/■015625-(1-231 x i— 0-229)*=0-027g|
Jt=0-1671 ; and the required depth A=r— Jt;=0'S3a
It will be noticed that In either case the length of B
arc is assumed ; should this not have been previoi
determined, the height can only be obtained from vain
of a and r through the tedious process of solving j
equation of a high degrea Thus, the formula for i
approximate area of a segment is

(2 -/id-Zh V -/d) ; where d h the dianaetej

Putting x= -3 ; this becomes a!^(2 v'4— 3a:+ 1):

15a

Numerical examples can be solved with this form^
by Horner's method, or more readily by the aid of the"
dual -logarithms of Mr. Oliver Byrne; modes not very
well suited to the daily wants of professional men ; not
is there any necessity for adopting this method, as 1
length of the arc must be obtained to calculate
hydraulic radius ; and in that case either of the two mtj
practical methods above exemplified affords a more n
solutioti.

THE HYDRAULIC SLOPE.

7. The Hvdraulic Slx)pe.

The hydraulic slope, inclination, or declivity, some-

les icrmed the gradient, is an important function in
dttes and discharges in open channels and unfilled
nilverts, even including those just filled. When ap-

icd to liquid flowing under gra^ty free from pressure,
■■■•:• hydraulic slope in any unit of length is the ratio of

jk difference of level of the water surface in that length
i ■ that length, or is the sine of the slope of the water
r- urface. Thus, if the difference oflevel in I 000 feet along
the central fillet of the water surface be 2 feet, then,

= V^=—H-= 0-002; and it is in this form that the
L luuo

inclination is most conveniently introduced in equations

J calculations of flow in open channels.

It should be noted that the fall of the bed of a

■ or canal is not necessarily any function of the

docity, expressed by the value S. The bed may pcr-

bc uniform in regular fall, and also exactly

parallel to the water surface for some distance, or it

may be otherwise, or highly irregular. When parallel,

the fall of the bed happens to be represented by iS ;

when otherwise, the longitudinal irregularity is comprised

in the term ti, the combined coefTicient for roughness

snd irregularity.

The slightest variation in S having so important an

effect on the mean velocity, its value in cases of channels

and rivers of slight inclination should be determined by

exact levelling operations on both banks between accurate

gauge-levels and carefully verified.

PKIXCIPLES AND FOJl.VL'L.e.

In canals and culverts.

In designs of canals for irrigation, water suppfl
or drainage, the hydraulic slope is generally also I
inclination of the bed, and this is determined to suit H
limiting velocities allowed in the canal, the maximal
being that nearly producing erosion, the minimum (
that just deposits sediment. When such canals exist n
only in design, but in operation, the actual hydraid
slope must be obtained by observation.

' In navigable canals the conditions arc sometiiq
similar, though more often, as the cjanal may cotisisti
several still-water reaches, a hydraulic slope does i
exist or is exceedingly slight.

In culverts and drain-pipes in their ordinary ste
not under pressure, the hydraulic slope exists as in open
canals ; the inclination of the bed or invert, arranged in
accordance with local conditions and available outfal]
being generally nearly parallel to it.

When a culvert is blocked, a low head of pressure n
accumulate ; the case then becomes one of dischai
under pressure, corresponding to that of water-pipes.

In water-pipes.

In pipes under considerable pressure, such as waW
pipes under a statical head of 50 feet or more, the t
hydraulic slope is not strictly applicable to any actual k
theoretical inclination, but is used for the theoretic \
clination from the point where the pressure is
any point of discharge under consideration.

The discharge and also the velocity at any potnti
a continuous scries of pipes under pressure arc thi

THE HYDRAULIC SLOPE. f

iue to the statical head, or difference of level between
iialct surface in the reservoir, or top of the stand-pipe as
;hc case may be, and the point under consideration ; the
vr;tTon at the point of actual severance and discharge
niy be treated as an orifice under direct head, and the
velocity calculated as that due to the head and section
!■:« all allowances for friction, bends, and contractions
ilong the whole course of the water from its highest
I'linL All such causes of loss of velocity are represented
by the effects that would be produced by corresponding
IS of head of pressure. The length of the line of pipes
d the sources of friction and retardation are here the
Unt factors in the calculation. Table IX. is given
bassist in obtaining such losses.

Water-pipes are irregular in their courses and in-
lations ; they are usually placed two or three feet
below ground, sometimes following its sinuosities, to pro-
'Kt ihcm from frost and damage, and are rarely alloived
1 1 rise above their mean inclination : should they do so,
- great loss of head results, unless air vessels are applied
i". those points, from which the air is allowed to escape
through cocks every two or three days. Under such

►^lar conditions, it becomes difficult to estimate the
of bead due to friction with much accuracy.
The other mode of calculating velocities and dis-
'■h.irges of water in pipes under pressure is to treat them
1 accordance with imaginary' hydraulic slopes or in-
linatkms from the highest water surface to the point
under consideration ; and to apply tlie ordinary formula
for flow given at page 32. This method presupposes
^jhat the pipes have a single inclination throughout from
^^k highest point of supply, and, even after making
^^■Owsncc, can only yield an approximate value of the

^id ■!■■■ x^oAc l^ifc tiie >• il far cadi pipe

«jii"ii^- ^JM- ii^ ypM^-t^ bovh ID^ and separate, u
^3ks obcaoBBd be preooRsoLaBd Ti>r iociinatkMis c
;^e. as «c£ as iIk ineaa KidHUion fcr tbc wbolc

viK^ k die iwciiMJiM tlwt wuld be adopted
BD^c ^iM^^M pBic daoB^faoK} outriicd oo the :
of tlie Aeaga. Tltc final ^adka^c can Aaa be calc
&om xay one of the p^ics. An example of this
tacbed to W«fciiig Tafal^ Xo. WIL

S. The DisTRncnox of Veuxxtt in Sect
OF Pipes axd Cuaxxels.

The laws <rf distribution of \'elocit>- in the secl
an open channel, canal, or ri\*er, are still incon
The most valuable information on this subject, quo
the remainder of this section, is that deduced by d
and Bazin, by Captain Allan Cunningham and by
phreys and Abbot, from the results of their exfe
experiments and investigations.

«».i DisTKtavTioy OF vjuocrrr in

A certain amount of k
(ram obser\-ation of the variation (rf wtadiy i
dianneb in the v-enical pboes^ boC ai ■
tlte horizontal planes at a soctna^ Bod
tody— and x-erj- little reJattvdjr — ycC bera ^
In Full cylindrical pipes, on the c
of velocity are comparatlveJjr s

UfuBpipta.
Tbe experiments of d'Arcy, to l8$t,

of velocity in (all pipes ex]
suited to metric measai

^="<i)'

or«(r-r)=H-3.r.v7S,

where V=centra! velocity.

v=the velocity anywhere at a dtstaoce r from the
centre^

A=the radius of the pipe.

S=thc loss of head per linear metre or hj'draulic slope.

This formula was deduced by d'Arcy from obscrva-
ms taken at from one-third to two-thirds of the radii
various pipes from the centre ; beyond \ of the radius,
is probable that the law does not bold good, and that
e decrement of velocity should be more rapid than
it indicated by the formula Under any circum-
nces, however, it is clearly established that the veloci-
i in a full cylindrical pipe are equal at all points
[uidistant from the centre, and thai the above law of
:rcmcnt holds good for the central \ of the diameter

en in any direction. In a pipe of rectangular section,

velocities arc equal at any four points, taken sym-

FRl.VCIPLES AND FOKMi'L/E. chm-. I

metrically with reference to the centre of figure in J
corresponding manner.

In small artificial channels.

In open channels, however, this almost mathematioi
symmetry is entirely absent, and the perturbation ]
duced near the surface of the water does not allow <
hope that a formula can be arrived at, which would giw
the actual velocity at any point in terms of the me:
velocity and the co-ordinates determining the position 0
that point. These perturbations appear to be more c
siderable in proportion to the diminution of velocig
and the increase of depth of channel, and are coinciden
with a depression of the locus of maximum velocity ;
extreme cases, the cur\-cs of equal velocity in the sectioi
cut the surface of the \vater very obliquely.

The following are the conclusions drawn by Baiia c
this subject : —

1st. For a very wide rectangular channel —

^Ms is)' I

where F,=central velocity at the surface.

ii = velocity at a point at a depth h below it

^= total depth of water.

iS=hydraulic slope of the water surface.
This law of velocity is proved to hold good for \
wide channels ; the cases under experiment give a prap^
ticaljy constant value of A'=20-0, the extremes varj'if
between \y2 and 24*9 ; — it would also appear that f
rectangular canal of infinite width, in which the inRuenc^
of- the sides is made to disappear entirely,
= 240 ;^the units are metric as before.

§S DISTRIBUTION OF VELOCITY IN SECTION. 75

Oxa, however, the depth of a rectangular channel
eat enough io proportion to the breadth to make the
Bcncc of the lateral walls show itself in the middle of
Bturrent, this law does not hold, nor does any law of
nenl of velocity seem possible, and incompleie
lalisations, in terms of the mean velocity, can
K be arrived at.
Kthen, r_ = the mean velocity in a canal, the section
Jlich is very great in proportion to its depth — and

^tcnttal velocity at the surface, the other symbols

tdng used as before,

'M the depth K below the surface is determined by the
pression f^j =i; whence h=0-577 ff, which is, in

fjcl, saj-ing that the mean velocity is found at about J
f^lhe total depth. This, however, assumes the before-
roentioned parabolic law of the decrease of velocity in
ttiJi vertical plane, an hypothesis only admissible in a
Wfj' !a;^c and perfectly regular canal.

In fact, however, and from experiments quoted, it

■ "'Ijears tliat the locus of mean velocity is often below J-

tiie depth, and more often below ^ of it ; and that

"iicn the depth of the canal is great, and the velocity

!, tlie curve of mean velocity approaches still nearer

Dttom, and goes as low as ^ of the depth.

iking the above relation V„=V, — ^Kv'RS, where

aV^vA, and A'=24-0, for a channel of infinite

; in this case also we get F,= V„CX + 8 v'^) as a

result applicable to this special case, which supposes ti
parabolic law applicable throughout the whole breadth a
the channel ; and this differs greatly from the results a
the experiments on such channels, which give V,= V,

The locus or maximum velocity is, however, nO
always at the centre of the surface, but is at a greater dept
in proportion as the depth of the canal is greater and tl
mean velocity is less, being sometimes as low as g th
total depth.

The determination of bottom (V) velocity can, v
rectangular canals, be alone made in the special case a
one supposed to be of infinite breadth ; for this cas
putting h = ff in the original formula, we obtain tl
velocity V^=V,—K^H1S ; but in all other cases no Ian
can be given. The greatest of bottom velocities ia i
the middle and the least at the sides.

The velocity along the vertical sides of a rectangull
canal is generally greater in the middle than at the to
or at the bottom ; but beyond this fact, the determine
lion of the exact velocity at any point of the side reoiaiii
a very difficult problem yet unsolved.

The laws of velocity in canals of semicircular sect^o
are far less complicated than those of rectangular sec
tion ; — the law of decrement of velocity is cxpreaeed u
the following formula l—

!w-'0"

the extreme values of the coefficient deduced from es
periment being lS-2 and 23-3 ; and the terms of th
expression being similar to those in the equation fti
decrement of velocity in sections of pipes before meg

^t DISTX/SI r/O.V Of VELOCITY IN SECTION.

i: — If in this we make r = B, we obtain, as for
r channels, the bottom velocity,
V»=V-t\JH3.
KAnd the mean velocity will be deduced thus : —

= V,~iK-/R!i: where ^RS=V^^/2A■,
ty'=\ + fKy'2d; where A'=21
= 1 + 11-9 v/T>
"Valuation differing but little from that deduced from
I We experiments on such semicircular canals.

klTie radius r^ of the circle of mean velocity of the
ion =fl. ^|=0■737fl;— which is saying that this
about three-quarters of the radius from the centre,
"licreas in fact it is farther.

Taking finally the two expressions for decrement of
fcldcity in canals of rectangular and semicircular sec-

■al expression may be deduced from them,

\ as under these circumstances absolute velocities
* be dealt with, it is belter to make use of relative
Cities, and by dividing each side of the general
iHon by V^ to transform it into the form

= ^ -'A ; which is therefore true for all canals

e ^ U a function of the relative (not of the abso-
\ co-ordinates determining the position of the point

78 PH/AC/PLES AA'D FORMCL^. cifAi

whose velocity is under consideration, their values be!
taken in proportion to the dimensions of the section.
With regard to velocities in artificial channels gei
rally, by far the most important result arrived at
D'Arcy and Bazin is the relation between the maximi
velocity and the mean velocity of discharge, represent
by this equation, suitable to metres :

yp = \-\-\A:^W\ andsince4=^; 7",-F„=14v'

these equations reduced to English measures be<;o

The advantage in gauging derived from the applica
tion of this principle is very great ; but the coefHcient
of reduction are doubtful in exactitude, as shown b]
Captain Cunningham's recent experiments on a largi
scale, and are certainly not suited to general applicatiod

In large natural channels.

The laws of variation of velocity in horizontal plant
with reference to different forms of section have not y
been satisfactorily deduced, such velocities have there
fore to be determined locally when required ; the hori-^
zontal curves of velocity again vary much in differenl
stages of the river or stream under consideration ;
records therefore of such velocities involve much laboui
and have not yet shown themselves of sufficient ]
tical importance to repay the labour and trouble of th«i
observation.

As to the variation of velocity in vertical plane3|
the following is the deduction of Bazin ('Annales dei
Pontset Chausstes,' Sept 1875, pages 309 to 351):—

DtSTKlBOTIOff OF VELOCITY IN SECTIO.V. 79

!be velocities of a current at different points on the
-. ; \-ertica] line vary as the ordinates of a parabola ;
.-. if i3 be the total depth,
ric velocity at any depth d below the surface,
C the maximum velocity at any depth d',

There Jf is a quantity dependent on d'.
i if M^=the mean velocity on the vertical line

k=I7-Jf[i-J + fJ)^ : where if =20 ./W
sC-aOv^IUrJ)'; when <f'=0, or the maxi-
mum velocity is at the surface,
this case, the parabola has the equation ;/=20i'
U-u d

But when the maximum velocity is below the sur-
I different value is given to M, and the equation
nmcs

d'

where x = -^

U

b

^(H)'

t P is the mean velocity (K.) of the whole section.
f then this new value of M is introduced into the
il equation above given,

Sb FRINCIPLBS AXD FORMULA

it becomes —^ = 1 + 20nM ftz£±^)

In experiments on regular conduits 6"5 feet wide t

value of— " varied between 109 and ri9 ; andiao

on the Saone, Seine. Garonne, and Rhine, the '
varied between I'l and 13 : the experiments of Hui
phreys and Abbot on the Mississippi correspondina
give a value of 1"02.

These results are hence both theoretically
practically correct and useful, and generally applicatjl
even on a large scale.

/» very large natural cliannels.

The laws of variation of velocity in vertical plai
of very large natural channels have been also fut!
investigated by Captains Humphreys and Abbot on t
great Mississippi Survey.

From their experimental data it has been deduct
that the velocities at different depths below the surfap
in a vertical plane, vary as the abscissa of a parabt
whose axis is parallel to the water-surface, and mayH
be considerably below it, thus proving the maximum
velocity to be generally below the surface ; the equa-
tion of this curve with reference to its axis, takine
the depths, relatively to the total depth, as ordinate!
was obtained in the form —

y»= 1-2(521 ^*B
wliere D= total depth of bed below Hie surface,
IB and ^ are the co-ordinates to the axis.

n

B I mSTRIBUTWN OF VELOCITY f.V SECTION. 8l

The)' also deduced that if rf, is the depth of the axis
■i the parabola, or locus of maximum velocity from the
■;:r[jce|thcn

<i, = (0-317 + 006/)fl

»l"^mii=hydraulic mean radius, and /=force of wind
'liiT positive or negative, and taken = I when the
■ifxityof the wind and current are equal, and =0 for
■■ ;rosi wind or calm,

The following are other important equations, with

~iTWl to velocity in vertical planes, deduced by

-iptains Humphreys and Abbot

(For symbols refer to page 12, Chapter I.)

Konaulic for velocity in any vertical plane ;

1-69
,l)i =— — — n-0-1856; only when i) 7 30 feet,

(iji, =(O-317x006/)D ; very nearly,

Mr.=ra,-(H'(§)'.

^(S)r. = F<i,-(im)'(l-§).

= F.^W(°'»''-'V^''-'").
" Miich equation (9) is a mere combination of equa-

B(3)»nd(8;.

ai rRI.yC/fLES AND FORMULAE.

For velocity in the mean of all vertical planes
following have been deduced :

(0 6 =_ili-,.
(r + 1-6)'

(3) i, -(0'S17+0'0</)r.

(3) P.-0-»S».

4+0-U/)-(P

ur. L

1

(4) P'»0-93« +

-o-M/'fODie^Ct*)'

(5) P, =0«3v+((M)16'(H)$/)(bv)^.

(6) P, -0-9Se(0fl6/-0-85)(ft»)*

(7) JJ^ =0-9S»+ {[0-317+0-06/]»-(M)6/+(M)l«} C6r)*.

(8) V =([l-O8ir„4O-O026]'-0-O456*)*-

The most important result of all these data and de-
ductions is the following, a fact of great practical use in
gauging rivers, that the ratio of the mid-depth to the
mean velocity in any vertical plane is independent of
the width and depth of the stream (except for an almost
inappreciably small effect) absolutely independent of the
depth of the axis of the curve before referred to, and
nearly independent of the mean velocity. The formula
expressing this is

where F_ is the mean velocity on any curve in the vertical
plane.

Fid is the mid-depth velocity.

V is the mean velocity of the river.

D is the depth of the nver at the spot

'■- *'*® , generally; and=01856, when i>730 feet

(i) + l-5)'

• 8 DtSTttlBUTIO/f OF VELOCITY IN SECTION. 83

application of this result to gauging is shown in
Lp'er II. on Field Operations.

VertUatic Velocity generally.
The following are Captain Cunningham's deductions
rcsultiivg from a thorough investigation of the subject in
crwmection with his observations on large canals,

ParaMic Formula.— \t seems natural to inquire,
■. whether the mean velocity past a vertical cannot be
.:id from velocity-measurements at only two or three
rits on that vertical. And here considerable aid may
-- derived from study of the velocity -parabola. Whether
- vertical \'elocit)--cur\e be really a common parabola
' not matters little: it must be admitted that it does
-Tt.unly approximate to a parabola. This approxima-
I" is quite sufficient to admit of its use in determin-
^: in approximate value of mean velocity.

■\iid first, it is clear that, as three data suffice to
--Wrmine the velocity-parabola completely, velocity-
^•;«urements at three distinct points on the same
"*ical will of course suffice to determine the mean
■l"city.
[The three points must of course be suitably situale
t-'-'^ a tolerably accurate determination.]
ITie first step is to find an expression for the mean
•-'■ficAf. Adopting the well-known property —

.\na of parabola between tangent and diameter=
! ■ Kircumscribing rectangle, (l), it follows that, the
j'Tiitta of dischai^eC passing by a vertical axis or depth
■ li equal to the Inclusive rectangle less the sum of
'^ panboiic areas above and below the axis,

ni=\'H~\{V-v;).z-i{v-v^) .in~Z). . . C2)

^4 PRr\C!FLES AKD FORMUl.-E. oiap. i.

where V is the maximum verticalic velocity, %\ is llw
surface velocity, v^ the bed-velocity, Z is the depth at
which V exists, 2 that of v.

Writing the equation of the cunr-e in the form

V— v=m(5 — r)',where m=-, and p = parameter. (3)

and writing i = 0, s=Hin succession therein (so thai "
becomes v^ and !,■„)

7— v,=m^',and T'— '.■„— m(fl'— ^)»,

Substituting these into the expression (2)

= VH- i mB' + miPZ - mHZ*.

=v^ + mHZ—^7nIP, ,

by substituting from (4). This is the working exd
sion for U, with which other values obtained In ter
observed velocities are to be compared.

Three-velocity Formula, — Now let three velo(
measurements ti^y/.v^, v,h be taken at •3»> depths >M,
^U, vH, (where \, ft, v are proper fractions,) and let it be
proposed to find an expression for the mean velocih
terms of these ; let this be —

where a, 0, y are numerical coefficients to be j

DISTRIBUTION OF VBLOaTY IN SECTION. ^

nbtracting (3) from (4), there results the following
il expression for v :—

v=v^ + 1t>nZz~7ns\ . . . (8)
— yJI.fi.n.vH'm succession, this gives —

Writii^ 1

=v^ + 2mZ.vff-mi^H\ . . (9).

■Kultiplying by a, /9, 7 in succession, and adding it
"fJlows from (7) that —

''={«+ ^ + r).V^ + 2mHZ ia\ + 0^^ + yv)-7nJP {a\^ +
iJ*<' + T»^) (10).

This expression becomes identical with (6) by

■taking—

^-5+7=1 ; a\ + 0^+yv=^ : aX' + ff/j^ + yv^^} ; (11).

These being simple equations in o, j9, 7 suffice to
determine a, ff,y in terms of X, ft,, v whatever values
these may have. The general solution is not of much
;'r3ctical iise : the most useful particular solutions appear

L-c when the three velocity-measurements are made
-iiaid-dcpth (jiM=\H) and at two points equidistant

B mid-depth (in which case \H + vH=Ii), so that—

= i:\+v=\, . . . (i2>

li reduce (11) to~

^+7«I; «X+iy9+7»'=i; <»XHi^ + 7''' = i ; C'S)-

Multiplying the last two by 2 and by 4 respectively,
I'sobtracting in turn from the first,—

S6 P/!IXC!Pl£S A.\'D FORMULM.

«fl-2X) + 7(l-20=0; aCl— lX») + 7(I-V)=-ij

Substituting X+v for 1 into the former, —

(a— 7)(i' — X) = 0; whence 0=7 (as v.X arc sup}
unequal), (l9

And from the latter, 2a. {l-2(X« + i'»)l, or 2o {(X+^

-2(x'+v'); = -i

whence, 0=7=

S{\-v)'

Hence by assigning simple values 0, }, i, ^ to X, fl
following simple cases result,

U=^(v^ + iv^B+Vu), or=JCS«ifl+2fj^+3«(^),Ci;

The first will be recognised as Simson's wcll-L'no<l
formula, that is of no use for practical determination
U, as it involves the bed -velocity which does not adi
of direct measurement. The other three give sun
values, easily applicable to practical velocity- measui
mcnt.

TviO'Vetocily Fomiultg. — There being only three equa-
tions (II) connecting the six quantities a. ,8, y.X,/*, w^-jl
seems worth while to inquire whether an express^
could be found for the mean velocity involv
city- measurements at only two (instead of three) ^
tinct points, as this would materially reduce the fiJ
work necessary io find the mean velocity.

It is sought then to determine a, j3. X, ft,, 50 u]
determine XI by the simpler formula —

vn. S DtSTXimUTtON OF VELOCITY Itt SECTION. 87

l/^ovxfl+^r^". . . (18).

Either by a similar investigation to the preceding, or
, dimply writing 7 = 0 in the previous Result (1 1), the
wjilions connecting a, ^,y are seen to be

a + 0^l,a\ + ff(^=^.a\'+ffn*=i, . (19).

^which it is clear that X, /i. are no longer independent ;
telving for a, /3 in the two first,

/i — \ /i. — \

d from the third, iX'— /iX* + /i.*X— i;*'=^ (X— /i),
IfbUowing equation is obtained by substitution, and
pling by (X—fi), (which is always possible, since X, ^
H be unequal) —

■^icii is the equation connecting X,^, from which in fact

or fi=

(22),

-*■ " i-

11' ihat either is determined in terms of the other.

■Thus the mean velocity (U) may be found from
n^-measurements at on/j' two distinct depths XH,
—whereof one is arbitrary, and the other is deter-
mined by (22) — by the simple formula (18), wherein a,
jre given by (3o).
Hence by making X=0, ^. ^, i, the following simple
oscs result,

I^=i(''o + 3t'j^), or=i(3vj„+4rj^), . (23(1).

t^=-iC*i'l» + 3r3„),or = K3t'i„+Tg. - (23*)-

These arc the simplest formula: by which the mean

S8 PRINCIPLES AND FORMULM. dui

velocity past a vertical can be determined from velodi
measurements at only two distinct points.

The first of the formula (23(1), above ' is by f&f I
best for genera! purposes, because it involves only 0
sub-surface velocity (piff). and that at the highest
level (§fl), and therefore admitting of more accuracy
its determination than those at lower levels involved
the other formulx. The last is of no practical use,
it involves v^, a quantity which cannot be practice
measured,

[It is not difficult to show that the two velod
measurements must always lie one in the upper th
and one in the lower third of the depth, t>., \ iiesbetwi
0, \, and (1. between \ and 1,]

Test of Formulii. — Denoting for distinctness'
the value of mean velocity derived from the ab(
simple formula (first of 2311), by u,„ it is writ
thus,

"-.-iCi-. + Sw^ff). . ■ (23a. J

The value of this quantity has been calculated foi
the 46 average vertical curves of the Roorkee Exp
ments, and is shown there in the sub-column headed
in Abstr. Tab. 3, 4 for comparison with the fiindamei
value TI=D-^S. To facilitate this, the discrepai
{u,„ — U) is also shown. These discrepancies will
seen to be always small (nowhere exceeding O'oy)
might be expected, and usually negative, showing
u„< £/' usually.

The closeness of the values of v„ U is involved
course, in the general approximation of the observal
curves to parabola:.

I Publlihcd tra ihc lini tloie, ll u t<lleved, by Cspt. Cunalngbuft

TlON OF VELOCITY TN SECT/OX. Bg

?eptk if Mean Velocity-Line. — By the term ' Line of
" -^ velocity" ' is here meant the stream-line in which
• average forward velocity is equal to the average
I'^n velocity past the vertical. To find the depth (AJ

inline, the equation of the curve (i8) gives (writ-
!i=fc^aod «=(0 —
;

U=:v^+2niZk^—mh^, . . (24«).

=v„+Tn^fl^— ^m/f, by Rcsu!t(16}, (34^).

whence A,=Z± ^iIi'-ZH + Z\. . . (25),
K ■^j. /i Z , /Zy ,,. ,

The quadratic in A, has of course two roots : but it is
lisiiy seen by writing (25) Jo form —

h^=Z± ^Hi^B-Z)-i-Z\ . . (25.^),

■alone root is always negative when Z<\H, and is
Vfcforc of no' interest ; when Z > J^, both roots are + ,
liieh &hov>-s that there are in this case two lines of

""■in velocity equidistant from the axis (as is evident
'Jn the symmetry of the parabola). It may be shown
0 that the larger root is always greater than {H, for
anting the larger root of (25) in form —

A,=Z+V(i£r-Z)' + ^/r', . (2Sf),
90 that

4^=Z + aquantily>i(ff— Z), whence /*,> J//. (2512),

i shows that—

* A* tliu wmU MlTCtpood 10 ■ line abtt'i lie surfait.

PRIffCrPlES AND FORilULM.

' The mean velocity Line is always below the Be^i'
depth," ... . . . . (:Q-

In the illustration of this by diagrams of observed
velocities, it is seen that the vertical line drawn througii
the tip of the mean velocity ordinate (U) cuts the ob*
servat ion -curves below the mid-depth in almost all cases-

It is evident that the depth of the mean velocity*
line (defined by /tj depends on the position of l!
maximum velocity line (defined by Z), and varies then
fore with the variation of the latter ; also from (25a)
follows that : —

'The relative depth of the mean velocity lii
(Ajj-f-J?) depends solely on the relative depth of ti
maximum velocity line {Z-r-B)' . . , (374]

The range of the maximum velocity line appears
the same diagrams to be from a little above the surfa
down to about mid-depth. The values of k^ cor
spending to various values of Z within this range <
shown below.

Value of ^-ff, -1, -J. o. J. it, \. i. \.

y/ilueotk^-i-H, "554, -560, -577. -598, -607, -631, o& -fAj, -an S^j

whence it follows that —

' The mean velocity past a vertical cannot be direct
measured in practice by any single velocity-mcasur
mcnt,' (27/

as the single measurement would be required in t*^^
mean velocity line, a line whose position is not knon
a priori.

' DtsTxiaar/oN of velocity in smctio.v. 91

in, taking the larger root of (25) (which is the
t interest), viz..

h^=Z + ^ i^H-Z)H+Z*. . . {zs bis),
^Itdearthat the surd is > — <2' when J ff> = <Z,
.■.A„> = <2Zwhen^< = >J J, . (28).

1 Now from the symmetry of the curve it is clear that
' ('*»«) *t depth z=2Z is the same as the
« velocity, i.^., f, =v^
ence —

[ The mean velocity (IT) > « < the surface velocity
\}*l»o Z> = <^H, (29).

't-velodty Approximations. — Writing down the
il values of V, v from Eq. (6), (8),

f=v,+ 2m^s— m»*, [r=Vo+77i^ff-Jm/r». . (30),

'I is manifest that there is no value of z (taken as a
'unction of the depth B only) which will make the
--neral vaJue of v either equal to U, or even proportional
V. in consequence of the presence of the variable and
-i known Z, The flatness of the velocity -parabola: is,
'u.revcr, in all cases so great that an approximation is
;>/^«'bJc. The closeness of this approximation depends
ofi a prior rough knowledge of the range of Z-r-H.
Now a glance down the column (Tab. 3, 4) showing
Ihe valuM of Z-t-H in the 45 curves of the Roorkee
Experiments will shoiv that the range of this quantity
ii— except for verticals quite close to the vertical walls
of the rectangular channel (»>. for all verticals more
than s' off the walls) — only from about o to J, and
tor this range of Z-t-1/, the value of K^-^-M has been

92 PRINC/PLBS AND FORMULM.

already shown to range from •%^^ to '667; with a
value of about 0625 = |,

Now the velocity corresponding to the value s=!
is from (30), —

and the difference between this and the mean veloc

which ranges from — -—-mfl"', when Z

to ■^^m}I\ when Z=\B.. . (31

In the other case. Near the margin of the rectangu
channel the limiting values of the quantity Z-^H are
and i, and the table of values of h^-i-H already giv<
shows that there are two sets of values of h^-^H
responding, viz., one between o and ■211, and one
tween "667 and 789, with mean values of about '
and 738. The former is the better for practical vel
city-measurements on account of the greater accura
of work near the surface.

Now the velocity corresponding to the value s=-^
1

and the difference between this and the mean veloci

which ranges from + — -m^*, when Z=^H,

to-gmff»,when^=iff, . . (32.

Lt DrsTR/Bvrroy of rsioc/ry m section.

l.,.__.

^Hi ({uanUly m ( = reciprocal of parameter) is always a
Hcry small quantity ; so that ' the several discrepancies
I 1' tr, 5 „, 17 „, 23 „,

1»2 192 300 ' 3U0

; shown are always very small quantities,' . (33),

'The two velocities Vj^, (;>,, at % depth) in general,
"1 f A" ("■■ ** A depth) near margin of a rectangular
i^rmcl are probably the best approximations obtainable
-nm velocit>--measiirement at a single point,' , (34),
Mid-dfptli-vthcity, (vh). — Writing s = ^ff in the
■:neral expression (8) for v, the mid -depth -velocity is
.Ml to be, —

i,t„=v, + mZff~imH\ (35).

whilst t7=v,+ mir£r— |mff', (by (6)),

»o that the difference V(fl— t'=^miH' is always a
positive quantity {36).

Thus in the velocity-parabola —

'The in id-depth- velocity is always > the mean
-. olocity by a small quantity, viz., ^'fm.H^, not depend-
ing on the position of the axis,' .... (36a)

It will be seen also that the discrepancy ^mff ' is
alu-ays > the greatest possible discrepancies with the

approxitnations last proposed.

[The property just proved, viz., that the ' mid-depth

linate exceeds the mean ordinate by a small quan-
is a property in no way peculiar to the parabola.
AH cxftcriment agrees in showing that as a rule —

'Tlie a^-ciage vertical velocity-curves are every-

aiu-a

94

PKLVCIPLES AND FORAWL^E,

CHAP. I.

where convex down-stream ; and are always very flat
curves.*

These two properties involve the property in ques-
tion ; for in any convex curve whatever the tangent at
the point M where the middle ordinate 'mM meets the
curve lies wholly without the curve, so that the curve
falls wholly within the circumscribing trapezoid ; also
the middle ordinate = area of circumscribed trapezoid
-i-depth ; and the mean ordinate = area of curve-8-depth
(by definition) ; so that the middle ordinate always > the
mean ordinate ; also, when the cur\'e is very flat, it is
clear that the excess of the former over the latter must
be a small quantity.]

This is fully borne out by the Roorkee Experiments :
the value of the quantity {v^h^ U) is given for every
series in Abstr. Tab. 3, 4, Col. 9, and it will be seen
from them that its value is positive in 40 out of the 46
Series, and zero in 2 more. The only cases in which
V\u< U are shown in following table : —

Serial
Number

Number
of Sets

Value of

Remarks

9
21

44
45

14
16

5
6

-•07

— •01
-•II

-•06

/ Several very low velocities about the mid-depth
\ (i.^., at 4' and 5' depth).

An unimportant difference.

These two curves on the exceptional vertical.

close to the 4' drop-wall are of cxcep-

i tional shape (not wholly convex), so that

the property (47) of a convex curve could

t not be expected.

It may hence be concluded that 'the difference
(v^jy— U) is always a small quantity, and usually + , so
that vjjsr usually exceeds U* (37).

1^! I>JSTRlBUT/Oy OF VELOCITY IN SECTION. 95

KnAo C-i-tiy,- — This ratio has acquired quite excep-

:iil importance of late years from the assertion, at p.

4 ot the Mississippi Report, of its approximate con-

■lacy under all circumstances at the same site, and

V proposal therein to utilise this supposed properly

■1 ilijchirge-measuremenL

From the result vjasC+iV"*^'- Eq.(36),it is clear

It the ratio t'-^V|^ is— in the velocity-parabola at

■ ate— not a constant quantity (unless mW be pro-

J to U\ nor a function of \J only (unless indeed

Pbt a function of V). The value of the ratio is in

f/+Jjmff'"

1

1 +

r NW from the admitted smallness of the quantity
':«fi' (the same as V\b— U) it is clear that this ratio
"■il be tolerably constant ( < 1, of course) at any rate as

i mugh approximation.
The conclusion ad\-anced by the Mississippi Report

I' that this ratio depends chiefly on the mean velocity

tfjoi the whole channel, at any rate in a deep channel.

^But the argument is based (see Mississippi Report)

the assumed value for the parameter — or

m

l'-*-\/0 V, and upon a further assumed relation that
t'93^ approximately {i.e., with sufficient approxima-
l for the purpose of proving the dependence of the
( U—ViB on 1^), Applying these two Results, the
6 v^a ^- U indeed becomes —

= *+T2ir93vf'*'''=^'^=

IG

I

(39).

q6 PftmClPlES AND FOmJVLM.

which depends in deep channels at any rate (in which |3
varies very little) chiefly on )l ; and this result is pro-
posed, at p. 293 of the Mississippi Report, as ' the ab9
lute numerical value of the ratio for any cur\'c i
actual observations.'

But the argument is inconclusive on account of tl
uncertainty (and probable incorrectness as genera! trullis]
of the two assumptions p=H*-i-'/^y and i/"=-93|f^
approximately. The assumption V=-^W approxi-
mately is obviously not true at all parts of a chauneL
for it is equivalent to assuming that—

"The mean velocity past a vertical (t/^) is appro
mately the same right across a channel,'
which is true enough throughout great part of th
width, but very far from true regarding velocities nca
the banks. Thus result {39) is not a general truth, ba
is at the utmost limited in application to those parts oTi
cross-section, the mean velocity past the verticals <
which is nearly the same.

In fact the real evidence of the proposed law ft
this ratio must be held to depend, not on the argumcn
which led to it, but, on the numerical comparisons e;
hibited (Mississippi Report, p. 294) showing —

1st, the values of the ratio V-trv^g (computed din:
from the velocity-data).

2nd, the values of its proposed equivalent, viz., of

-(■-^^^/f)

3rd, the discrepancies between the above values.

These are shown in the M ississippi Report for 1 5 cast
viz., H Mississippi curves, 2 of Capt. Boilcau's curvi
from small canals, and 5 curves on the Rhine. Tl

DtsrsfBUTiov OF rsioc/ry in section. 57

vrrrpancics shown are certainly surprisingly small
" ifae 8 Mississippi curves, in which they do not
atted ^ per cent ; ivhilst in 4 of the European curves
I tiKfiise to 2 to 3 per cent.

I'pon this evidence the important conclusion is
I town lib.) that—

'The ratio of the mid-depth velocity to the mean
idocitj- in any vertical plane is practically independent
I'lhe Jcpth and the width of the stream, of the mean

■ ^udtyof the river, of the mean velocity of the vertical
J^e, and of the locus of its maximum velocity. In
oiiitr wonls, it is a sensibly constant quantity for prac-
ticjl purposes.'

And upon this conclusion it is proposed that the
"■!rf*ork for computing the total discharge of a lai^e
iiimcl .should in future be limited to mid-depth vclocity-
"iiurcments.

The practical value rf this conclusion depends
i!!^%on the amount of error likely to be made in its
plication. Now the value of the ratio (39) proposed
' 'Jives unfortunately the unknown quantity t'( = mean
- jcity of the whole channel). If an approximate value

■ ihis were known a priori, it would give the value of
ratio in question with sufficient approximation.

l! was apparently supposed (Mississippi Report)

■ : the ratio in question varied within such small limits
I. -■ alt circumitatues whatei'er (even in different
.rncis) that it might be as.sumcd sensibly constant

C\\ practical purposes of discharge-measurement of

■■■ cbiinncU. The additional evidence now avail-

--.^ by no means confirms this hypothesis : the ranges

reragc values of the ratio in question— ;> of the

^^veragc values

»S rXMC/PLES AND FORMUL.i. cm

average experimental values of 0"-*-"jh — are given
below from all the known published cases.

Mississippi

Rhine .

Small Canals, CapL

Ijke Snrvev .
Irrawaddi
Connecticul .

ReferTDDQ to Origiul

Miss. Repon, p. 194

Barin Eiperimelits
RepOTU of 1868-70
Repoil of :87s. Appx. C.
Repon of 1878, p. 350
Roork« Expu., Tab. 3,

■09» W97*
'961 to-gtS

'04S M^l

Thus it appears that—

' The ratio P-j-Vja is liable to range from about
1082 to -giS, !>., about 16 per cent' . . . (40)1
an amount not fairly negligible even in the rough pfo*
cess of discharge-measurement of large channds.

9. Discharges of Rivers.

To determine with accuracy the dischai^e of a
ordinary or large river, independently of vclocity-obsep
vation, is at present impossible. To this general trull
there is only one exception, the case of a long straighl
and uniform reach of river, whether canalised artificial]]
or naturally ; then it may be treated nearly as a canaL

If it be required to determine approximately I
discharge of a river from its section, slope, and conditioi
as regards roughness of bed surface and irregularity ; t
section may be sounded, and the hydraulic slope i
taincd by levelling, but the required coefficient (») <
* PrinicJ -ojii in Miuiuippi Kepoit.

mma. 9 l>ISCaAKG£S OF M/TMJLS. 9;

roughness and irregularity mast be gaoeed hy aa ex-
perienced hydraulidaa from comparisoawidiotlia- rhns
and their coefficients;. (See Kutlcr's local nian of ■ far
natural channels in Table XIL) Tliis bane ^"^^ ^^
value of e may be calculated b>- the fannaU or otcaiaed
from Table X 1 1., and the calculation of dtadaree cam
be effected through the general Ibnnola

■ Q=A.V=A . c. too yiiS.

^m It is obvious that ii is preferable to take at least a
'kw velocity -observaliona. (See Gai^i^ Chapter IL)
There are also two odier theories of tkm, or modes
of approximating to rrvcr-dischargcs without vdochy'
observation, that are of some practical value unda
certain conditions : beddes a large mmiber of fbnnatz
nhose merits are dcmorLstrated by comporisoa fin
Chapter 111, Hydrodynamic Formnlz) to be vety
inferior.

Of the two former the 6rst is thai of thipoit ; it
iT'^Iccts friction on the sides of the section of Bow, thu*
nsidering motinn in all \-erticaI planes to be the same,
■rill dealing with horizontal laminx only ; the ntriace
Umina is considered to be in the ccmdition of a scriid
gliding over an inclined plane, and each lamina below,
except the bottom one, is urged 00 by its own weight
and its cohesion to the upper lamina ; the bottom fillet
i.t retarded by tts adhesion to the bed. Putting this in
the form of an equation, summing, rejecting certain
i, integrating and applying three numerical coefTi-
puit obtains a result, which for English feet

S.RA

-0-082 + (tMKWT +(rtl 14 «57 .

PRIXCIPLES AND FQR:ifVLM.

It is this formula that has produced more coi
practical results generally than any one of the formula
having fixed coefficients; next to it, in order o^ correct-
ness, coming the Chezy formula, with a fixed coefficient
e=i. This theory- assumes that the uppermost lamina
m<«"C4 invariably with the maximum velocity, which is
not the case ; the neglect of the friction of the banks
might not vitiate results if applied to large rivers or
shallow channels ; it is probable, therefore, that a modi<
Gcation of this formula in accordance with correct di
of the relations between maximum and mean velodl
might render it \'ery useful and practical. Hitherto
formula has been generally treated as a pipe -discharge
formula, and as a modification of the Chcj^y tj'pe
theorj', however, is one pre-eminently adapted to
rivers, and the results (see Article in Chapter 1
HydrodjTiamic Formul.'e) are undeniably correct as gi
approximations. For more information, refer to Dupi
' Etude Theorique et Pratique sur le Mouvement
Eaux courantes ' (Paris, 1S48), and Claudel's Tal
which contain extracts therefrom.

The second theory is that of the Mississippi Suro
mentioned in the Mississippi Report, Philadelphia, i8<
which deduces the new formula, mentioned as giving
most correct results of all yet known ; it is, how
unfortunate in its formulae being rather inconvenient
some respects. While, therefore, the investigation
deduction of the formula is valuable on account of
experimental data applied to it, the result is not pi
tically useful ; as the foimula was virtually set aside
the Mississippi Survcj', whenever careful rive
was carried out, in favour of other equations dcdui
from veIocit>--r»bsen'ation.

or

DISCHAHGES OF RIVERS. loi

In)«ork of this scope, it is impossible to go beyond

Ittnereoutlines of the demonstration adopted. Adopt-

\ the notation of the Mississippi Survey given at pages

& and 12, it may be stated as follows.

The theory accepts uniform motion and the usually

ipted application of the laws of uniform motion, but,

hwarding force, denies the stability of position ofma.\i-

01 velocity, and makes allowance for the resistance

VUk air on the water surface, as well as for the effect of

The process of reasoning pursues the following
^liatlons obtained for the forces : —

^hidir

(1.) iC!/^^=i(f +«,;»''- ]^+J-P

both sides by Ggl,
ig P.=O-fl3v + (O-016-0-06/) (6i)*
r,=0-93« + (00()/+0-35) (fev)'

<s^=*y^* w^ 1

putting ITsJp, where 7 practically = X for large rivers.
(3.) -4^=4 (0-93t) + -0167 (1.0)'=^ {«)=(:;«•

(4.) C=

AS

tctical observation C=^^. hence

IDS PKIACIPLES AND FOKiVaL.-E.

In this equation there are practically only four vari-
ables, A,p-'r W, S and s, and for ordinary natural chan-
nels^ nearly=l'015 IT; henceif the values of any three
are given, the fourth may be obtained, the transpositioiu
of the equation laeing —

;6.)

(7.)^ = -^

\ 195J J

(8.) J>^

I95S'
„ 195JS

I

Now « is a variable, of which only two absolute values
are known, viz,, that for a rectangular cross section, and
that for an ordinary river section, which are —
»=«+0-167&*tf*
«=0-93v + 0167 &*(;'.
Substituting these in (S ) and solving, we get for rect-
angular channels

(9.) v= %/O-OO646 + (195fl,iS')*-0-08fcV.
For ordinary river channels,

(10.) «=(v'-O0816-l-{225fl,S*--O96*)*;

For lai^ rivers, where R>\2 feet, and where b=

J-- — __j = 0-1856, the first term may be neglected, and
[n -hi '5;

this latter equation becomes —

(11.) v=([225fl,S*]*--0388)';
If the discharge is known, and also two of the four
variables in equation (s), provided they are not A and v,

BKUDS AND OBSTRUCTIONS. 103

jthcTtwo variables may be computed by eliminating
iiTiknown N-ariablc in the second member of that one
t.Llranspositions of equation (11) whose first member

■'.': variable sought, by substituting for it its value

::uced from the equation (I2).

So difficulty will be found in performing the calcula-
% except when S andp+ W are the known variables,
■ iv-hich rate an equation of a higher degree than the
vund cannot be avoided, and successive approximation
"iiutbe adopted as follows : —

Assume a value of A, and find two values of v, one

:r m equation ( 12), the other from (to) or (9). as the case

11 require ; these values of v will not agree, hence con-

' -lie ateuming new values for A, until the resulting

■iliiM of V are identical.

The above-mentioned Mississippi formulae apply only
■ 'he dischat^es of very large rivers ; their adoption is
'■ 10 be recommended in any other cases.

■ 10. Bknds and Obstructions.

The irregularities of a river materially affect its
ijcity; the following remarks on this subject, by
j;iUins Humphreys and Abbot, are instructive on this

Even on a perfectly calm day, there is a strong re-
^itance to the motion of the water at the surface, inde-
pendent of, and not mainly caused by the friction of the
»ir ; the principal cause being the loss of force, arising

KH FRIXClflES AND f ORMOLU. owr. i

- from the upward currents or transmitted motion cause]
'by the irregularities at the bottom. There is also &'..
' almost constant change of velocity at various depths, ::.■
'suiting from the wind in a great measure ; and cddic^
'changing their position and magnitude cause variatior^
' in the velocity of tlie river at a given point, and thci':
'again are influenced in intensity by the wind.'

Such irregularities are of course beyond calculatiur
others again may, in some instances, have tlieir resuli
approximated to, and allowances made for them, by con-
sidering a certain portion of the head on the stream j
neutralised by them ; and these are known as bendsi
obstructions whose effects arc within the range of ca]
lation. Generally the disturbing effects of lateral b
and curves, and of shoals and obstructions, constita^
vertical bends, as well as alterations of section, cannot
calculated with any practical accuracy. It is. thcrera
best entirely to avoid such difRculties ; but when t
cannot be done, the following formula; may be use
preference to neglecting the allowance.

The old general formula for loss of head, ft, due ti
bend in a canal, river, or water-pipe, is of very doubl
value ; it is

where c is an experimental coefficient generally I

at the fixed value 0-5184 ;
a = the arc of any bend, not exceeding 90° ;
k, and H. the radius of bend are in feet, and I' is in u
per second.

The total loss of head, due to the bends for which!
lowance is to be made throughout a course, is then t
sum of all such values h, obtained.

^^^B BEX^DS AND OBSTRUCTIONS.

A'ltvr bends. — A more modem formula suited to
1". crs is thai adopted by the Mississippi Sun^ey, it is—

134 '
v.hcrc ii = angle of Incidence of the wafer in passing
ir.d the bend: — it is, however, always assumed that
ith angle is one of 30°, and the efTect is estimated as
-i^tothc number iV whether integral or fractional of such
-ndsor deflections of 30° ; and this enables the formula
^10 be put into the simpler form- —

A' 1-'

A=.

536

=AF'xO'O01865.

TV vilucs of this formula, for various velocities and
'■:'ib,*re given in Part 2 of Table IX., and an explana-
' 0' example is attached.

hft-btnds. — A formula more suited to bends of
: :;« is that of Weisbach ; it is for cylindrical pipes —

K='.

^.

180' 2y
nI for rectan^tar Cubes—

0131 + 1-847

©"}

but as the bends of pipes, knoivn as quarter bends, are
ECTieraJly taken as 90° ; the value of the factor in either

-=0007764 1".

Itis formula r and R arc the radii of the pipe and of
■nd,an<] the other terms are as before. The loss of

^SB^asb

io6 /'A/JVC/riES AND FORMULAE

head due to bends in pipes is, however, genera
quired in relation with discharges, not with n
ties of discharge. The values approximately giveoi
this formula have, therefore, been tabulated in this for
and are given in Fart I of Table IX. ; an explanato
example is also attached to it I

Obstructions. I

While the above formula may be thus employ)
for the present, it must be noticed that they are mere
approximately correct, and that extensive and numeroi
careful experiments are yet required before an accun
determination of the head, representing the loss ofcffi:
caused by a bend of every sort and condition, wilt 1
arrived at.

The ordinary formula for calculating the r
resulting from an obstruction in the section of i
channel is that of Dubuat ; it is —

where A, a, are the normal and the reduced
areas of flow.
S is the sine of the hydraulic slope of the river,
andois the experimental coefficient for discharge tt
the bridge opening taken as a sluice or oril
Now, as in most cases S is less than O-OOl, th«
may be neglected, and taking 0=0-96, o'=0"92, ai
formula becomes—

For other values of o, suitable to any spccta] ca
corresponding value of w' must be applied in the o|
formula.

11 OH/F/CES AXD OVERFALLS.

The %-alucs of this are given in Part 3 of Table IX,.
^n explanator>- example accompanies it.

II. Discharges from Orifices and

OVERKALLS.

discharge from orifices and overfalls, which to the

generally resolve themselves into sluices,

and water-cocks, is a subject that was fully entered

>hy hydraulicians of past times, and to which very

information has been added by recent experimcnlal-

Nor is it by any means likely that further contribu-

■nill be soon made to this branch of hydraulic science,

have recently been to that of channel-discharge;

lea! interest attaching itself to the exact de-

ilion of discharge of a sluice or a weir not being

u of the amount of exactitude already attained.

II accepted information on this subject is to be

with but little variation, in the older books,

Ithor had little choice left to him, in compiling

them ; much of the following was reduced from

translation of d'Aubuisson's hydraulics, for

of a copy of the original.

Setting aside the experiments of the more ancient

icrs, it may be assumed that the discharge from

iBce under theoretically constant pressure is

il = A Y=A.o-J'tgH

"herei/=tbe head of pressure of the orifice,

Q=thc coefficient of reduction obtained by experi-
ment on such orifice,

Fsthc mean velocity of discharge.

loS PRINCIPLES AND FORMULAE.

The first of the more modern hydraulicians toobi
experimental values of o, on a scale lai^cr than the p
vious very petty experiments, was Michelotti : his <
pcriments conducted at Turin in 1767, under heads!
pressure up to 22 feet, determined coefficientsof reducti
.varying from 0615 to 061 g, for circular orifices, upl
6 J inches in diameter, and coefficients varying from o^fiT
to 0"6i9 for square orifices, up to 3 inches in length I
side. The next important experiments did not so milB
include increase of head as increased dimension of Oj
ing. Messrs. Lespinasse and Pin, Engineers of I
Langucdoc Canal, 1782 to 1792, made experimenW 4
rectangular openings, or sluices 4265 feet broad, a
having heights- varying from rS75 to iSoj feet, un<
heads on their centres- of from 6-3 to I4'S feet;
coefficients deduced varied from o'Sg4 to 0-647, the n
being 0625 ; they also observed that the discharge ffd
two sluices opened at one time side by side was I
double that from one sluice. In 1S26 at Metr, 3
Poncelet and Lesbros deduced a law for the dctertni|
tion of coefficients of discharge of rectangular orifii
under various proportions of head of pressure and del
of opening to width ; these coefficients, ranging from 0*M
to 0709, are given in Table XII. The next imp<
experiments recorded were those conducted by M. (
Bidone, at Turin, in 1836, on orifices on parts of v
the contraction was suppressed, the extreme of suppn
sion being a case in which the whole of the contract^
was suppressed by fitting an interior short tube to t
inouth of the orifice : his resulting formula of discharge
was for rectangular orifices —

OKiriCES AK£> OVERFALLS. 109

'or Circular orifices,

■Tc p is the portion of the perimeter P whose contrac-
■ \h suppressed.

Abaut this time also some further experiments were
_-lc bj- Caste! and d'Aubuisson ; and some by Borda
mvifices in sides not plane, but of compound forma-

/« tmaU orifices generally.

The results of all these experiments show that the
r limits of the value of o are 050 and 1 'OO for
» in all sorts of sides, and under all conditions, and
0 and C/O for orifices in plane sides ; also that
1 mean value of 0 for orifices in a thin plate is
I, Kowe\^r. is perhaps moretrue for small circular
i for any olher class of them. In this case

r rectangular orifices of a similar class, the special
« of o, ranging from 0572 to 0709, given in Table
t be applied to the general formula

V^o

v'5^

rder to determine the mean velocity of discharge,
I when niuitipHed by the sectional area gives the
itity dbcharged per second.

\ffttt ef initial velocity. — In the special case In which
Pieaervoir of supply, still being kept at a constant
lUsly affected by the velocity of the water

no FKJNCIFLES AND FORUVLM.

supplying it, the dischat^e of the orifice will be m\
mented on this account, and then

where ir=the initial velocity of entrance.

Attacked cltannel. — When an open channdd
tached to the orifice at its exit, in such a nian(|
the sides and bottom of the channel are continiu
those of the orifice, the coefficient of contraction 11
the same, except when the head on the oriticel
than 2^ times the height of the orifice ; in this latfl
the coefficient may have to be materiaily reduced,
extreme case given by Poncelet and Lesbros, being o
of a discharge through an orifice 0'i64 feet high.undeil
head of oi iS, gave a value of o=0-452, while without
an attached channel the value of o was=06I2 ; furthcTi
when the level of the attached channel was exactly at the
same level as the floor of the reservoir of supply, the vatiM
of o was reduced to 0443. The !aw of reduction t
coefllicient necessary for these cases is not yet given id
a definite form. The inclination of the attached channel
when less than one in 100 did not affect ihe coefilicienU
in any way, but when increased to one in 10 had I
effect of increasing the coefficient from 3 to 4 per ceoL

Orifices witk mouthpieces attached wci
lime of the Romans known to have a greater dischai^
than those without them. In order to effect this ii
it is, however, necessary that the Icngiii of the attached o
additional tube should be twice or three times the dia
meter of the orifice, otherwise the fluid vein does 1
entirely fill the mouth of the passage. The experiment
of Michelotti and Ca-itel determined a mean coefficicn

OJtJJ'/CJSS AND OVERFALLS. in

itchaise for cylindrical mouthpieces of 0'S2, the

cn»c5 being 0-803 an<l O'^SO ; the singular effects

&ttccd under some circumstances by the application

cytindrical mouthpieces are more curious than useful.

«iic»l co«\-erging mouthpieces increase the discharge

- Vi'.ghly : the experiments on them of Castel, engi-

li the waterworks of Toulouse, are exceedingly

: ting ; ihcy demonstrated that under varied heads

/tSiuicnts of dischai^e and of velocity were practi-

lonstant for the same mouthpiece, and that for the

iihfice of exit the coefficient of discharge increased

"1 i%\ for a cj'lindrical mouthpiece in proportion to

release of the angle of convergence of the moulh-

■- employed up to 095 for an angle of 13^°; and

'. beyond this angle the coefficient of discharge di-

Tiiitiet to 093 for 20°, and afterwards decreases more

"Jiy. The length of mouthpiece employed in these

_/Ti js well as in the former was 2^ times the diameter

■ 'heofificc. Some experiments by Lcspinasse on the

-1 of Languedoc showed the enormous increase of

lianjc effected by using converging mouthpieces;

:tioutfapic<:cs were truncated rectangular pyramids

■ ! feet long, the dimensions at one end 24 x 32 feet,

'he other ^^xfe feet, and were used in mills to

ii- the water on to water-wheels ; their opposite

ijcw were inclined at angles of 1 1° 38' and 1 5° 1 8', and

the head employed was 9*59 feet ; the experiments

resulted in determining a coefficient of discharge varying

&«m 0976 to 0987.

Conical diverging and trumpet -shaped mouthpieces
still further increase the dischai^e from an orifice : the
experiments of Bernouilli, Venturi, and Eytelwein have
thro«'n much light on this subject, and showed the cc-

IIS pRmapLss Aim

efficient to lie between 0*91 and r35. Venturi coii*
eluded that the mouthpiece of maximum discharge
should have a length nine times the diameter of the
smaller base, and a flare of 5^ 6\ and that it would, if
properly proportioned to the head of pressure, give ^
discharge i '46 times the theoretic unreduced discharge
through an orifice if) a thin side.

Sluice gates, large openings, &c.

It may be observed, however, that although the
minutiae of discharges under certain experimental
conditions have been sedulously preserved, there
is yet considerable doubt what coefficients should be
used for large sluices and wide openings of difTerent sorts.
It may be unfortunate that experimentalists should
dififer, but at the same time the circumstances, under
which the amount of discharge from a sluice is an im-
portant consideration, only occur generally to those who
are capable and have the opportunity of determining it
accurately by experiment themselves.

The ordinary coefficient for a sluice of moderate size,
for small lock or dock-gates, or mill-gates, is generally
taken at 0'62 ; that for a narrow bridge-opening, which
may be considered as a large sluice, at 082 ; and that for
very large well-built sluices, very wide openings out of
reservoirs level with the bottom of the reservoir, and
large bridge-openings of the modern type, at 092.

The term iT, representing the effective head of pres-
sure, is differently estimated in various cases : in ordinar>'
cases of sluices, supplied from a reservoir above them,
the head is the difference of level between the surface of
the water in the reservoir and the centre of figure of the

■r.T II ORIF/CES AXD OVERFALLS.

iiice;1ntt when the sluice is drowned, that is, has a
luceptible depth or water in the tail race standing
above the sluice itself, the head is the difference of level
rfthc water above and of that below it ; in bridge-open-
ingi ils«\ th^ head is the difference of water level on the
ap^bcsm and down-stream sides of the bridge.

The most recent experimental determination of coeffi-
cients of discharge for head-sluices supplying small chan-
m1» is that of d'Arcy and Bazin ; the results of these
opcnktions will be given, with the account of the mode of
^juging adopted by them, in Chapter II.

Theabo\'e includes all the general deductions about
rifiasthat arc likely to be of any use to the engineer ;
: more practical collection of coefficients of discharge for
nfices is given in Part 4 of Table XII. ; and the value
f the expression V=o i/'dgli

inxn in Table X., for various heads, and for all the
• iiies of o that are commonly used ; some explana-
t examples also follow that table.

The discharge of pipes tinder pressure.

"his subject may be treated as one closely allied to

jp discharge of orifices in one respect. If at any point

K ■ pipe or series of pipes under pressure the continuity

of the pipe be cut off, the discharge at that point will

obviously be thai of an orifice under pressure, provided

^^|ic necessary free fall be allowed ; the dimensions of the

^■jdSee will be those of the section of the pipe at the exit.

^^B3 tbe bead will be the statical pressure, less a reduction

^^ bead representing the friction throughout the whole

coarse of the series of pipes of supply, and another for

oontractim at enlrj' and at exit

lU I'MtMSCIHMS AMD MUtOZM.

In £rtu^ practice, this meAod could alone be OOO'
ver.ieTiily Applied at ihe e^tremit\' of a series of pipes for
direct deiemiination of discharge ; but having obtained by
this c-r any other method the discharge at any one point
:r a line of pipes, the discharge at any other point along
the sazie line may be reladx-ely determined by making
3..!?-.\-ance for the friction developed in the intermediate
Icr.cth by a representative head.

A mere common mode of making calculations ofdis-
ch^«:e. pressure, and diameter of pipes under pressure
has been :n accordance with mean inclinations of the
various g:eneFaI lines of pipes in a series, and by appl/'
:::^ the ordinary' formula for flow (transformed for dia''
c;<::ers of cjlinders^ as before given

g=cx 39-27 ^Z&P

It is. howe^-er, ex-ident that this method of assuming
,1 r?.can hydraulic slope taken from a point where the
■ rossure is zero to the point of contemplated discharge,
.ir.d treating the discharge according to the principles
of flow, from a summit due to that hydraulic slope, is an in-
exact method ; for it is ver\' evident that the same data
as bases of calculation might apply to two very different
conditions of length of pipe, thus neglecting consider-
able amounts of friction.

Overfalls and Weirs,

An overfall may be treated as a wide rectangular
orifice in an ultimate position, where the head on the
upper edge is zero ; and its discharge may be there-
fore computed in the same manner as that of an orifice.

ORIFICES Ah'D OVERPM

iThc discharge of an orifice is according to the para-
ge titcoty —

re I and i, are the heads on the top and bottom
;e,accl uris the width of the orifice; but if H=mean
n the centre of the orifice, and d is its depth when
ie orifice becomes an overfall, this formula becomes

)ing this, and putting wcL^A, the sectionaJ area,

«=■"*« ■'■^<'-«.)

I aod as (f is comparatively small, the last terra may be
ii«gi«tEd, hence

Q=oA\^2^: and 7=of v-agF

B IT is the head on the sill of the overfall.
The value of the coefficient, o, varies according to
K conditions of the overfall. It was determined by M.
el, at Toulouse, by a large series of experiments ;
d also by Francis, in the Lowell experiments referred
to to Giaptcr II. on Gauging. (For obstructed overfalls
»oc also a paragraph following.;

The experiments of M. Castel showed that, for the
accurate employment of a general coefficient the dimen-
xions and conditions of an overfall should fall within
one of the three following classes.

isL When the length of the overfall sill extends to
the entire breadth of the channel, and the head on
the «iU is less than one-third the height of the dam or
banier, the coefficients remain remarkably constant.

jLWCZFLES AXD FORJUULjE. chap. L

^ cs£x froci 0*664 to cr666t. Hence generally for

j'^=-^

r=.d. Wlxc the la^th of tbe over&ll sill is less than
the e=:tire breacih of die diannel of supply, but is'
er than a quarter its breadth, the coefficient lies

between tbe tvo extrexnes of 0*666 and 0'598, and is
strictly dependent 00 die ratio of the length of sill to
breadth of channel ; benoe it is for the following relative
lengths of sill : —

kacd

isofall CoeflScicat

0-SO

0-613

(MO

0*609

0-30

o*6oo

0^

0*598

z£ s2 CacSonK

tS£ 0-666

C-93 o^sS

C'30 0-647

G-:^ o^SS

C 5: 0-624 ;

3rd. If the !er. ~:ii oi the overfall sill be equal, or even
only nearly equal, to one-third the breadth of the chan-
nel, the coefficient remains ver>' constant, var}'ing only
between 059 and 0*6 1. Hence generally for this case,
which is particularly favourable for gauging small
streams, o = 0'6o.

In other cases, that is, when the length of the sill is
less than a quarter the breadth of the channel of supply,
the coefficient depends on the absolute length of sill,
and requires determining specially ; it increases from
061 to 067 in direct proportion to the diminution of
absolute length of sill.

Veiocity of approach. — With reference to the three
cases suitable for practical purposes, the experiments
of M. Castel showed that when the sectional area of
the overfall was less than one-fifth of that of the normal
section of the channel of supply, the effect of velocity
of approach in the channel did not modify the value of
the coefficient ; for other conditions, the modification

OA-JFICES AND OVERFALLS.

f^ccsiary was not determined in a very satisfactory-
! jrra : — the new equation for mean velocity of discharge
being changed from

into F=of v/23(i/-i-0 033H''J,

where W= the surface velocity of approach, not deter-
mined from observation, but from its assumed ratio to
the mean velocity. Perhaps therefore it is preferable
to modify the coefficient, o, into a new coefficient o,,
'- < >mpriaing the allowance, thus

'.=» K'-^y-S)^

.>. here A is the head due to the velocity of approach, and
// is the head on the weir sill.

Attacfud citanneh. — For the special cases in which
channels are attached in continuation of the sides of
the overfall, the coeHicients in the experiments of
I'oncelet and Lcsbros were reduced by 18 to 33 per
tent If, howc%-er,the fall to the channel is more than 3
feet, no reduction is generally made in the coefficients.

It may be noticed that the head on the sill used in
the above expression is that in the centre of the over-
fall, which is independent of the rising of the water at
tbc wings, a phenomenon to be observed in almost all
cases ai weir dischai^cs.

In all the above cases, it is supposed that thin edges
as of metal sheets, or one-inch waste-boards, are used ;
(or broad or round-lipped crests, the coefficients will
reqttirc reduction. Sec the coefficients given in Part 5
of Tabic Xa

ObitrutUd (HtrfalU. — When obstacles occur on the

n8 /•JtmC/PLES AiVD FORMVLM.

sill of an overfall, as dwarf pillars or blocks, a dedw
in the discharge over the sill is made not only on &
of the reduction of section, but on account of the
tractions resulting. Francis's formuia is appUcaU
these circumstances in cases where the length of w
equals or exceeds the head ; — it is

i2=i«>/%.(<-oi»H)fl'.

wheren=the number of end contractions,
(note that n=2,when there is no central obstructk
i=Icngth of weir sill,
IB-=A the sectional area of dischai^,
and 0=0-6228.
In case the weir sill has the same breadth i
channel of supply, n=0 ; and in that case

Q= 3-332 iM
This, it will be observed, varies from tliat of Castel, n
under the same conditions, when o=0-666, gives

Q = 3-563 fZ/'.

Partly Drowned OverfalU. — When a weir has t
water above the edge of the sill, it may be treated
combination of an overfall with an orifice ; the '
portion down to the level of the lower water as an
fall, and the lower portion from that down to tl]
level as a rectangular orifice, and the discharges calc(
separately for each. The same value of ^ is ua
Doth cases, H being the head due to the overfal(
is, down to the level of the taiUracc.

Some further values of coefficients of weir disd
arc given in the accounts of gauging in Chapter II
&id in the computation of discharges from over£dl

f.U DtSClfARCE FJlOAf LOCAS, BASINS. &v.

Jdlies of discharge due to various heads and various

iifidents may be obtained from those given in Table

ti by reducing the velocities there given by one-

; the results mu!tip!icd by the section of overfall

e then the required discharges. The method thus

d enables the same table to be used in computing

le discharges of both orifices and overfalls. A table of

itf cwHidents is given in Table XII., and some cxpla-

y examples accompany Table X.

'J> Efflux or Discharge from Prismatic Vessels,
Locks, Basins, Reservoirs, or Tanks.

The following formulae given by d'Aubuisson may be

K"^sidered useful for reference in the cases in which they
required in engineering practice :—

First Case.
Simple discharge from a reservoir.

'ist.) When the reservoir empties itself through an
Orifice or sluice with free exit.

Velixiliis. — The ratio between the velocity at the
of discharge and that of the water in the reservoir
inverse ratio of their sectional areas.

If ff=: actual height of water in the reservoir ;
height due to and generating the velocity of dis-
and A and a are the sectional areas of the
if and Ihe orifice respectively.

UD PRINCIPLES AND FORMUL^C CM*r. t.

Dfscharge.—K reservoir emptying itself through an
orifice in a given time would discbarge a volume equal
to half that due to the head at the commencement, kept
C(»stant during the same time. For such examples
^>plicd tn locks, see Table X.

Tiwu. — The time in whirh a prismatic reservoir
empties itself is double that m which the same volume
would be discharged if the initial head had remained
constant

The time of descent, f, to a given depth, d=H~k,

and the quantity discharged in a given time, t,

and the mean hydraulic head, H, under which the same
quantity would be dischaiged in the same time is —

where H and k are the heads at the b^inning and end of
the time of discharge, the reservoir receiving no supply
during that time.

(and.) When the basin or reservoir receives a constant
supply during the time of dischaige.

If j=quantity supplied per second,

t=time in which the surface will descend the
depth, x=il—k.

■ -r-r. 13 DISCHARGE FROM LOCKS AND BASINS. ill

hen there is no supply, or g=0, this equation resolves
•'■M into that previously given.

f 3rd) In the case of tliere being no supply, but the
J charge instead of being effected through an orifice is
cuntlucted over an oi'erfall, having a length of sill =i,

3 J

Non-prismatic reservoirs are extremely difficult to
deal with, and the investigation of any special case here
' juld be comparatively useless.

Second case.

ifAfn etu reservoir empties itself into a partly filled

reservoir.

(1st) When each of the two reservoirs being excced-
rgly large practically preserves its own level, the com-
lunicating sluice being below the lower surface of watci-;
■ -.en if ff. A, are tlie heads ; a the sectional area of the

the dischai^ Q=oa^2g{li-h)T'

P(2nd.) When the upper reservoir being exceedingly
targe preserves its own level, and the lower reservoir
having a definite area {A), receives the supply through a
sluice of a section (a), required the time ( in which the
lUilacc of the lower basin will rise to a certain height.

If U, h, be the heads on the lower surface at the bc-
ipuning and end of the time, (,

I

t rtUfCtrtSS and FOIlitCL.e. ci.«f, t

'% friMMti. like that pmiously given, is useful fin
HMHiqg tbe time oecessaiy to fill a lock cbamber;
KM &^=Ct OF tbc le%'cls become tbe same, the cxx is
* t£<amai locka^ and tbe sectional area of the sluice
f Ic AfciOiiind btun tbis equation.
(jRiJ Wtea Midter tesenw recei\-es any supj^)
ID site, if tbc suriaces are original!
and tbe cominunkation sluice '
of one nQ rise and tbe other faU.
B'J.HMCtfceaectioPSof tbe two vessels,
Jl Ws the beads at dw bcfmning and end in A,
^jltke beads at tbe beginnmg and end in d.
•aidie sedMoal aiea of the pipe or sluice,
t=tHBe darnc wfaicfa tbe sluice is open.

il>'*

^•B \.U-k)- ^(A+£)x~AH-S/^

«Bd if it be iei;vired to knor tbe time f to which the tw<
;m«K«s win be »e«J ; in that case. «-y=i^±|?

MlA+B) Jig.

Thif i^-vitfSilk is OMirenient for determining the time
A>'**^i<>^ *; trn^T^ rf»e water in tbe two chambers of a
y'v^i^^V'- ^■^ V t5»e suae letid, by means of a sluice ol

CHAPTER 11.

ON FIELD OPERATIONS AND GAUGING.

i

^^^RBblCI Bi«aiurciiieat of diicliaige. 2. Gauging by tccl&ngiilar oveifalls.

^^^V }. ApplUnos sod iiuimmenis for the tneaiurement of velocilics.

^^^V't- Bal'lwin uid Whistler's gauging by menus of sniTace velocities.

I^^H }. Fnncit's gnoging cansk and streams with loiidiid tubes. 6. The

■' UisiBlfipi field opetalions for guiging wiy large riven. ?. Field

i>|i>mtioiu in gauging cierasses : uul coiapuUtian of coi^Scienis.
& Ciptiio llumpliteyii'imptoredtyilein of gauging nTcrs and cana);,
ud General Abtui's mode of dctenoiaing a dischai^ on any given
illy. 9. The ctperiments of d'Arcy and Bniin on the Rigoles de
Chuill]' el Gtodbals. to. Velocity obbcmtlions an great rivers in

K'^'ulll America. Iiyj. J. lUvy. 11. (7a|jlain Cunningham's experi-
Bt* on the Ganges Canal, iz. General remarks on sy&lems uf
igiog, and condusions ihiTefrom.
dii
cai

Direct Measurement of Discharge.

direct measurement of the dischai^ of a channel
can be obtained by means of gauge-wheels.

channel is widened until the water flows at a
moderate depth, less than five feet, over a horizontal
arid carefully constructed apron which is divided by
piers into a number of equal openings. At each of
these openings a gauge-wheel is placed, which fits the
opening cv-cry way within a quarter of an inch. Sheet
piling is driven across the head of the apron and along
the banks approaching it for some little distance, so as
to force the whole of the water of'the stream to pass
between the piers and drive the wheels. The measure-
ment of the water is determined by the number of revo-

124 OA- FIELD OPERATIONS AND GAUGING,

lutions of the wheels, which should be all coupled I
one shaft and be made self-recording on a diol-facc
by the dimensions of the wheels, or spaces bet
their blades, as well as by the depth of water [
over the apron, which is observed at intervals of a
five minutes on gauges erected for the purpose.
method of obtaining a discharge is expensive, interfi
with navigation as well as the passage of the water,;
is therefore very rarely adopted.

2. Gauging by Rectangular Overfalls.

The water of a canal or stream is made to disci
itself over a single horizontal dam, or over a
small overfalls specially constructed for the pui
The discharge over overfalls of certain dimensioru
under certain circumstances, is known by many i
of experiments to be correctly expressed by a for
containing the required data and dimensions, knotf
Francis's formula ; it is

where i=Iength of weir-sill.

i/=head on the weir from still water,

7i= number of end contractions.

If the weir-sill is of the same length as the bread:

the channel of approach, n=0; if less tlian it, and

is no central pier or obstacle, n=2 ; each pier or a)

de involving two additional end contractions.

Taking ^25^8-025 and o=06228,

Q=3-33198p-0I/ti7lH*

I;* GAUGING BY HECTANGULAR OVERFALLS. las

Hiu gi«s results within one per cent, of absolute
ctitude. The dimensions in this formula being talcen
t, the discharges will be in cubic feel per second.
: following conditions should be observed in
l^ng by rectangular overfalls.
\h- regards form of construction : —
1 1. The dam in which the ovcrfai! or series of over-
■ is placed should have the sills truly horizontal, and
ludesof the overfalls truly vertical : the dam itself
idbcverticBl all along on the up-stream side, but
B rills should all be sloped off on the down-stream
le at an angle of 45° or more with the horizon ; all
* edges of discharge should be sharp and true, after
'fteing which the water should discharge itself unob-
ajucted.

3, In order to obviate the necessity of allowing for
the velocity of approach in the channel, the area* of the
''^■^faIl — ;>., the quantity^x^, must not exceed one-
"Hii the area of the channel ; otherwise an allowance
iLit be made on this account, as given in the para-
'ft})h on Weirs, Chapter I., Section 1 1,

,). Should the velocity in the channel of supply no1
" uniform in all parts of its section, arrangements ;

made to make it so; this can be done by placing
■itmgs, having unequally distributed apertures, a
ijss the channel, and as far from the overfall as po:
'||^ and letting the water pass through them under a
■mnU head.
, 4. In addition to the above it is absolutely necessary
tt the air under the falling sheet of water should have
^communication with the external air.
IHth regard 10 dimensions : —
', Should the overfall not extend to the entire width

ia& Oy FIELD OP£SATtO.VS AND GAUGING. '

of the channel of supply, there should be at least a
Terence at each end equal to the depth on the ovcrl
so as to produce complete end contraction.

6. When the breadth or the overfall is equal to d
of the stream, and even under all circumstance!, I
depth on the weir should be less than onc-thiid \
height of the barrier,

7. The depth on the weir must be always less t!
one-third of the length of the silL

8. The head on the overfall, H, should never be |
than 0*2 feet ; it is better, also, to make it more i
05 feet and less than 2 feet

9. The fall from sill to tail-water should not b
than half the depth on the weir, in order to en:
free fall.

The following practical directions suitable to streaj
and moderate rivers are given as examples, where ord
nary care and accuracy is required.

First caj^.— When the discharge is supposed to [
less than 40 cubic feet per second : —

First, according to the above rules, make H greater
than 2 feet; and H%.l less than one-fifth of the channf'
section ; let / be greater than '3 feet, but less than oi"
third the width of the channel ; and. to ensure a fn 1
fall, arrange so that the lower edge of the sill may ii' ■
be less than half a foot above the tail-race. Under the :
conditions the coefficient of discharge to be used will be
<i = 0'623, and any error should not be more than ooe
per cent

Before constructing the weir, observe the s
velocity in the channel (F,) and the transverse :
(J ) ; the approximate discharge will then be y, = V, x J
and assuming a value for I as before mentioned, obti

C/iVC BY RECTANGULAR OVERFALLS.

itie for H by means of the ordinaiy formula, making
of the approximate discharge for this purpose, H
be from i to 3 feet, and should such a value not
It. from the application of the previous conditions,
mother value for I, so as to secure this condition, as
to retain the other conditions before mentioned.
this is gained, the opening may be cut of the
ired dimensions in one-inch ptank, and the dam well
and as, in practice, the dimensions are not likely
be very closely adhered to, they should be measured
in when the orifice is completed, and applied in
formula before given.

5etond out— When the supposed dischai^e is more
40 cubic feet per second, but is manageable : —
Rnd the approximate discharge at the spot from
section and velocity, when the surface of the stream
level with a fixed mark on a post or stone, at from
to 200 feet below the intended site of the weir.
Ig previously selected a place where the stream is
in width and inclination, construct the dam so
thai the weir-sill may be equal to the full breadth of
the channel, and square the ends of the opening with
,'!nnking, Put a gauge at each end, with the zero at
;"; level of the upper edge of the sill of the overfall,
-hich should be from i to 5 feet above the fixed bench-
mark.

When the water is up to the mark, read the height
on cither scale ; take their mean, and use it as a value
B tn the weir formula before given to obtain the
ity and amount of discharge. If necessary, obtain
flirfacc velocity of approach W, and make suitable
•nowancc for it as before mentioned under the head of
wdr discharges in Chapter I. In this case o=0'666.

onciu

IzS OA- FIELD OPERATIONS AND GAUGING, out

3 Api'Uances and Instruments for Veloci
Measurement.

There arc many cases when it is not a(]\-isabU
construct a dam or gauge by overfalls, and also c
where the simple calculation of dischai^e due to
hydraulic slope, and the terms of its cross-section, d
not give sufficiently accurate results. Under these (
cumstances velocity observations must be made, l
other data correctly obtained, so as to obtain from tl
the required discharge, which, when divided by the i
tional area, gives the mean velocity of discharge;

In all cases where velocity must be observed 1
advisable to choose a straight reach of channel hav
a tolerably uniform section ; it is also advantage
that the bank should admit of the measurement {
straight line parallel to the general direction of
channel, and at right angles to the line of intended r
section of observation, to serve as a base for triang
tion. and location of courses, and sections.

To obtain perfect uniformitj' of channel, a flui
timber lining to the reach of well-Joined plank m
constructed, giving about two hundred feet of pcrfet
uniform section ; this gives the means of accura
measuring the dimensions of the stream, the wh<^
the water of which is forced to pass through it
means of sheet piling at its upper entrance. Itsbi
not produce any sensible disturbance in
of tlie water, and not interfere with the navigatkii
passage of water. Velocity obsen.'ations arc then i
cither at the middle section or on a measured Ic
along the flume, at such intervals that the voriatio

tmSTJtaiaJVTS AKD APPUAKCES. i

1 velocity in section shall never be very marked,
mmatton of the products of these representative
'ic-i by their corresponding portions of sectional
,;.e5 the required dischai^e. A long and accu-
-oostructcd open aqueduct in perfect order answers
• purposes of a flume.
. ii!ing all such opportunities, the channel itself
: ix: employed in its natural state ; in this case the

■ M various velocities on the bed and banks should

■ 'led from time to time during the observations.
id any exact determination of the water section be

ible it becomes necessary to resort to soundings,

may cither be taken by means of a surveyor's

\'.-i.\ chain, with a suitably heavy leaden weight

tied to one of the handles, or with a sounding line.

dclciminalion of the position of each sounding

in narrow reaches be best made bj' stretching a

^ictoss, and measuring the distances of the sound-

-[■ointa from one bank along the cord. In wide

I-:.! where this is impracticable, the sounding points

Id be fixed by angular observation and connected

-\. the base line of triangulation at the moment of

siunding either by an observer with a theodolite on the

iboTE, or Willi a pocket sextant in a moored boat.

The fall of the water surface at all states of the
clunncl is one of the data generally required. To
detccTDiae this, a gauge-post is erected, driven into the
ETOUnd at each sounding section, and the heights of
tfce water shown on them continually recorded so as to
4dw all variations of depth ; the connection of level
^— . Mij the two or more gauge-posts is made by levelling
; from one post to the other, or from both to a
.i bench-mark. In many cases the fall of the water

ijo ON FIELD OPERATIVSS A.M> GAVCIMC. cinf"-

surface is so slight that the ordinary level and stave;
cannot give sufficiently exact results ; instruments <■''■
gi eater precision must then he used.

An ordinarj' gauge-post may also be too coarse [«
indicating the slight variation of the water surface during
the period of gauging ; in that case a superior appliaoct,
B hook-gauge or a tube-gauge, is necessary.

Boyden's hook-gaugf.~\%. is well known that the capil-
lary attraction of water about any simple rod-gaufic f"f
determining water level will falsify readings. To obvi^'.v
(hat defect this gauge has a hook at its lower end. wlm i'
can be raised or lowered by turning a screw ; when li"
point of the hook is even a thousandth part of a fw.
above the water surface, the water around it is sensibl;
elevated by the capillary attraction, and obviou^v
distorts the reflection of light from the surface, wlW'
the hook is lowered just sufficiently to cause this disM
tion to disappear, the point of the hook must coincul^
with the water surface ; a true reading, exact within oo:'
of a foot, can then be read, by means ofavernierattaclu
to the rod of this gauge which is graduated to hundrcilii
of a foot As this instrument can only be cfTectivL'
used in still water, it is held in a box, the inclosed m-u
communicating with the external water only by mt n
of a hole ; or, if the depth at some distance off is i'
object, by a pipe leading from that place to the bole L"
the box ; any oscillation of tlie water surface ia the bflta
may then be diminished or nearly rcmoveil by pvti^^l
obstructing the hole or communication at will. ShrwM
perfect rest not be attainable, a good mean position
the point of the hook may be obtained by adjusting ii
a height at which it wHIl be visible abov-c thcwatcr »u-
facc for half the time. It is convenient to haveobHH

J^\^i^iM£NJ'S AMD APFLrANCBS.

V maidc with s small sctnispherical knob on it, so that
etfl-staff can then be held on it for taking a sight with
pltnMnuncnt.

I Simn'i tubf-gauge is, unfortunately, not descrit>cd
\ k sufficient detail, nor are drawings of it given in his
Kecherdies Hydr^uUques.' It seems, however, to have
bitn a glass tube having a mouthpiece of only a milti-
mcUe in diameter, and that it enabled variations of
Wter level of one millimetre to be easily read ; it is
Wee extremely probable that it resembled in some
raspwts the velocity gauge-tube of d'Arcy, used for
liWng velocity measurements, hereafter described. It
iS" in fact, evident that an instrument on this latter
principle, capable of indicating variations of velocity
>"lh precUion, would also indicate with exactness the
''if::ttnt of the withdrawal from, or submer-iion of its
t'jiitfipiccc in, the water, and that this motion could be
^Mly manipulated with a clamping and a tangent screw.
The following are the different instruments and ap-
i-anccs for mea^iuring velocity ; but most if not all of
i'-« involve the application of a special coefficient of
-uction due to the particular appliance, in order to
■ Uin the actual velocity of the water in feet per

I. Surfaa fioad. — Surface velocity may be very

nply measured by observing the time of transit over a

I 'wn distance or length of a reach of a river, of any

!^;ht floating body, a wafer, a ball of wood or corlc,

la, partly filled bottle. This method is coarse, and

icious ; a later float may outrun an earlier one, whf^n

B is much local variation of velocity.

. Loadiit rods ami tubts. — Mean verticalic velocity.

; the mean velocity past any vertical axis, or the

13a OA' FIELD OPERATIONS AND GAUGING.

mean of all the velocities from water surface to
bottom under any point in a vertical plane, is meas
by a loaded wooden rod or hollow tube placed vcrtiq
having a length nearly equal to the depth of
channel. The time of transit of such a rod will I
give approximately the mean velocity of the vert
plane of the water in which it moves. These tubes
generally weighted inside and capped, as the pail
metal tubes of the Lowell experiments hereafter ■
tioned, thus obviating the necessity of attaching wdj

The loaded tubes and rods used in tlie velo
observations on the Ganges Canal by Captain Cunn
ham will be described hereafter in Section 1 1 of
chapter, which is devoted to those experiments.

Another recognised mode of observing mean verta
velocity consists in lowering from the surface tOi
bottom, and raising again to the surface any ai
tive self-recording current meter. This is an open
requiring extreme care ; the meter must be suf^cifi
weighted, and, if necessary, also managed by a cord |
an additional boat moored up stream so as to ensun
moving vertically up and down ; ihe lowering and raj
of the meter must also be evenly and steadily man^
so that the results may not be falsified.

3. Floated frames. — Mean sectional velocity <
approximately obtained in small streams and canal
one operation only by making a light covered frames
nearly the size of the whole cross-section of the stn
and so arranging it by floats and weights that it
assume a vertical position at right angles to the t
of tlic current ; its time of transit can then be 1
and this will be the approximate mean velocity ol
iect'on.

■tr-j /xsrxLA/eyrs asd appuancss.

Kocil
hull

4. Dfublt floats. — These are used for sub-surfact;

A weighted float, consisting of ball, or cube of wood,

liullcw tin weighted with lead, is sunk to the required

Ih, being attached by a cord or thread to a small

upper float on the surface of the water ; the upper float

luring made of cork, light wood, or hollow tin, carrying a

:al stick, or wire, for convenience of observation, and

length of cord being so adjusted as to prevent the

ited float from sinking lower than the depth at

the current velocity is required. The time of

lit of this double float, over a measured or a caku-

distance, is observed, and is supposed to represent

velocity of the stream at that depth, independently

coefficient of reduction.
Another form of double float is a pair of equal hollow
lb connected or linked together, the upper one on the
surface, and the lower one weighted sufiiciently to keep
'! a( the certain depth ; the velocity of this double
'i'Jit. as observ'cd on a measured distance, is supposed
' ' be that of the current at half the depth of the
«cr ball.

Tbc double-floats invariably used in the Mississippi
jrity were kegs without top or bottom, ballasted with
Hps of lead, so as to sink and remain upright; they
re 9 inches in height, and 6 inches in diameter ; the
ffacc floats, when of light pine. 5-5 x 55 x 5 inches,
[.L-n of tin, ellipsoids, axes 55 and I'S inches, the cord
■-tenth of an inch in diameter ; for observations more
in J feet below the surface, the kegs were \z inches
by 8 inches in diameter, and the cord nearly
iths of an inch. It was believed that neither
of the surface float nor the force of the

wind directly afiected their velocities to any apprcciali

5. Instruments of angular tneasnrfinntt. — A quad"
rant having a graduated arc has a string attached t
its centre, and a ball attached to the string, which =
immersed in the stream. The current moving the ba -
produces an angular change from vcrttcality in the po.:
tion of the string ; the velocity is tlien equal to t
square root of the tangent of this angle multiplied b
coefficient, which is constant for the same ball only,

6. The tension balance. — A ball is immersed in t
stream and attached by a wire to a balance, whi
registers the amount of pull. Another vc
method requires a smalt plate instead of a ball, whfl
is connected with the balance, and which is dire
opposed to the current

The tachometer of Briinings is the best known I
strument of this type. It consists of a plate fixed J
one end of a horizontal stem, which moves in the s
of a vertical bar, by means of which the instrument citi
rests on the bottom of the channel or is suspended frd
above. A cord of fixed length is fastened to the o^
end of the stem, and, passing under a pulley, is attacfJ
to the short arm of a balance, on whose other e
weight is suspended, being placed in such a positiorj t
the equilibrium is established with regard to the for«
the current under observation. The position of I
weight on the graduated arm of the balance iiidica^
the velocity observed.

7. T/k rotary screw. — A light metal screw, ^mu
to that of a ship's patent log, will, when sufama
in a current, rotate at a \clocity approximate to I
of the water in which it is placed. If on the 1

INSTXVATE.VrS AND APrUANCES.

jftbetcrew a thread U set turning one or more worin-
i, the number of revolutions of the worm-whcc!
bill indicate the iipproximatc velocity of the water, from
h, by applying a coefficient of reduction applicable
Bthe particular instrument, thus including all allow-
K for friction and other causes, the true velocity of
KflKcurrcnt may be obtained. There are several current
\ man of this type : Saxton's, Brewster's, and Rc'.y'g,
hnciflcr described, arc all modifications of this form.
Si.iiDcof these instruments are not suited to great depths
jndhigh \"elocities ; others are made self recording in
iitfh a wray as to make allowance in the indicated
number of revolutions for the loss of velocity by friction ;
itie latter is a great disadvantage, as it is always practi-
ally necessary to test each particular instrument, and
'nakcusc of a coefficient, however small it may be, in
"der to obt&in accurate results.

The earliest now known instrument of this type is
ihc hydromctric mill of Woltmann, used by him in 1790.
lewingson its axle resembled those of awindmiU, and
e square copper plates, set at an angle of 45°, having
kr sides "082 feet and their centres at 164 feet from
k axis of rotation ; for small velocities the size and
Jance of the wings was doubled. In great depths
I instrument was attached to a bar and lowered from
iKtTarm between two boats, and the instrument put
)Ut of gear by means of a cord at any deptli.
■ type of current meter, from its convenience of use
ibscrving velocity at any depth, has been re-invented
liy times,
Da the gauging of the Parani and La Plata, by Mr,
, the »cf«w current meter, with .some alteration*
jl fanprovetncnts made by him, was invariably adoptoit.

■iS^maPiave^z} opera rioirs»

For ordinary currents the screw used by Mr. Reiij
consisted of two long thin blades of German silver, havio
a diameter of 6 inches, and a pitch of 9 inches ; t
thread of its axis worked on two worm-wheels of 3 inct
in diameter, one wheel having 200. and the other I
teeth ; each revolution of the screw moved tlic fin
wheel one tooth onwards, the second wheel moving 00
tooth onwards for each complete revolution of the fir
wheel ; this allowed of the continuous reading or4Oj30
revolutions ; the two worm-wheels had graduated div
sions around their circumferences, corresponding to !
teeth in number and position, which were read off at fl
index through a glass plate covering them. A nut »
also used for clearing the worm-wheels from the thrca
of the axle of the screw, by means of which the instn
mcnt was either put in gear or out of gear by hand ;
wire attached also enabled this to be done from ab<
when the instrument was at any depth.

For strong currents, the screw-blades were short
and stronger, and made of steel. Some of the sere
used were only 4 inches in diameter. The divisions <
the circumferences of the wheels were found to be t
near for convenient reading; 100 and 101 divisioi
would have been preferred to the existing arrangonei
of 200 and 201.

These meters were generally used for observb
velocities of more than 10 feet per minute, their correcU
results being absolutely correct within I inch per minu
of velocity. They required extreme care and contJnu
watching : the slightest bend or damage to a scrci
blade, or any clo^ng or accidental tightening of a sere
being liable to vitiate results.

When in good order, exposure to a gentle breue

-iiitnt to Veep the instrument revolving i—faiiing
, cleaning and oiling, or readjusting carefully, is
^ Jiitcly necessary. In order to keep a check on the
"Ki^rvations, a second current meter should always be

^^BRr principal advantage of current meters of this

^^Hnption is the convenience with which they can be

^^W»d, and their unvarying utility in observations at

■ } depth of water.

I Tlu differential tube. — Pilot's tube is a glass tube

nl « the lower end ; it is sunk to the required depth

• iiJ ils lower orifice directed against the current ; t'

' iiicity is deduced from the difference of water-level i.

^^Uocand that in another free from the effect of the

'irmL The first improvement of this instrument is

u of Dubuat, who gave the orifice of the tube a funnel

i[ie,and closed it by a plate pierced with a small hole,

' -1- considerably reducing the objectionable oscillations

'he water in the tube. The next is by Mallet, who

Tiinated the horizontal branch of the tube by a cone,

:ng an opening of 2 millimetres, and made the tube

1" of iron with a diameter of 4 centimttres ; he also

■duccd a float and stem which, elevated by the force

;hi! current, indicated heights on a graduated scale.

^.r- last improvement was that of d'Arcy, hereafter

(icscribcd.

In the experiments of d'Arcy and Bazin, on the

Rii-oles of Chaiilly and Grosbois, the gauge-tube of

■rcy. a de\'cbpment of the tube of Pilot, was gene-

>' used for taking velocity observations.

Pitofs tube, used in 1732, demonstrated the principle

I difference of water-level, h, shown b^ the two

c vertical and the other curved, and directed

ijS O^r FIELD OPEKATIONS A\D GAUGING. CBj

against the current, was that due to the velocrtj'
that the latter could be obtained from the for

making use of the formula V*='2gK.

The error in this was caused by the fact thftlfl
water in a vertical tube immersed in a current sti
lower than the water surface outside ; the diffetfl
being a quantity dependent on the square of the I
citj- immediately below the orifice. In addition taa
Pilot's tubes had a serious disadvantage in tbatl
oscillation of the water within the tubes, whose orif
were of the same diameter as the tubes themselves,!
not allow the difference of level to be correctly obse

These objections are entirely removed in the I
proved tube of d'Arcy, which has an orifice 1*5 i
metres in diameter for a tube one centimetre in dia
in addition to this the lower portions of the tub(j
which the orifices are attached have a small diam
and arc made of copper ; besides this, two cocks
introduced which add greatly to convenience of msti
lation. The lower cock, which can be worked by al
and lever, enables the orifices to be opened or closci^ "'
any moment from above, and thus allows the differcn'
of water-levels of the tubes to be read off at Ici^iii
after withdrawing the instrument from the water. "!■
upper cock, after the water in tlie tubes is drawn up 1
the breath at an upper orifice, shuts off the air, .v
enables the difference of water-level in the tubes, win
is not affected by dilatation or compression of ^i
atmosphere, to be read off above against a scale.

This gauge-tube is described in ' l^s Fontaines !'i.
liqucs dc la Viilc dc Dijon, 1856,' and drawings of it .1
given in the ' Kccherchcs Ilydrauliques ' of d'Arcy \
Bazin, 1865.

: latter the vertical glass tubes are V2^ m. long,

all capper tubes below them being inclosed

per casing, 077 m. long, 006 m. broad, and

thick, terminating in a sharp wedgc-ihaped
reduce the effect of the perturbation of the cur-
lie tubes themselves are affixed to an upright of
xwood, which is graduated and supplied with a
; the whole instrument being attached to an iron
1 on which it slides, and to which it can be fixed
ire at any height ; a handle turning the instm-
directs the orifices in any required direction ; and
ditional movable wooden arm is used to enable
ttrament to rest by means of it on any crossbeam
r from which the observations are being taken.

taking an observation with the instrument it is
to take a mean of three maxima and minima

: following is the theory of the determination of
nictent of reduction ft in the formula F=/i ■•/igh
ly instrument.

a single ciu^ed Pilot tube be placed in a current,
RTtth its orifice directed against it, and recording a
; h', above the natural water surface ; secondly.

dircctetl with ft, and recording a loss of level, h",
' that of the natural water surface ; and thirdly,
directed at right angles to the current, recording 3
if level A'", then —

V' ....,■. y.

I40 Off FiELD OPERATIONS ASD GAUGING, <

and finding from tables the values of velocities F J
Y' corresponding to the heights A' + A" snd h'+h""
abo\-e equations become —

F=;*r; and V^/iT' ;
hence there is a constant relation between the tl

height — due to the velocity of the fillet undcf e

sideration, and the quantities /*', h", h'" ; and the o
cient of reduction can therefore be obtained for any M
or form of orifice by means of a few experiments ;
when once the coefficient of reduction for the instniiw
ii determined, it is unnecessary while observing vdoi
tics to make further use of the level of the water, |
which the instrument is plunged.

9. Grandfs Box. — A box, having a small hole in^
wdc towards the current, is sunk to a certain depth )
withdrawn after a certain time ; the amount of w3tef|
the box indicates the velocity at that depth.

I o. BcUeaif's A ir-Float. — A glass tube of fixed lenj
is immersed in a position parallel to the current;
upper end of the tube has a conical mouthpiece fitf
it of »nj' con\-cnicnt size ; the velocity of passage e
(•lohtilc of air through the tube indicates the vcloci^
the current.

W. ^fatijvn't Currmf-vu/ei'.— This instrument, j
»'IHW»l by the Author in Berar in 1870, is a spring i
Mtnr, or «n adaptation of the principle of the !
bMUnr« <v vrci);hing machine to measuring a sub-sui
v^lfH-ltj- nt any point excepting at the exact surfac
ut the pCTinwICT : it admits of convenient testing 1
XTfiflcAtlon by direct application of weights,

13. Dt Pttyvdits Torsion Currmt-met^.— Thtfi
ciptp of this instrument is the estimatioa of ctu

S.tLOMrjArS £XP£Jf/ME.V7S. 141

' nn the twisting a£ a wire : it reads to minute frac-
'^f a foot per second.

■jrac of these modes of measuring \-riocity have fir

:'icsent practically fallen into disuse, on account of

vtiy limited range of thdr applicability ; others, on

' 'nlrary, have been severally adopted by various

■ Lilicians in modem times, to the entire exclusion of

T.-^t It tikay be nnticed more especially that some

ilicm merely afford a mean of a velocity. var>'ing

"J^iliout an extended time, and from this cause falsify

. liaJuced velocity for any special moment of time ;

Tsue inconvenient to manipulate, and a few yield

ii:ate results whatever coefficient of reduction may

"•- :ipi;lied to the special instrument. The accounts of

Wupng operations given in the following sections of this

fluptcr illustrate the use of some of these appliances.

k

>DGING Channels bv means of Slkface
Velocities only.

The experiments of Messrs. Baldwin and Whistler

"" discharges of canals of rectangular section are worthy

"f itoticc. They obtained discharges on the canals by

"leans of surface velocities and flume measurement, and

simultaneously gauged the actual discharges by gauge

"■heels, with the view of determining practically the rela-

lion between surface velocity and mean velocity, for chan-

neUof acertain size conveying water at certain veEocilies.

In one case the flume was 2732 feet wide, with depths

of water from 752 to 814 feet, having surface velocities

from 3x17 to 3'34 feet per second ; the observations de-

"i a mean coefficient of velocity -857. the cxtrcmci

: -838 and -856. In the other case, the flume was

1 feet wide, with depth ■ of water from 7 67 to 8S5

I4a O// FIELD OPERATIONS AND GAUCtNG.

feet, having surface velocities from i-gi to 277 E
second ; the observations deduced a mean
for the surface velocity of '814, the extremes beip
and ■S46.

In other cases, the data of which are not forthce
the cocfticients of surface velocity were -835, -830, \
and taking -829 as the mean of the five results, it c
favourabiy compared with De Prony's coefficient I
obtaincd«from experiments on wooden troughs iS ill
wide, having depths of water from 2 to ro inches
velocities varj'ing from S" to 425 feet per
Another point which Messrs. Baldwin and De I
agreed in determining was that their coefficients s
be slightly reduced for lower velocities and ino
for higher. The result is that the proportion \
the surface velocity and the mean velocity of dis<
for rectangular channels in plank, and within t
limits of velocity and proportions of cross-section, |
be said for practical purposes to lie between '8 ani
Under similar local conditions, therefore, the (
of acanal of rectangular section can be rapidly oblau-
by a few surface velocity obserx-ations, the inclinai
of the water surface, and the measurement of its setii'
Recent experiments, however, show that the above la
of velocity does not hold generally ; hence this motii. -
gauging does not admit of extensive application, '^m

;. Gauging Canals with loaded tubes ; ^H

Francis.
Under the tlicn existing arrangements at Lowe],
daily account was usually kept of the excess of water. 1
any, drawn by each manufacturing company over anc

: CAVGl/VC WITH LOADED TUBES. 14J

- the quantity it was entitled to under its lease. In

i.iry dmcs, occasional measurements were suffi-

' ■- , but when water was deficient, frequent measure-

r.i^ n-ere made. In the latter case, the following

i= '.he usual course of proceeding : —

A gauifing party, consisting of one or more engineers

.ViAi3i>tant5. ivas assigned loeach flume where mcasure-

ilUnecessai^'; and arrangements were so made that the

^-.Tvations for a single gauging occupied about an hour.

: intervals during the day being occupied in working

i;t.Se results, which were immediately communicated to

c manufacturers, so that the machinery might be ad-

ii^wJ to tlie amount of water they were entitled to draw.

The following arc the dimensions of the measuring

Jinci used, and the quantities of water usually gauged

1 ihem ; the depth of water in the flume generally vary-

i'li from 6 feet to 10 feet.

klcrriniic lo>y lun); by yf wide, 1500 cub. ft. p^r sec

Ap!>leion tjo jo Mao „ „

Lowel), M. C. 130 30 joo „

MidiJIcio 150 to 20a „ „

rracon i&> 66 1000 „ „

Dooit loa 4a Gix> „ J,

S'bc loaded tubes used were cylinders 2 inches in
r made of tinned plates soldered together, with a
^ of lead of the same diameter soldered lo the lower
I having sufficient weight to sink the tube nearly to
iquircd depth, thus leaving generally about 4 inches
e lite water surface. A red-paint mark was made
now the amount of immersion required, leaving a
6 between the bottom of the tube and the bottom of
»nal of I foot The tubes were of thirty-three dif-
bt lengths, varying from 6 to 10 feet ; six of each
A were provided for this purpose.

144 OX FtBLD OPERATIONS AND GAVGiNG. OM.

In order to adjust the tube precisely, it was placed
a tank made for the purpose, and small pieces of lead we
dropped into tlie top of the tube, and rested on the
of soldered lead, and more were added until the tuft
was sunk to the required depth, when the orifice at Ih
top was closed by a cork. The tubes were allowed
remain Roatlng for some time in the tank in order
discover any leak. If they leaked, they were taken a
and filled with water to discover the position of the lea
when the leak was soldered and the tube adjusted agiil
The centres of gravity of the tubes adjusted were l")
to I '90 feet from their bottom ends ; and thus bcft
low, the tubes had a strong tendency to remain vertid

The tubes were put into the water by an assist!
standing on a bridge below the upper end of the
a thing requiring a little practice to do well ; he stoi
with his face up-stream, with the tube in hand, t
loaded end directed downwards, but slightly up-stica
holding it at an angle with the horizon, greater or 1«
depending upon the velocity of the current. At 1
he pushed the tube rapidly into the water at the an
at which he previously held it, until the painted ml
near the upper end of the tube reached the surface of
water ; he retained his hold of the upper end of the I
until the current brought it to a vertical position, w
he abandoned it to the current

There were three transit timbers placed across
flume, the middle one equidistant from the other h
their up-stream edges vertical, and distinctly gradi
in feet from left to right. An assistant stood at Ci
transit timber to note the transits, and the assistant
the middle transit timber observed the depth of vri
in the flume at each tran^t in a box close to him betw

\ CAt/C/XC WITH LOADED TUBES. 145

: aiuDg planks and the wall gf the canal, which com-
r .'incited with the flume by a pipe about 4 feet above the
tr^tum. The box contained a ^aduatcd scale, divided
I tokindrcdthsof a foot, the zero point being at the mean
cloaion of the bottom part of the flume between the
-:(w ind lower transit timbers. The bottom of the
'-iint t!%i very nearly horizontal ; the elevations to ob-
U:nthe mean were taken at 32 points, giving an extreme
liifTcrence observed of X127 feet in one case. The course
of ihc tube, denoted by the distance in feet from the left
iids of the fiume when the tube passes the transit
timbers, was also observed and called out by the assis-
bats; tbc mean course being obtained by adding the
;s at the upper and lower transit timbers to twice
kai the middle, and dividuig the result by four for a
n distance.

: ustui method of observing the transits was by
K of an assistant carrying a stop-watch beating
T'seconds, who walked down and recorded every
IBI htmseU'; but when greater exactness was re-
iiiitoI, an electric telegraph made for the purpose was
■li, by which the transit observers communicated
it-iHts to a seated observer from their stations, the
' ^M of signals being noted by him to tenths of seconds
::!jrding to a marine chronometer placed before him
' tling half-seconds :^an assistant was also required to
i^ back the tubes to the up-stream station. In the
iijl mcth»d before stated, a party of five was sufficient
' all purposes. The observations were made at di.s-
-cea apart about 15 feet in the cross -section, as may
■ seen in the following gauge record for one set of ob-
* T^ations ; the mean velocities of the tubes for these mean
- 'taoccs were calculated and plotted on a diagram of

1 146 0,V FIELD OrSK.ino.VS AXD d^^^H

^^^^B Gaugf record of th( quanlily of vaUr falsing /jbJsU^

^^^H flume. May 1 7. i860, btlveeit 10-30

aWii-3oA.i|

^^^H ftet ; Unffk of immeried part ofhiit, S-4frft. 1

ProKxtt J

H if Ml 11 1 li

■ H J^ If k 1 r

<tlocUfud

3-073 'J

^^^H (yO I'toa -3 'S5

^^^J

^^^H t'S a-i5tj I'g 1-6 17a S'4Si

^^H 3' a-jiS 3-2 a-i 265 8450

^^^H l-S a-47J 4-4 4S 4-45 S'470

^^H t' 3-37J 6-z 5'4 580 S'445

^^^H T'S 3'59] 8'3 loj; 9-15 S'43B

^^^H 0- i«73 97 10-4 lo'o; 8-440

^^^^M IDS 3-Soo 10-5 S-8 9*6j 8-470

^^H 'it '^'J "*'l 'O'^ "'^ ^'483
^^H 0S 1-778 I3'8 155 M-^S 8'49<>
^^^H IS- 3-8<M 15-1 iS-o r6'6o 8-500

^^^K H a-j73 i;-o »>'4 iS?^ 8'498

^^^H ft >'59J 18-0 17-8 17-90 S'505

^^^H m S4j> i^'T 190 I9'}5 tiios
^^^^H 71- 9-a8o 31-1 30-g jioo 8-513

1 1

^^^H 214 •-»< ij-4 39-3 >6'35 S-533

^^^H n4 ■t)7i i6'5 197 >8-io 8-495

^ J

^^^H J7 i-i58 ar-o ij-> 9610 8-483
^^^m m fiiS 9S-A ^5 1755 S'495

_5 ■

^^^H » a-iu )■« J4-3 Ji-«5 8550

^^^^H .44 I'soo 31-1 jo-o 31 vj 8-630

^^^^H .^ 1-158 u-j tSi 30-30 8-610
^^^H M« f«tt M* 3^-7 i$t-S 8-635

^^^1 » l-U' J>-5 J5« J57S f-6j'
^^^H W4 »<«,«S jtT-S »-S 30-50 8«»

^^^B » tfit «a-i 40-j 4030 8-578
^^^H • «».> M'O S9^ 3930 S-STS
^^^H 1^'. *'^ ••« <(><« 40^ S-560

^^^H 4H« - ^ —

^^^H

^^H ^ ttH M>« ir« io«o s^

^^^m » »«» .H-) 33<C ]j«, s-6^

m

"■so*"

^^^H tt- ****• t^H 4"-* it-oi 8-«ra

«-4i7 «

i-afi*-

^^^^^^^^^ Ikug'sm

^

-■^

UVGf.VG WITH LOADED TUBES.

'.ir.Ti paper having the mean widths in fL-et of the
iT,e <calcd on one side, and the other calculated velo-
■ -^ tor those widths scaled on the other : a curve join-
; these points was then drawn on the diagram, from
tiidi the mean velocity for each foot in width of the
umewas scaled off and entered in the record ; from
"fW the mean velocity due to the total width was
tbtjincd. In this case it was 2-43 1 1 feet per second ;
Jiid since the mean section of waterway between the
upper and lower transit limbers was = 4l'7fi x 8'52!I4
- 35fi-lB8 square feet, the approximate discharge
i 2-431 1 X 35tM 88 = 865-929 cubic feet per second.

To obtain the true discharge from this approximate
'»u]t. an empirical factor, depending on the difference
■'' iKtwecn the depth of water in tJie flume, and the
'■■-■jfih to which the tube was immersed, divided by the
-fpih of water in the flume, was applied : the expressior)
■■'correction being 1-0-116 («(*-0-l). The value of
iiis expression for various values of A is given in the

le following at p. 148.
rln this case d, the quantity before mentioned.

_ 8-5294 -8-40OO.
8-5204

!00152 ;

■ bcnce the true discharge
=-965-929 X { 1-0116 (v00r52-l)}=86359.

xrki. — These observations were made in a flume
1 below a quarter bend ii^the canal, which caused
Klocit}' to be much greater on one side than the

To obviate lliis, an oblique obstruction was
i near the lower cm! of the bend, which removed

L I4S ox FIELD OPERATIONS AXD

■11

TMt0fa>mei«mforJ>iidurges ol>lt,i>ud fnm 71^ ^

1-0-116(1

^Sftrtmt

Vi,luapf^{.fr,

jm tKt LcweU Exptri^

o-™>

t:«m<:-

z«^-

c»»

■

"*"

"°"

''™

tiM

-OQO i»nto

■m

WS*'

-0*0

96S40

■OGO

-983«9

•OSO

•OBI 11MM3

■ISI

-W479

■041

9S811

■061

^SmS

«t

^^H

«B ixn&ti

■OK

■9W39

■042

9S783

■062

■98*7*

•on

^^^H

sm 1-W515

•m

■99*>i

043

98755

■0S3

98*48

^a

^^^B

■OM tt»*M.

■OM

■99363

■044

98727

■06*

■98MS

■m

^^

^)i6l«>J4o

■IBS

■993*6

■04S

98699

■0S5

■98203

m

OOfi ix>oa6i

■OK

■99*90

■046

9867*

■ree

•98.80

W i-ooiSg

■<07

•99154

■047

9S64S

■0£7

■98157

Ofl

DOe fooiu

'028

•99*19

-048

■98619

■068

■981J5

•aa

009 trx>a6o

■m

99185

-049

■9859*

•068

■98- 13

■OK

■m i-oa»o

-030

Wts«

■oso

■98566

-070

■98091

•030

Oil ■9994J

■m

■991 iS

■061

■98540

-071

■9S069

■091

■OH ■99*»9

-032

■990S5

ou

■98S«5

■on

■98047

•on

■00 W837

{B3

■99053

■063

•98489

■073

-98oa6

M

^^^1

■014 99787

-ou

99011

■as4

■98464

>Q74

■9S<Mt

-OJ

^^^H

■016 -99739

-03S

■9S990

■0&6

■98440

■07S

•9»83

■n

^^^V

-016 99693

■03S

■9S959

-o»

■984.5

-076

•9796*

•09

^^^^

-017 -99^48

■037

-9S9J9

-067

■9S391

■D77

•97941

■n

1^

■018 -9961.4

■038

■98899

■0S8

9S366

-078

■979W

■09

L

-019 ■99561

■039

■9S869

'0&9

9834=

■079

■97900

-OS

-loa

1

^

,,^,.o«.n.^o.o.onn.s.

•■»• ""' ^ rSS n,.king it so as to » „„, ^
,,rfri di*''"^'' , second •, its ""St* * „.„sit

<"' *"■ *" "^ S^ to attain tK. s.»^ J ^^^^,,

„dUpe"«<^"'7" i, timbers. l»'"8'/r;u,u=; I"

"•'^""" " ;S^Sion obse-^at^- '^ ^^ ^„„„
i«8e """ uSsoto 1°°''*''° f in to a certa.n
Ti'-^.^'fy^ "■"■'"'' '" Se.e "v,.h tbe poles,
ires«l»ril.e« "^V "^ ^ „„, to '»«*" ^„, si, inches
^' ""'"I it^mmersed. reach to ab«» ,^.

.hKh 'l"-:^; "TlSlts .ill »« "S'Sfgi ,r, .t -.ill <»
'"" "^ rrir=s«-«^'°" "">; '' Tnding the arc.

="*^i:ars^-----'^''"'

ON FIELD Ol'EI^ATlONS A.VD CAVGING. ciiaMT

6. Field Operations for Gauging the Missi*;
sippi River and Tributaries, by Captaiss
Humphreys and Abbot in 1858.

Soiinding-s.—Thc strength of the current, the depil'
and width of the river, and the floating driftwood, all
combined to render an accurate measurement of the
dimensions and area of cross-sections a difficult operation
on the Mississippi. After various experiments, the fol-
lowing system was adopted, by which accurate work wtt
(lone even in the highest stages of the rii
middle stages were usually selected for this purp
being preferable to the low stages, during which tbt
would have been exposure lo oppressive h(^at and disc
and more favourable than the high stages, when I
liifficulties attending accurate measurement were grcatC

Preparatory to making a cross-section of tlie I

whether for general purposes of comparison or for dct

mining a discharge, a base line, varying in length from
400 to I 000 feet, was measured along tlie bank near the
ivater's edge ; an observer with a theodolite was stationed
at each extremity of this line. The one directed the
telescope of his instrument across the river, so as to
command the line on which the soundings were to be
made ; the other prepared to follow the boat with hi-
tclescope, in order to measure its angular distance fron
the base line when each sounding was taken. The boat.
a light six-oared skiff, contained a man provided will
sounding chain, a recorder with a flag, and three 1
men. The strongest kind of welded J3ck>chain was i
])Ioyed, to which bits of buckskin were attaclicdl
inter\-als of 5 feet, smaller divisions being measured VI

iUSSJSS/PPI GAVaiM

[«i! in the boat The sinker, varying from lo to 20
ind«tnueigh( according to the force of the current,
m a leaden I»r whose bottom was hollowed out and
*nn«J wiih grease, in order to bring up specimens of the
bed of the river. The patent lead was also used for the
litter pur^wse. The boat was rowed some little distance
above the proposed section line, and allowed to drift
Aftii wiih the current, the sounding lead being lowered
DOriy to the bottom. By this precaution, the deflection
of the line by the force of the current was prevented.
When the first observer, stationed opposite the proposed
•Wion line, saw that the boat had nearly reached it, he
m«l a flag as a signal to take a sounding, and then
tarefaily turned his instrument so as to keep the vertical
-i*[ of his telescope upon the point where the chain
''•■vi the gunwale of the boat. The recorder in the
^ it, seeing the signal, waved his flag to the second
■-;inccr to follow the boat carefully with his telescope^
^iic man with the sounding chain allowed it to slip
li'idly through his hands until the lead struck the
• "om, when he grasped the chain at the water surface,
■■ii! instantly rose to a standing position. This motion
-1- the signal for arresting the movement of each tele-
'-']«:, and recording the angles. The recorder in the
-.1; noted the depth of the water, and the nature of the
Doiuxn soil adhering to the lead. By the angles
measured at the base line, the exact position of the
Mending, which was never mure than a few feet above
; below the proposed section line, was ascertained. The
cess was repeated until soundings enough had been
liken to give an accurate cross-section of the ri\er.
il lines of level were then run up each bank from
i-alcr surface to points above the le\-el of the highest

OX raU} OTKMATtOS

floods wben sadi points existed, or to other convenifl
Generally, the triangles were coinpntij|
sad 1^ woric plotted before leavii^ the place, ii
to Cn I9- additioiial sound iags any gaps whkb 1
appear oa the diagram.

At places where a series of daily vdocity obscrvatM
was to be made, addttkmal precautions «-cre taken, ai
two independent sections, 300 feet apart, were soundj
with the ^eatest care: Soundings, repeated frora I
to time opoo these lines, uniformly showed that no si
sible changes took place in the bed of the river,
mean of all such sections, when reduced to the i
stage tJi the Ti\-er, was accordingly always taken for i
tn»e cross-secdon at the localitj'. The change in a
produced by any change of \cv^ in water surface c
then be readily computed from the plotted section,
determine the daily changes of this level, a gauge-r
graduated to feet and tenths, was obser\'ed daily, it-
correctness of adjustment being frequently tested ti;.
comparison with secure bench-marks. An accurate
knowledge of the area of the cross-section on any given
jay was thus obtained. The tables of soundings for
tach cross-section, which u-erc all numbered, also dcnol
the distance of the sounding from the base line, 1
depth of high water during that year, and tlic nature
the bottom.

Velocity Measurements. — Narrow and straight ]
tions of the river, where the form of its cross-st
approximated most nearly to that of a canal, where i
waters of the highest floods were confined to the chann r
by natural banks or by Icv^s, and where the river at all
stages wa.s free from eddies, were selected for the ^
manent velocity stations.

! depth and violence of the rii-cr rendered the
iflimnent of its velocity, especially below the surface,
edingly difficult. Of all the methods known for
■mining this quantitj-, that by double floats was
d to give the best results. The method of conduct-
; these observations was as follows : — Two parallel
(.'-sections of the river having been made as already
kJ. zoo feet apart, a base line of the same length
II laid off upon the bank from one to the other, being
e at right angles to both. This length was sutR-
ent to ensure accuracy without being too great either
Ffcr objcrving many floats in a day, or for avoiding local
[ tftuges in velocity. An observer with a theodolite was
tttioncd at each extremity of the base line. It is evi-
dent that, when the telescopes were directed upon the
rii-cr, with their axes set at right angles to the base line
lf>e»iertical cross hairs marked out the lines of sounding
upon the water surface, and that the time of passage of
■1 float between these lines was that consumed in passing
MO feet Also, that if the angular distance of a float
from the base line when crossing each line of sounding
was measured, its distance in feet from the former could
readily be computed, and its path fixed. Upon these
[irinciplcs the observations were conducted. Two skiffs
were stationed on the river, one considerably above the
upper, and the other below the lower section line, the
rmer being provided with several keg floats, At a signal
!r.m the engineer at the upper station, whose telescope
wa-i set upon the upper section line, a float was placed
in the river. The keg immediately sank to the depth
allowed by its cord, and the whole float moved down
toward the lower line. The observer at the lower station
followed its motion, keeping the cross hair of his telescope

rik^

15* OX FIELD OrESATrOJfS AND GAUGING. .

dirvcted constantly upon the flag. At the word '
uttered by his companion, when the float crossed |
upper line, he recorded the angle shown by his infl
ment, and then, setting his telescope upon the lower 3
watched for the arrival of the float In the mcantj
the observer at the upper station, wbose theodolite )
ported a watch with a large seconds hand, recorded I
time of tfunsit of the float across the upper line, I
then followed the flag with his telescope. At the w
■ mark ' given by his assistant, when the flag cro&sedfl
lower line, he recorded the line and angular dista^
from the ba^e line. The float was picked up by*
lower boat By this method, the exact point of cro
each section line, and the time of transit, were i
tained. When the velocity was not too great, the !
was noted by the engineer at the lower station alsi
guard against error. A stop-watch was sometimes U
As it was evidently impossible to observe floats daiB
all parts of the cross-section, the best practical m«|
found was to adopt a uniform depth of s feet for alW
floats, distribute them equally across the entire riv
and afterwards divide the resulting velocities into gn>uj
or divisions within which the variation of velocity iv
but slight ; a mean relative velocity, and a mean relai -• ■■
discharge, for each division was then computed, the m.:
of the latter being an approximate mean discharge
the river, which, when divided by the area of the wtu
river section, gave a mean relative velocity for the whi.,i
river. The resulting discharge, when multiplied b
ratio of the velocity at the assumed depth I'in thb C
feet) lo the mean velocity for the whole vertical <
gave an accurate mean discharge of tlte river for |
place and day.

*. THS mSSISSIPPI GAUGING 15s

CaMputation ef Discharge. — A separate plot of cacli

ii/s velocity measurements was made in the following

—Lines were draw-n upon section paper to re-

cnt the section lines, the base line, and the water

The distances from the base line to the points

teach float crossed the section lines were then com-

d by a table of natural tangents, and the points laid

» on the plot Straight lines connecting the two

Hiding points indicated the paths of the floats,

c of course nearly perpendicular to the section

The time of transit in seconds and the depth of

kfloat were inscribed upon these plotted paths.

I The diagram resulting showed that the velocities in

tnt parts of the section increa.-ed gradually and

le uniformly with the distance from the banks until

pthrcad of the current was reached, and, since these

idties were found to vary but very slightly for dis-

s of 200 feet apart except in the immediate vicinity

Vtbe banks, the diagram of the daily velocity floats was

I by parallel lines 300 feet apart, the first being

E At base line, and the mean of all the velocities of floats

f'l) tach division taken as the mean relative velocity for

tbt division and recorded. For the shore divisions,

unless the floats happened to be well distributed through

tiicm, the mean relative velocity was assumed to be

rr^Lrht -tenths of that in the outer edge ; a rule deduced

om a subdivision and study of the velocity when

: ioroughly measured in these divisions.

For checking and making interpolations among
■■rective observations of any day in a division, the day's
t\ tffk was also plotted in a curve whose ordinales were the
cmn v-clocilics of the different divisions, and whose

k

■M

^iMietbr ifiqumr-Kif tfteh-nticftfrp«in^> t

tr mer d^nd. braoi^ (rf* ft oacnro! fc;rTD.tfie9
■ Mww tmML de ifivisuuB HOC' itnenual, jw^f j

Sdft&rtraee Each dtuinonal i

i tiRf as imiMU feiapTc ndocttr. and tfae 9
I relative or a

fa<f tne QiCil aRKOK tltB iwofa mctlun, the a
oeait veJuutjp of iftc t
pMtaBoa was BMote ay tugiinlniiift, smi 9
i^ofsbUecanenctrii far tfae pBrpose.

C BBC lll> hll U V WBBCB WeiC 0086 (

s fisc fea bcJDv t&c 3ai£uce. it was mn iwjf I
e of tke laeio,'

r.

i-.-^

.fjm-o^Kior-^

^].R

and tatitifif them b)r it, Ahs getting Ilic tnie d
whidi, when dinded bp tfanr corre^iondin^ amu d
croM-sectioD, gate the final and correct mean '
The nnaterical values of the above expression a
were obtained in the following way, and put into ti
form ftf the table given.

The days on which obsen-ations were made i
grouped according to even feet of the computed i
proximate mean velocities, it being assumed that tlM
effect upon the desired ratio, produced by changes i
mean velocity of less than one foot, might be ncglecte
Kach group was then examined in connection with t

' S*> Miiiiitlppi vdocily notwioD, pane u, Cha|>Icr L

I

TUB. JUISSJSSiPFl CAfGlNG.

Atccord, and days were rejected until only calm days

Anse on v.'hich tlte wind blew directly across stream,

those on which when combined the wind effects

itioced each other, were left The resulting mean day

incu^ group was then equivalent to a calm day, so far

T'd effect was concerned. The following mean

-iiies were then deduced for each mean day by

■i:iij the sura of the quantities by the number of

going to make up the mean day, viz., an approxi-

- mean velocity of the river (w), a gauge reading,

. >\emce a mean radius (r), and a mean velocity five feet

■« the surface (t'), found by taking a mean of the

. 'ilaied velocities of all the different divisions.

e values being substituted in the equation,

(A-

gal3o<^s5, making d,=OZnr, and 6=

1-69

(D+l-5)'-

S when D 730 ; the value of 17^, was computed
ined.>
^xt this value of (/,, was introduced into the same
n again to obtain new values of U, first for a
§fl=0, secondly for a valueofrfsr, thus getting the
! and bottom velocities denoted by U" and U,.
itituting for Uiesc their values in the following equa-
tion, together with those computed for Ud,, d,, and r, the
le of U^ was obtained

^1

■

1

■

■

1

■

1

^^1

158 ON FIELD OFEftATlOXS AXD OtCCISC. M

Mimmffi g

ApproH-

VTcd

WW

Wkd

LCKAL>TV

^iilTirf

*

*T"

4-.

Culuitibu.

I-6816

■90759

■9MJ*

■«»«

34440

■92300

-v^

■W«74

3 '654^

■937»9

;ss ;

4'S097

■9*400

■95407

4-34=6

■wgos

'9S8>»

■96&)9

(.■6^96

■95406

■06361

■WIJI

7-4i82

■957St

■96iS«

■973*5

8'jl63

■95983 ■96747

•97S»3

Vicktbuig

3;6oj8

■93881 ■was*

•95846

■94544 ■95458

■96433

S5571

■95161 -96017

■96S9S

67363

■95631

■9&440

T>7>64

7-OSJ9

N«lsh« . .

4-6901

■945M

■95SOI

■96«M

Atipnai-

WUKI

U'l.llIT

^^.l^'I^^T

C»li»

7

¥

Y

Fm

iHlHOlUlt

r6Si6

■97040

•98750

1 ■00511

I -01357

'■^s

■97737

■99192

I -007 J I

I-OU9*

■995"

fw.;67

10M48

.r5"i7

■<*S46

■99^.

t■ot>^l<o

101903

4\H"6

■98713

■99717

1-00689

•■01793

(.■64'>6

■99837

rt«773

i«.7i;

■99035

■99891

1-00762

1 ■01648

■W"»

■99917

I ■00756

.■O.S98

VleUlmtH

J*>.iS

^TSiS

■9S056

I ■00037

i-oina

44"0

ySjio

■99300

100307

'■«'337

S5"'

■llSfiqj

99613

1-00557

ifliStS

hsfi

■v»w»

•99833

l«07oO

1^1604

yxjjag

■W006

NMi'liM

«4(»i

■v&i»

■W4331

1130*66

lt>ljM

i

A calm m wlad

•1 licfat UcUs to Ox cumcDl ^ U ; a hiuncaa^

CKEyASSE-DISCiJA/HiE. 159

■-he resulting value of JT^, also the values already
-jci lor V and r and b, and giving/ its value suc-
i-ly for each of the various forces and direction of
ind, in the following equation : —

(0317 + 0-06/1(l(>r-r')-25

'] (i-)*

(tabic of ratios for the stations was computed.

■The approximate discharge for each day at each

ion was multiplied by the ratio in the table most

irly corresponding to its approximate mean velocity

ain the true discharge, from which tiie true mean

f was then obtained.

Field Operations in Gauging Crevasses ev
Captains Humphreys and Abbot.

The phenomena observed in the discharge of water,
through crevasses, or breaks in levies at seasons of high
•nxu. were —

I. That the effect of every crevasse, even though as
.ri:c aa J27 feet wide and 15 feet deep, along the line
: \cvie, extends only for a short distance from the bank ;
m the above instance, il did not afiect the line of motion
of floating bodies passing 200 feet from the natural bank,
•X 300 feet from the break in the levfe

3. Between the crevasse and the outer limit of its in-
fluence there is always a movement of the water towards
the break from all points below and above, which in-
creases towards the break, and rapidly diminishes on

i«o OH FIELD OfSMATTOMS AMO CdCOlK. c

reaching the ground in rear of dclrvtt, wbciv it s^
in every direction, bat inga% towards the awamps.

3. There is a sensible slope alaag the coune of
movement.

4. I n passing the break, whetber by a cascade 0
the water is higher in the middle of the opening [fa
eiliicr side

The following was the ordinaiy method of ci

a discharge. Knowing, from measurements made a

the cessation of the flow, the high-water depth of I

given crevasse, which was estimated on the line oflrt

If no material exaavation was made there, and on i

batcure in front of the lev&, if boles vceK dugufl I

line of the break ; the depth on the given day was f&u

by subtracting from tliis high-water depth tlie slind

the ri*-cr below high-water mark — a quantity which »

ntw*)"* known either from local information or from

Conipari.-iun of the nearest river gauges. Taking 0

I mfprescni this depth, and w the maximum width of I

■ ttviassc aAer cessation of flow ; and knowing fromcX

I Infttniution the date of breaking of the lev^, and tb»

p •.vssation of flow, the width of crevasse of anydesjl

<\>w)i.t be computed ; and the required dischai^

^\-Mi.) **s then assumed to be equal to the contim

l^y(Wlt »*f this widUi w, the depth D, and tlie v«Io<

r ^w x/)xt-; the velocity when V was 1

1^. ... . . , --Vrn-S-SI8vi)(CastersweirformuI

' ..renter than 3 feet, V was takei

)> - '1I formulx for discharge correspoi

CREyjSSe-DJSCHAXCB.

17

anambers of days of discharge which have pre-
3 the given day, and JVstotal number of days of

mt of correctwn for special cases of crevasses.

c are cases in which the conditions of the flow

Ucr vere considerably modilied ; such as when the

fewas so far distant from the river that the depth at

e of the natural bank was much less than that at

e of the lev^e ; or when treesT a growth of sap-

r other obstacles existed in front or in rear of the

1 of these causing a diminution of dischai^e.

a the reported depth of crevasse included that of

iisly existing excavations on the line of lev^, in

it cases the resulting calculated discharge would be

mgh, and it then became necessary to apply in each

a special coefficient of correction. The coefficient

"'or cre\-asses flowing into the Yazoo bottom was thus

-crmined- The areas of these bottom lands and their

' ilcrsheds were as follows, in square miles : —

Vuttj botiom 7Ho~

Ytioo nlcnhol 6740

U. Fnocu' botiom 6900

Si. Fnndt' witerabcd 3600

TeniKisec and Kenlucky botloin . . , 750
TmncBcc and KcDiacky witcnhcd. . ■ 95oo_

The yearly rainfall in feet was —

tAt Nnr Hinnony, Indiana .... j-ga
Al Wd Skktn, niinois 4-01
JU Si. LouB, Minouri 5-18

Man dbwnEiII It bcsil of region ..... 4'3S
Al Uciephu, downfall for miijdlc of ti-£ion . . 4'4S

Al Jackun, downfall [01 Fool of regiuD .... 4'99

I«> ON FIELD OTBRATiONS ASD GAUGING, i

Im
Mod foi «hol< rtgioo 4'W

Giving total yearly downfall,

•- 3* 600 >c 4-6 x (oSSO)'- i 437 136 141 000 cubic fccL

To obtain the total yearly drainage, the dischargi! -.'
Columbus, together with that of the Arkansas and VVh;t!
Rivers, was deducted from the discharge at Vicksburi,
and from this also a deduction was made an accountof l^■-
river during the year between Columbus and Vicksbut^
being lower by a mean difference of 63 feet througlioiii ^
mean widtli of 3 300 feet for 589 miles in length; th"
getting the drainage

4 372 572 737 200
Channel drainage 69 786 6Q4 800

Total yearly drainage 4 302 7Sfi 152 400 cubic ft

And ratio of drainage to downfall is hence
4 302 786 152 400

4 437 126 144 OUO

=0-96 nearly.

Next, the total rainfall for the Yazoo basin, area 1 3 S ; -
square miles, for from December i, 1857,10 July i"
1358 = 3-64 feet X 13 850 X (5 280)' = ! 405 461 657 (l"
cubic feet; the mean rainfall 3-64 during tljat tim
being determined from the mean of the registnttv
falls at Memphis, and at Jackson, 319 and 408 f
applying to this rainfall the coefficient of draid
before determined, the drainage from the Yazoo b
1 349 243 191 300 cubic feet

The area of the Yazoo bottom was dry on I
I. 1S57, but at high water July 15, 1858, it had « n
depth of water of 3 ■08 feet over an area of 6 Soo •
miles; having received between those dates *"

» ABBOT'S XSETllOm

8-08=583 885 209 600 cubic feet, and the dis-

f the channel of the Yazoo, the sole outlet, was

during this time = 1 408 6G5 6(M) OOU cubic

mce. 1 9»2 550 809 600 cubic feet represented

quantity which, entering the Yazoo basin

those dates, eventually drained off into the

sippi ; and the total amount of overflow from

sippi basin into the Yazoo basin was

2 550 809 600-1 349 243 191 300=643 307 C18 300

C feet ; this quantity as computed by the uncorrected

e formula was —

I 7S8 IS3 600CXX) ;

hcncctherequiredcoefficient of correction for the formula
equals the former divided by the iatter= nearly J. This,
tbereforc, holds good for the crevasses in the district for
h it is obtained, and the same principle may be ap-
il Co other districts.

aj OF Gauging by Mid-depth Veloci-
ties, Proposed by Humphreys and Abbot.

The details of field operation to be adopted differ
*reonling to the size of the river, ist. If the river be
null and considerable exactness be required, the boat
dould be anchored at various equidistant stations, the
tanks being considered two of them, and the station
itiul mid-depth velocities measured by any of the
■ own methods ; the number of stations being sufficient
' ' prevent the velocity of the water between any two of
Tn from varying materially. 2nd. In the case of a
i:^c river, if the depth is uniform, sufficient accuracy

O.V FIELD OFERATlOttS ASD CAVCING. cmat.

m»y be obtained by obsemng the times of transit of J
hrgc number of double floats well distributed across lb
rivTi section, the kegs being uniformly sunk beneath (h
surface to a depth equal to half the hydraulic
ndius of the river. Should it happen that the
tion is not sufftcicntly uniform and symmetrical to add
of this, the site or reach is ill chosen for the
TV results should then be plotted and grouped illl
s of equal width, and the mean result for (3^
I calculated, including, of course, intcfpolatd
s should any be missing.
The dqtth of water in the river should be noted on i
ponnsaent gauge-post during the observations, or befoe
9mA aAsr. % this method the results obtained will be
te iIk icst cue absolutely, and in the second case oearifi
mdeoMd by the vrind, no matter what its direction tf

TteacAod of computing the dischai^ ftom tlH'
^JlBanMiais vJU vaty according to the accuracy i^

**^

AMfmAif — A dose approximate result tnay^
% telane « mean of all the different station
■it-depKlt \«lodties, and applying a cocfRdefl
■t*S$ tit tMCcandotij for ordinary ri%-crs, to obtain
HK 'w>eciq «tf t)tt river- In this method there a
«f tn«r-«fucb \'eT>* nearly balance each othi
of the different di^isiot
between the mid-depth and me
* Mqrwtviicsl plane, and the above cocfficieD
F«r A Rctangular cross-section,

- W" crcfttcr ptecisioa be required
* vehicAy of discbat^ of the riv

r.ay be computed by substituting the grand mean
•he station mid-depth or division velocities for U^.
'.c- foUowing formula,

-. s'onnula U deduced by substituting for [7„ its value
j; in the general expression,

vA reducing the resulting equation.

As has been already stated, when the mean radius
wcttds 12 feet, 6 = 01856, and underany circumstances
■' 3 . The formula therefore g^ves at once v

'-^ mean velocity of the river ; and this simple method
:: quite exact in ordinary river sections, though not ap-
j I :ib!c to rectangular sections.

Third method. — Should, however, a very high degree
■ accuracy be required for testing formulas, or constant
•^fScients, an amount of exactitude affected only by in-
-'iniental errors of observation may be secured by sub-
tuting the different observed division mid-depth
udtics successively for F,o in the formula

I

w

tfie results will be true values of the mean velocities
of the different divisions in terms of ?'* and known quan-
tities. The sum of the products of these expressions, by

corresponding division areas, should be placed equal
product of V by the total area of the cross-section ;

166 OX FIELD OPERATIONS AND GAUGING. CBAP. 0-

and this equation, involving v and v^ and known quanti-
ties, will give two positive values oft' ; the less of which,
corresponding to the actual case when the velocity is
greater at the axis, is the value of the true mean velocity
of the river. This method, though accurate in principle^
is probably not so good for ordinary purposes as the
previous more simple one, which neglects the latter at-
tempt at extreme accuracy and involves less observation »
and consequently less instrumental error, as well as les3
labour.

General Abbots Metliod of determining on any gmr^
day t/ie disc/targe of a large river that has hee^
previously surveyed and gauged.

The previous field operations consist of a survey ancJ
numerous soundings of a straight and regular portion o^
the channel between two bench-marks, A and B, fixed
permanently near the water, whose relative levels are
accurately known. An accurate plan of the river betweea
these points is necessary, the mean cross-section derived
from the soundings, and a series of careful gaugings of
the river on permanent gauge-posts. It is desirable that
the course of the river between A and B should be as
straight and regular as possible, in order to eliminate to
the utmost the effect of bends, although allowances
almost invariably must be made on that account The
points A and B should be well chosen, as far apart as
practicable, and distant from any eddy, and be placed
where the current on the bank flows with equal velocities.
The latter condition is necessary, because water in
motion exerts less pressure than when at rest, and if it
moves rapidly past one bench-mark, and is nearly

ABBOTS METHOD.

i^r'

at the other, a difference of level independent
t motive power of the stream would vitiate the
nations.
On the required day the vi^ater surface at each end
reach, A and B, has to be simultaneously referred
sirate levels to the bench-marks, to obtain the
ncc of level of water surface and the gauge depths
more is required. A calm day should be

be farmuU to be used
I on velocities :

that given in the para-
[^(W)08l6 + (225r, ,/«)' -009;.*]*

tettns of which have been already explained, except-
; in this case h is the sine of the slope of the water
» corrected for bends, and is obtained numerically
ubtracting the value of A", due to effect of bends
! Paragraph on Bends) from the total fall between
level stations, and dividing the difference by the
I distance between them, measured on the middle
of the channel

the method of successive approximation must be
ted to find the value of v in this formula. The fol-
gfbnnulie give the value of each variable in the
; equation in terms of the others and known
Taking ^=0-9.1v + 0'lfl7 I'iw, and assuming
,^)I5 ir, should it not have been measuied, — then

U95r,J

^(p + F)_A*.

p + fT-

!•+»■ =

168 Oy FIELD OPEXATTOKS AND GAOCiNC Giur.li.

F.^r small J/''^-?":.-.— Ger.er^ Abbot modifies the
above formula into the followiiig, where t< is the value oi
the first term in the expressioQ for r —

I J 1-

+1>

2-4

or putting If =000816 and Jr=r-

r^ I \/lf+ 225 r,v^«- ^ Jf j *— If v't^

in which the term involving JT may be n^ected, 1
streams larger than 50 or 100 feet in cross-section ; a
for large rivers exceeding 12 or 20 feet in mean radios,
but not 's/M may be n^lected. The following taU^*
facilitate the application of the formula.

r

M

_ 1
'" i

9

JT

Lov.ir

' 1

0-0037

010930

6

0-400

9*602060

2

0-0073

0-0855

6

0343

9-535294 /

3

0*0065
0-0058

0-0803

7

0*300

9477""

4

ox>764

8

0*267

9-42651 1

5

0-0054

ox)733

9

0*240

9-38021 1

6

0-0050

orfjoy

K)

0*218

9338456

7

0*0047

0*0685

12

0*185

9-267172

8

0-0044

0*0666

14

0*160

9-204120

9

. OtX>42

0*0649

16

0-I4I

9-149^19

10

oxx>40

0-0634

18

0*126

9-100371

12

0-0037

0*0610

20

0*114

9^56905

14

otx>35

0*0590

22

0-104

9-017033

16

otx>33

ox)573

24

0*096

8-982271

18

0-0031

0-0558

26

0-089

8-949390

20

OXX>29

0-0544

28

ot)85
0*078

8*919078

30

0-0024

0-0494

30

8-89209?
8-672098
8-380211

60

0*0019

0-0437

60

01047

100

0-0013

ox)369

100

OX)24

ON SRENCH RICOLES.

TUE EXPERIMEXTS OF D'ArCV AND BaZIN ON
THB RiGOLES DE CHAZILLY AND GrOSBOIS IN
1865.

These experiments, in small channels under various

nditions, were made with the principal object of ob-

t^ing coefficients of reduction due to various surfaces

1 and banks ; their details cannot fail to be inter-

Xng to those intending to gauge channels of any

^^Sscription.

The canal of supply was Bief No, 57, of the Canal
"^ Bourgogne, from which the water was taken into a
'^Cciving chamber through four iron sluices, 1" wide, and
**ing capable of being raised o-40™, having their sills
tt 0^6o" below ordinary water level of the canal. This
^^vtamber was s^o" wide by 1400™ long, having its
^Bottom O'So" below the entrance sills ; the gauge-sluices
^Bftening from it into the channel of experiment were of
' brass, twelve in number, each having a section of passage
when opened of 020 x O^O", and having their sills
0"4O" above the bottom of the chamber, and o^o" below
the sills of the entrancesluices before mentioned. These
orifices resemble those of the type employed by Poncelet
and Lesbros, and would, according to them, require a
coefficient of reduction of discharge of 0604, provided
that the effect of the velocity of approach be neglected ;
in thi" case, however, it augmented the discharge, and an
allou-ance had to be made on that account The water
in the chamber was constantly kept at a level of O'So'"
abm-c the centre of the gauge-sluices; an appliance for
sbcming the slightest variation of its level being continu-
ally watched by a sluice-keeper.

170

ON FIELD OPERATIONS AND GAUGING. CUF. i

4

The channel of experiment was 450™ long beforc \
commenced to bend towards the river Ouche ; it wa?
water-tight, and was lined with plank-s of poplar : its fall
for the first zoo" was 0*0049 P^'' rni^tre, and for the next
250° was 0002 per metre up to the bend, after which \v-
fall to the river for the remaining 146" was 00084 \'>
metre. The dificrent provisional constructions for
ploying various inclinations, and sections of difft
forms, were cnade in plank within this channel, the
being filled with rammed stiff earth. Nails were di
into the bottom of the channel at various points to sen
as bench-marks, from which every variation in depth
water could be obtained with exactitude. Most of i
experiments were made by successively opening i
twelve gauge-sluices, having one fixed section s:
amount of supply in each case, and thus twelve resu
were obtained for comparison in every experiment ce
ducted.

The velocities were principally observed with d'Arcy
current-meter, but in some cases also with floats,
latter were sometimes simple wafers, and some!
pieces of wood or cork weighted with lead, 2| ti
in diameter, and i inch thick ; their times of t^an^j
over distances of from 40 to 50 metres were noted
chronometers indicating fifihs of seconds, and the mean
of five or more observations, in which the float folli
the course of the axis of tlie clianncl was adopt*
finally correct

The following was Ou modi of determining the n
jncftt of discharge at the off-takt.
The coefficient of discharge at the foitr cntt
sluices was determined by closing Uiv lower slttkcs I

. rtrcv5

'■■:m

!^.9 O.V FXENCff Jf/GOLES.

■ 'ting the time in which the former filled the chamber
1 1 * certain height ; in this way the following coefficients
were obtained for a head on the sill of from O'SS" to
070', whco one single sluice was opened at a time.

Salt* OUMd. Corffidenl.

OUh 0-645

020" o-639

0'3O- 0'63i

OW- 0-621

Wiicn the four sluices were opened at once to the full
height 0*40"", the coefficient was 0*637, instead of 0*62 1,

U was hence evident that, in order to obtain a suffi-
:'-!itly constant discharge, the use of the second set of
'■ H'lve .ilutces became absolutely necessary. The condi-
tions of construction of the latter did not, however, render
the contraction complete, and hence the coefficients of
foncclct and Lesbros were not applicable to them. In
"Jur to have effected this, a chamber large enough to
' '^ireiy annihilate all velocity would have been necessarj-,
'■"■ sluices should have been farther apart, and their sills
should have been at least O'Go*" above the bottom of the
cliambcr. It was hence necessary also to determine the
cixfTicicnts of disdiatge for these sluices by direct obser-

..Uirla

In June 1857, experiments were made with this ob-
' 1 , a portion of the channel was closed up, and filled

"lining one, two, three. &c., up to twelve sluices at a
■ic, 4nd the volumes thus discharged in a certain time
' fully measured. The discharges per second were in
■c cases from oro3 to 1-242 cm. ; and when each
■n-c (vaa opened separately the discharges varied

'•vmoiozz and 0'i037 cm., giving coefficients vary-
^ from 0645 to 0-658, The irregularity of the latter
■ CQosidercd due to the irregularity of form of the

172 ON FIELD OPERATIONS AND GAUGING.

bottom of the portion of channel filled not allowit
exact volume to be calculated : hence a mean coe
of 0'6^o was adopted provisionally for any numl
sluices open at one time. In i860, it was dctermil
obtain this coefficient with greater exactitude!
further experiments were made : all the practical 1
were carefully reinvestigated : the influence of the
tions in depth of the bief or canal of supply was e
ally found to exercise no effect on the irrcgularitie
gauge used was supplanted by a glass tube hai
mouthpiece of r millimetre in diameter, by mo
which variations in depth of water as small as I
m^tre could be easily read. The results under
conditions were thus : —

For a dischaige from I sluice, Ibe coeflicieiil wu o-^JJ

6 „ and upwudi to 12 o-by»
For a sluice raised only O'lO"" instead of b«i
opened, the coefficient was found to depend
number of other sluices open, thus : —

Vli'hcB 1 Qiher b opeaed full, the coelGcieoc for ihe pvlly

opened one ii . . . . 0*630

2 o<S7

3 o-eto

S and upwiids 0-663

The dettrtninalion 0/ the coefficttnl for reduction J{

current'tube.

This was effected by three methods —

1st — By comparing the velocities obtained byi

of the tube with the surface velocities shown by

' SKENCJi X/GOLES.

The data according to the floats were obtained in
clunnels two metres wide, having a discharge furnished
:■■' ii\-e sluices open at a time : the results gave a coefS-
'^;tfi! vai^'ing from 0-98 1 to ro39 as extremes, and roo6
■ -the mean of all

ind. — By moving the instrument at a known velocity
:i i mass of still water. The floats and the current-tube
rt'jic drawn by men for a distance of 450 metres, each
• : metres furnishing a set of observations ; the obliqui-
■'.• of the course of traction furnished the principal
li'tacle to arriving at a very exact result The velocities
"^ployed varied from 0609 to 2-034 metres, giving
efficients of reduction var^-ing from 1015 to 1053 as
xiremes, the general mean of all being 1034 : this was
'^WMidered far too high, and the results of this set of ob-
^W'ations were therefore entirely discarded.

3rd, — By measuring by means of the current-tube the
■-Incilics at a great number of points in the transverse
-lion of the channel, and comparing the discharge cal-
culated from these velocities with tliat determined by the
ftperiments previously described ; the points referred to
"'^fe distributed rectangularly in vertical and horizontal
''"« ; the discharge of each rectangle was calculated, and
"^ sum of these discharges was employed to obtain an
approximate discharge of the canal These comparisons
Eavc results varying from 0968 to I -039 as extremes, the
Emend mean of all being 0'993.

The mean of the means obtained by the first and
.'fiird metJiods gave a coefficient of nearly unity, which
"^ therefore adopted for the instrument under trial.

Having thus securely determined the amount of dis-
chirgc passing down the canal of experiment at any
liine, the levels of the water surface and its inclination

&.V riELD OF£SAnOKS AND GAUGING. OUi-i

also at any time with exactitude,
ifca at any point being also known, and
of reductJOR for the current-tube being
anned so exactly that any velocity obsen'cd by
of it was absohttdy correct, tbc experiments for oboio-
ag coefficients of discharge under diiTerent conditiom,
and (or otMsnii^ the ratio of the maximum vclocil)-
to that of the mean velocity of
were undertaken.

' disch^^fl
; coefficieniT

ThtfevK^ed rtmlts of that expm\
The first was titc determination of the coefficient
ia the fonauta A =~^ where R is the mean hydraulic

raffias, S the inclination of the water surface, or sine ^
ks slope in one m^tre, and V is the mean \>elocilyof dii-
Chugr.

The coefficient was considered to varj- in four al^
cones of channel

1st — When the bed and banks of the channel «<
■ade of wi^plancd plank, or of cement :

=(M)00I5

(,.-)

he data no which this was based are those of series Sl^
t cf Batia's experiments, those of the Aqueduc des (dfr
IHX5 dc Dijon of d'Arcy, and those of Ilaumgartcn on
tke Canal Rotjuefavour.

jai— For bed and sides of ordinary plank, brid:

i!.=(HKK)19 (l +^)
whkh this was based were, for plank tweh

O.V FKENCll R/COLES. 175

fs of experiments of Bazin, and twenty-nine of
hMt ; for brickwork, the series of experiments No. 3
iirin ; for ashlar, those of the Rigole Mar^e de Tillot,
Aqueduct of Cran, and the series No. 3 of experi-
.-hj of Bazin,

■ jnt, — For channels of rubble :

■ c, = 0-0OO24(l+2|»)

mimi based on Baiin's experiments on the Rigoles de
tiroibffis, and the Marseilles Canal.
14th.— For earthen channels :

■ . =0-0OO28 (1 + if)

iBebcpcriincnts on which tliis was based were those of
d'Aicy and Bazin on the Rigolcs of Chazilly and Gros-
Ws, on the Marseilles Canal, the Canal du Jard, those
ofDubuat on the Hayne, of Funk on the Weser, and
those of various en^neers of the French Fonts et Chaus-
,*it» on the Seine and SaOne,

f second result was the following formula for
= l+Wv'c^or y — 7=\i'/R8;

win the form most useful in the cases in which maxi-
mum velocities are observed as data for gauging,

F= F,_ 14 yflS.

I tallies of c, fromooooiS to 0-003 the correspond-

» of 77- become thus : —

^ s= the mean velocity of discharge.

= the maximum velocity observed in the section.

176 ON FIELD OPERATIONS AND GAUGING, CHAP.B.

;

X

0-00015 0-854

0-0005 0-762

0-001 0-693

0-002 0-615

0-003 0-566

The above expression, involving terms not included
in that of De Prony for the ratio of maximum to mean
velocity of discharge, does not admit of comparison wiA
it ; but is evidently calculated to supersede it entirely.

The reduction of both of these results to English
measures is given in Chapter I.

I a The Gauging of Great Rivers in South

America, by J. J. R£vy.

The account of the most recent operations in gaugiflS
very large rivers conducted by J. J. R^vy, given io
R^vy's * Hydraulics of Great Rivers * (London, 1874), in-
cludes a description of the method he adopted in cur-
rent observations on the Paran4, La Plata, Parani dc
las Palmas, and the Uruguay, from which the following
brief risunii of operations is taken.

It seems to have been a work of some time and diffi-
culty to find a reach of the Parani sufficiently strai^t
for conducting gauging operations and velocity measure-
ments ; a hundred miles of the river were searched un-
successfully, but at last a reach straight for many miles
was found. Here the river was about a mile in breadth^
and the soundings showed from 5 to 71 feet of water ; a
gauge fixed in the stream did not show a variation of

ON LAKCE TlDAl RIVERS. ijj

Bie water surface of as much as a quarter of an
.'twcotj'-four hours ; and the inclination of the
Brfacc in one mile was very nearly nothing.
! observeil by levelling for one mile with a 14-

I, on equidistant staves placed 300 feet apart,
ttian O'ot of a foot ; it was therefore practically
le under the existing state of the river bank,

s not adapted for levelling, and with the instru-

band, to carry out levelling operations with any
; as it would have involved ten miles of

an passable ground, and probably required also

Tsuperior instruments.

I found that for the surveying and trlangulation

bcr calm weather or clear weather with a gentle

i absolutely necessary ; — for current obser\'a-

in days only allowed of operations being carried

line of 3 OCX) feet was measured on the low-
bank of the river, with a steel tape of 300 feet ;
were set out at right angles at each end of it,
direction of a river-section-line for soundings ;
points in the neighbourhood and on the
ik were triangulated and tied into this base line.
'Jings. — Those on the lines of section were taken
lead and cord ; the length of cord was measured
Ipc at each sounding, each of these measure-
ling one minute ; the position of each sounding
by angular observation, with a 3-inch pocket-
iving readings to one minute, on the two flags
:h end of the base line. The angles were ob-
(rom three to ten seconds each. The number
ings taken tn the section varied with the ncces-
^em : it was necessary to show, and hence also

178 ON FIELD OPERATIONS AND GAUGING. CBtf.n.

to find the points in the river bed where there was a
change of lateral slope, however many they might be,
but in places where this slope was regular and gradual
the soundings were not considered necessary at closer
distances than from one-twentieth to one-tenth of the
breadth of the river. The section of the Parana, where
its breadth was more than 4 800 feet, was sounded in
two hours and sixteen minutes, after all the preliminary
arrangements, drilling of the men, &c, had been properly
carried out. In plotting the section, the position of each
sounding was fixed both by means of the complements
of the angles observed at those points, and the calculated
distances from the base.

Velocity vteasurements, — These were made with the
screw current-meters previously described. As the velo-
cities had sometimes to be observed at great depths, the
ordinary method of lowering the meter to its position by
sliding it on an iron standard was utterly impracticable,
and the following mode was adopted. The current meter
was attached to one end of a horizontal iron bar, 9 feet
long, 2 inches wide, and half an inch thick, which was
suspended by chains passing through rings attached to
it from a boat moored over the required spot ; in order
also to prevent the current from moving the bar from its
proper position, cords from the rings of the bar were also
attached to other two boats, one moored lOO yards up
stream, the other 100 yards down stream. By these
means the current-meter could be used with good effect
in water up to 100 feet in depth, and in currents up to 5
■P(iile.s an , hour. Four sailors were necessary in taking
current observations in this way. The observations of
velocity were generally taken by an immersion of the
current-meter for about five minutes, the time observed

Oy LARGE TIDAL klVERS I79

i being generally a few seconds more or less,
rerc allowed for in the resulting calculated velocity
Enute : a second checking obser\'ation was also
>• made by an immersion of one minute. The
was put in or thrown out of gear by means
c leading from it up to the boat, thus allowing
Bf pccTcnting the revolutions of the screw from recording

Kives on the dial faces at any moment
'l"^ gaugings carried out, observations of mean
ic velocity, giving the mean velocity in any plane
c surface of the water to the bottom, seem to
fci« been preferred wherever practicable. For these
ejscj, in which it was necessary that the current-meter
d be steadily and evenly lowered to near the bottom
j a^in to the surface, it was found advisable
■ to work it from a platform between two boats,
\ 12 feet apart, moored by four anchors, and to
c two suspending cords marked at every 3 feet
■nately red and white marks, as guides to those
; and raising them ; the cord attached to the
»in boat was not, however, considered necessary
■Dperation, the up-stream cord preventing the in-
yeX from going farout of the vertical direction. In
rations the instrument was put in gear by hand
tening a nut on immersion, and put out of gear
. corresponding manner on withdrawal from
In taking surface velocity observations, the
Lmeter was screwed on to a wooden staff, 3 inches
\ half an inch thick ; the revolutions of the screw
Ing after withdrawal from the water being at once
a by hand so as not to vitiate tlie record on the

9 dtttrmitialioH 0/ ifu equation of correction for each

i8o Off f/ELD OPERATIONS AND GAVGIUC. ClUfc

current-meter was conducted in the foUowiogway.
was tested at a low velocity by drawing it through a <
tance of 1 89' 6 " in the still water of a resenoir in a d
of 2' 30" giving a velocity of 759 feet per minute;
average of these trials gave a recorded number of r
lutions of 172, or 688 per minute : in the same way!
it was tested at a high velocity, and showed i/frlj
volutions per minute for a speed of 18364 feet
minute. The equation of correction being that fl
straight line, two points alone are necessary to detent
it : on referring these to rectangular co-ordinates a
diagram, and joining them, the true velocity correspo
ing to any number of revolutions of the instrument cc
be scaled off from the rectangular co-ordinates to the
suiting straight line. Or taking it algebraically, if z 1
;'/, I, and ;/,. be the corresponding pairs of co-ordini
for low and for high velocity,

then y=cia! + 6, and yi=cw:,-l-i;

and 6 =2(^1+^— ac,+a;)=— 6'811 ;

hence y=0-9962 i— 6-811,
or in the form more useful forobtaining the true veloc
31, from the number of revolutions, y,

pj = l-0038lsf + 6-837.
On applying to this equation a value ory=0, we oW
as a result that this particular instrument would ocas
record revolutions for a velocity of less than tr\^
per minute.

llouHy Ohicrviitmis.— \x\ consequence of the rt

i8i

■ 'td being tidal, and having a variable current, it
Ticccssary to moor a permanent observatory at a
'anient point in the deep part of the river on the line
. tion, and make hourly observations of the current
1 :t throughout the day and night The tidal rise
Tail was also registered at every quarter of an hour ;
■metric, thcrmomctric, and wind observations were
iivi nrcorded.

The current observations, both surface, mean, and
<iib-*urface. were taken with R^vy's current-meter from
"i.il! boat moored temporarily fore and aft on the line
-i-iion already sounded, its position in each case being
i.imincd by angular measurement with a pocket sex-
lir.ton the extremities of the base line, which fixed it
*ithin a few inches. For this work two sailors, two
jjUcliors. and several hundred yards of line were neces-
^B The current observations were taken at the surface,
^■depths of 4, T, ID. i6,and 23 feet, the latter being
^^Bot above the bottom. The mean current observa-
|SS were made three times in each case, and were
found to check each other within 16 foot per minute in
'^Wr^iticins giving 80 feet per minute. The time of day
iif the current observations was always noted, and check
^tism'ations were also taken from a fixed level, so that
tlw observed tidal variation might be applied, and the
^^of the tidal wave — a disturbing cause far greater
than that due to the inclination of the water surface in
s of these rivers — thoroughly investigated.
L convenient mode was adopted for testing the
tncss of the reach of the river at the section in
\ ihe velocities were observed. The centre of
I of the river section was found an^ marked on
ing, and also the centre of gravity of a section

i8* OJV FIELD OPERATlOm AKD CAUGISC.

whose depths represented the surface currmts
convenient mode, either feet per minute or per i
the horizontal distance apart of these two cer
gravity indicated the amount of effect of a bend in I
reach at that section. In the Rosario section oTl
ParanA this was ^ of the width of the river, xcA
section was considered favourable ; in the Pahnas
it was as much as -^ the width of the river, and tiuti
not considered favourable. I n cases where a ver>' sC^
reach is not to be obtained, the position of a sectiai
observation is recommended to be taken at the po
of contrary flexure of two reaches curving in oppo
directions.

Conclusions. — The conclusions arrived at by M. lU
from his study of the current observations on the La Pla
Paranii, Parani de las Palmas, and Uruguay, were—

1st. That at a given inclination surface currents
governed by depths alone, and are proportional to
latter. 2nd. That tlie current at tlie bottom of ari
increases more rapidly than at the surface. 3rd.
for the same surface current the bottom current will
greater with the greater depth. 4th. That the ini
current is the actual arithmetic mean between that at 1
surface and that at the bottom. 5th. That the
current is always at the surface, and the smallest «I
bottom ; and tliat as the depth increases, or die surf
current becomes greater, they become more equal, ni
in great depths and strong currents they practically
come substantially alike.

Remarks. — The consideration of the foregoing
as welt as the study of the original books, leads ta
further conclusions— that these observations and exp
oicnts on tidal rivers have yet thrown no light wfaate

•K Large canals.

I laws of velocity in ordinary rivers unalfected by
UTTcnts. the two matters being distinct and sepa-
-■ . that a more complete account of the tidal action
these South American rivers might have rendered
. records valuable and useful ; and that the further
'lection of the Woltmann meter or water-mill by M.
vy pro\'es its suitability to gauging operations on a
! .7 ,-e scale.

II. Captain Cunningham's Experiments on
Large Canals.

The sites at which the experiments were made were

those mentioned in the Table on the next page, this

iiblc a!so describing generally their conditions, and

mentioning the period o\-er which the experiments were

•nducted at each.

An examination of the longitudinal sections at these

r .ichcs shows extreme irregularity of bed, deep scouring

■^ri high silting in various places, and considerable de-

[.ifturc from the original bed slopes ; in this respect the

■iiditions were extremely unfavourable. The cross

scinkms, however, were moderately regular in form, and

portions of reaches in which no general depression

occurred were invariably selected. The supply of the

canals was very variable ; the requisite control over the

water was effected at the falls at the tail of each reach

by raising or lowering the crest with balks of timber.

Gauges, citlier permanent or temporary, were set up at

each »ilc, and soundings taken at each cross-section of

obiervation. The sections in earth were mostly rough

, or coarsely formed sections ; those in the

; were dther simple or stepped approximate

ON FIELD OPERATIONS AND GAUGING.

TabU of &fes of Obstn'aHoti oh the Gtmgts Canal and Ht |

branches. ■

-£

5

il

CtttODel

1

Si»

1

1

i

Bed

Bonk.

Fidrenlh

ft.

.,.

™».J^

J

mile . .

160

;oco

Earth

Earth

NUnl. to Ud

.8781 No«?r

bcr «a D^
c«mh«. l8;8,
Apfil. l8n

,150

"1

7000

Clay and

August, iS:i^

Soknl em-

1

Ixnilden

to D««>ntji

1,.

■ ■!

7000

^1

85

10

3S0O

Ma»nry

vertical

tlecemb«,:Sl4.,
la Apiil. \i1U

Soluiitwin
aqnedncu

8S

.0

iSoo

••

Febfu«rj.
.877. to I^-
ccmber, iV?^'
April. 1879
FebniuT. \t\S\
Dccernb*!.

April. 1S79

Eebra . .

iSo

uj

6500

Earth

Masonry
dope

Janu.rjr t

J.oli . .

.85

loi

6500

Kamhem .

55

6

980

Eillh

Right jEioli

il

41

190

M«rth.'.879

4

So

Mirenpur .

3)

So

Pnoom. .

9

5

85

:; 1 .,

rectangles, the steps of 14-mch tread and 13-inch I
not continuing down to the bed, but terminaiting V
cally.

The range of external conditions under whidll
observations were carried out at the two principal !

ON LARGE CANALS.

'85

Sotani embankment and the Solani right

!lBct,was extremely great — with high and loiv sur-

:isdients, high and low water, and through gruat

'i' regulation at both the head and the tail of each

:: this rendered the results in these two cases highl>

iMo. The experiments on channels in earth were

■ ^drded out under such an extensive range of condi-

^^nd afforded far less valuable results : extended

^Hoent on them is yet a desideratum.

^Bcceding to details and remarks on the velocity

^Bements : the terms adopted for velocities of

^^p sorts by Captain Cunningham have the merit

^Hnt clearness. Taking x, ^, s as co-ordinates of

raeih along current, across it, and in depth respectively,

r depth, h for breadth, A for area, and ( for time,

le itlocitics of different sorts are thus distinguished :

~L Average velocity at any point :

(Ftoat velocity, the mean of forward velocities or
d parts of velocities parallel to the current axis
b any point in a cross-section :

Kor \v?x-^x. I

0) I

I Mean yelocitj- past a vertical :

P or v?s~i-h.
I Mean velocity past a transversal ;

t/or \vdy-T-b.
I Mean sectional velocity :

For I \vSydz'*-d.

IRG ON FIELD OPERATIONS AN.

In discussing the subject of instruments for
ing velocity, the obliquity and crookedness of
of a float is not considered objectionable, as il
motion gives a representative forward velocity ;
the opinion that all floats and many velocit
afford a correct average of velocities during the
actual observation may be correct, the objectii
result is not true for any single instant of tim
noticed. Among the enumerated advantages
are that they afford direct measurement of
interfere little with the current, are not liable t
may be easily repaired, are cheap, and may be
streams of any size. The nearest approach to
of a bank possible with floats was found to be
inches. The sites of the experiments being vi
able to the use of floats, they were exclusijiely
the systematic work.

At each site of observation an upper and
rope were strained across the channel, to marii
tremities of the reach under experiments, and i
d ants were attached to these wire ropes at fixed
suited to the intended paths of the floats ;
velocities obtained were treated as actual veil
the middle point of the float course. The
admissible from tlie float course was, in channi
wide and upwards, 2 ft ; in those of 70 ft »-id<
wards, 1 ft. ; and in those of 25 ft., | it ; the utmi
tion being allowed only about the middle of th
near edges and banks a less deviation was a]lovi<
a third of the abo^e. The dead run of tiic flo
the upper rope to allow of relative equilibrii
established before timing was generally 100 ft
narrow channels 50 ft, Moored boats were

^fcl.ll ON LARGE CANALS.

■ ; Oiling and catching the floats, the number of men
ach field-party with the boats and floats varied Jrom

' ncen to nine men.

Tht timing was managed by two thoroughly trained

tstrrers, a caller who watched the floats, and called as

. h float passed the upper rope, then ran to the lower
-[■cand called again just when each float passed the

-icr rope ; the observer sat with a field-book and a

■■-'\ half-seconds chronometer at a midway place, and
: -irdcd the times by ear alone. The maximum error
v'.iiiittible was half a second. In this respect there was
> jreai improvement on the timing by watch adopted in
"'-■'•. InlcrnationaJ Rhine observations. The usual length

"run adopted was 50 ft ; in exceptional cases, where
'!ic tendency to deviation of the floats from their courses

j^^ greater, a 2 S ft nm was preferred. Three timings

re made and recorded, and the mean taken ; all defec-

' f observations were rejected instantly in the field ;

r force of wind and the gauge-reading \*'ere invariably

■ :iirdcd with each set, as well as the distance of the
'■It paths to right and lefl from the middle of the
ram, the brcadlh of water surface, and the sizes of the

'■ 'lis or tinned tubes used. The speed of these timing
j<cryations was much affected by the number of
'(.;t courses that turned out bad ; as several floats
*we often used unsuccessfully in one set on one float
0'*urjc The deduced velocities were taken out to
hundredths of a foot per second, the hundredths being
'rt:ated as approximately correct The velocity of 5 ft.
'-" second was considered unusually high ; the maxi-
iiim error in such high velocities, due to half a second
1" observation, was therefore one-twentieth or 5 per cent,
*!id in low velocities of 1 ft per second one per cent

QBHRWr FIELD OPERATIONS AND i

As to gaugts, both still- and free-water gauges *
adopted at various sites, and these were cither perman
or temporary. In the permanent stiH-watcr gauges i
poo] with fine passages of communication afforded agooJ
place for the gauge ; for temporary still-water gauges, a
3 in. stand-pipe was erected in the bank', and maik w
communicate with the water by a J in. lead pipe wilh a
contracted nozzle ; float sticks of 3 ft., 6 ft, and 10 \l~,
were used with indicators for convenience in reading.
The oscillations of the water in free-water gauges were
troublesome, especially in high wind ; the practice was
to observe the maximum and minimum reading io half
a minute, and to use the mean ; with temporary free-
water gauges the difficulty was higher, the plan adopted
was to make firm bench-marks less than a foot below
the temporary water surface, and scale depth to surface
wilh a brass rule having its thin edge directed up-streanL -
Free-water levels were proved to be slightly above s
water levels. The average of water-level at both I
of a section was invariably determined and used ; tiie '
differences of level frequently being very marked and
much affected by the wind. Gauge- readings were made
at the beginning and end of each set of observations a
the mean adopted.

Soundings were taken both along the croiss-secttl
and along the courses, and at distances 50 ft. apart ai*"
wide channels, and at 25 ft. apart in small channels;
these had to be repeated after any presumed change in
the bed and banks, and the average depths were maJ'.
dependent on the mean water-level. The sounding rct!
were wooden rods \\ in. square, and from 1 1 ft, to 15 ii.
long, protected by iron shoes and having rings above for
convenience in withdrawal. The readings were scco by

stream.,—

^: die"
1 and
made
IS and. J

1*3

r eAfKO.

jlobMrver on the bank and read to a tenth of a foot,

uionally even this couid not be done with certainty.

Both the direction and the force of the wind was

soided at the beginning and end of each set of obscrva-

; but the anemometers did not compare favourably ;

id the wind data obtained can only be looked on aa a

(q;h estimate of the wind. The reduced levels were

d to the datum of mean sea level at Karachi ; all

f ipeciil levelling was done twice over with an excellent

I W in, level, and no discrepancies exceeding ooi ft. were

I illmwd. The computation of the final hydraulic ele-

iMnts from the observed data was exceedingly laborious ;

wt that, as well as all work admitting of check, was

Wrificd by two persons independently.

Vfisleadiness of molion producing variation in

Wocity was investigated, and a large series of experi-

■"Oits tabulated to demonstrate the eflfect ; the conclu-

"On being that the amount of velocity variation at one

"id the same point is liable to be at least 25 per cent

"'^the mean value. Under such circumstances single or

-tjirhed velocity observations are nearly valueless ; but

"!'-■ assumption that synchronous measurement cannot

, -.ibly be secured in actual practice is perhaps ovcr-

ucd; it would certainly be very expensive. Falling

: k then on average velocities, the conclusion is applied

' :ii averages should be formed from about fifty values ;

" 1^ course of the four years' experiments was accordingly

-iiirely regulated on that basis, and the measurements

dijnc in groups.

Thf systematic fioat velocily-measumnents were also
made in as rapid a succession as possible on either a
J or on a transverse axis, in groups of three at
h point, thus :

ON FIELD OPERATIONS AND CAVCISC. CH»ML

At ttirfbttk At the poiDt n

At a depth of I ft. At aeit point.
At a depth of 3 ft. i

&C. Al point [leatest right tank.
At the poiui neu to the bed.

Also SIX rod velocities, the whole forming a set 1
only other systematic velocity work was central s
velocity measurements, which were done in groid
4S in as rapid a succession as possible, thus forn
set of another sort Sets were then taken up in s
sion under nearly similar external conditions, so \
the water-level remained nearly constant and the I
moderate, up to a limit of about sixteen sets. But I
water-level changed more than 01 ft., or the wins
ceeded 15 ft. per second, the field work was 1
closed.

Such sets as were executed in sequence wete J
combined into one series by tabulation on the i
sheet, each series admitting a maximum range of 11
level of 03 ft., irrespective of the state of the wintd
only to some extent irrespective of the surface slcM
the site. This careftil mode of combination is a |
advancement on the method often adopted etsewU
combining sets on different verticals in all depd
water, and sometimes even at different sites.

A conclusion drawn from tlie plotting of the
is valuable. Notwithstanding unsteady motloi
average velocity at a point is probably constant I
similar external conditions, any departures fro
law shown in the velocity curves being due to i
ciency of velocity observation.s, to irregularity of o
of bed and banks at the site, or to irregularrty a
channel above and below Uie site. The 1

O.V LARGE CANALS. 191

t, of unsteady motion being the ordinary norma]
of flow, and of the vertical interlacing of

D lifkcs, is strongly insisted on,

Wttk regard to longitudinal slopes. First, as the

bed slopes were very irregular, an average bed slope,

""it to the fall between two adjacent permanent floor-

■ divided by the distance between them, became the

icpresentatively useful quantity. Both the average
iuriace slope of the water for a long distance above and
below any site, and the local surface slope at the site,
were always iJetcrroincd with great precision, the surface
tlopc per I CXX3 never exceeding 04S ; it was a matter
of extreme delicacy, in which the reference to water-
level wasmore important This was done simultaneously
bjr two observ-ers in calm weather on each bank, in some
cases only. The condition that the real surface slopes
il opposite banks are not generally equal was not fully
recognised till a late period. The amount of surface
&1! deduced from gauge readings above and below site,
Aipplemcnted the slopes deduced by levelling, but was
in many cases imperfect from the CDnditions of control
ofthcreach. The conclusions derived from thediagrams
"f surface gradients are that the local surface slope de-
pends jointly on the surface falls both above and below,
bw that the latter by no means sufKce to indicate the
fonocr. It is also observed that the mean velocity and

trge at any site was more dependent on the value
sur&ice slope than any other element.
r/ace tonvexity received the attention of Captain
Cttninghara. Noticing the theory that the pressure in
• fluid in motion is always less than the mere hydrostatic
% and comparatively less with more velocity, and
KDioo that lateral motion would sectionally enforce

t flELD OPBJUTICSS AUD GAUGty^ \

s emnrexi^ in the mkhSe^and Aus fbcm ao a
btive taycT above the Aou of ""»^™"
sectioo, be mnaxfes ttiat the above is true,e
sectional convexity, wfakfa is almost wfaottjr i
The otwervations for convexity were exceedra^l
cate and tedious ; j-et fnxn a scries of them, 0
the Solani embankment main site, the coodnaoitfl
drawn ' that the surface of water in mocioo in a|
straight reach with toleiably uiufbnn bank is, c
avcrag% neariy level across'

Such a general law seems almost unaccoQBta
abstract reasoning, and may be tnie only for s
conditions and circumstances, probably under ]
irregularities of bed above and at the site ; I
deduction is one that cannot be set aside, alii
undoubtedly requires the light of further and cxl
special experiment under higher velocities, and I
strictly uniform conditions of bed and of section.

While concluding this notice of the prclin
conditions under which the experiments were mJ
conditions sufficiently involved and irregular to f
the most arduous of hydraulic enthusiasts — we I
notice that it seems surprising that the Go^■el
did not make some grant for largely improving
rendering regular the beds of the canal in the vidnl
the sites before experiment ; also that a bolder co(
hcnsive method of meeting the expenditure wouldl
been conducive to continuous work. The str
Against difficulties, as well as the labours of the a
taking, had to be met by the unsparing energies a
experimentalist; and though under such drcumsE
results redound more greatly to credit, it is mudl t
deplored that his efforts were thus fettered.

ON LAKCE CAXAtS. tgi

Wtixg tfi verticaiic velocity curves, or observations
)' past a vertical, it may be noticed that ail sub-
velocities were obtained by liming double floats.
• ere of two patterns, one a ball of acacia wood,
_n diameter, boiled in oil and loaded with lead ; to
irface cork disc, 2 in. in diameter and § in. thick,
:hed by a brass wire 0*012 in. thick ; the other
f copper 0x32 in. thick. i| in, in diameter, loaded
; to this a cork surface disc, i in. in diameter,
Ick, was attached by an oiled silk thread ^ in.
Velocities being obscr\'ed at every foot of depth,
Ji as ninety floats were used in a set, and three
Bons were made at every point ; defective courses
tde up by subsequent courses, and the mode of
5 that already described with surface floats and
c velocities were plotted to vertical axes, mostly
ticals, on a scale exaggerated ten times for the
city ordinates ; the curves formed were approximate
ibolas, having general features agreeing closely with
s of Bazin on a smaller scale ; the errors
; employment of floats are such as to produce
ittcr than they should be. From these were com-
e mid-depth velocities v^, the bed velocities t^
1 velocities V.
■Oid-depth \-eIocity at every vertical was found
^ect to great and rapid variation ; thus disproving
1 of constancy asserted in the Mississippi
ir which no proof was afforded by observations ;
[ability was proved to be less than that of either
c velocity or the bed velocity. It was also di.s-
tat any marked increase or decrease of cither
^ the maximum, or the mean velocity was ac-

1^ ON FIELD OrERATlONS AND GaCGING. i

companied on the whole by increase or decrease I
whole of the velocities on the same vertical.

The calculation of the parabolic elements c
velocity parabolic was thus effected :

Taking the two general formulae, P = p (Pi
p[v^-v)=z'~2Z z, where Z is the depth of i
velocity, -p is the parameter, a the depth to any poiri
known values being v^ji-ipt'o corresponding to 0,1
these ivere substituted for v and for s in the abov<|
tile equations solved for p, Z, and V. Theace
p= t .

r=« +-.
p

The parabola determined by each group of thTcel
being usually different, the most probable pardbola^
determined by the method of least squares,
laborious but correct. An investigation of paratfl
variation showed that the data did not admit of suffn.:'
accuracy in the determination of the value of p to ci
its dependence on the external conditions to be C
The depression of the line of maximum \-elocityb4
to be not sensibly affected by the wind but largcM
to air resistance, and dependent on the suffaM
near the site, but the quantitative connection c
be traced.

The summation of velocity past s vertlu
effected through various combinations of the trape
Simson's, cubic, and Weddle's rules, suited
number (n) of equal spaces (fc) ; of which the foil
are the general expressions.

CW LARGE CANALS. 195

+ ««) + *(«.+ ■■• +v.-,)42Cv,+ ... +«„.,)[

+ . . . +r,., + !^) + Cr,+ . . . +«,_,)

f5(«,+r,+ ... +v.^, + rv,)}

e deductions with regard to mean velocity ( U) past

J are that its line is always below mid-depth, but

I cannot be directly measured in practice by any

I velocity observation ; that the mean velocity past

J vertical is dependent on the surface fall in the

■^r sub-reach, but cannot be deduced from it better

; from any primary velocity. It may be deduced

n two velocities by the following formulie ;

(/■= J (V, + 3vj ) ; or U= \ (Sr^ „ + 4v, «) ;

or 17= I C4Vjff + 3Vfa).

Bch the first is considered the most convenient

value of V may also be obtained from a single ob-

lon with a loaded rod in depths not more than 1 5 ft.

; rods preferred and mostly used were i-in. tin

Kpainted and marked for immersion, loaded with

I, and adjusted with shot ; they were made in

f 6xcd length, but wooden rods were also used in

Ir water. The bed and banks had sometimes to

i to admit of tube observation. The tube velo-

Were compared with double-float velocities for pur-

I of experimental test. An investigation of the

\ of rod motion results in a conclusion that a proper

\ is from o*94S to 0*927 of the full depth, when

KJmum velocity is at within one-third depth from

X, and from 0927 to 0950 of it when that is at

D one-third depth and one-half depth.

•96

Oy FIELD OFERATIOSS AfCD GAQi

Proceeding to transverse vttodty cMrver, «
whose ordinates are thefom-aTil %-e1oddesatdI p
a transverse base line in a transverse section, the
ing is an abstract of the obscn'ations efTectcd, whii
made under varying conditions of water-iex'cl at

Surface velocities . .

Mid-depth velodites .

Bed velocities . . .

I Mean velocities . .

o series comprising 109 sets 1

The surface velocities were obser^-ed with pifl

3 in. by j in. ; the mid-deplh and bed velocities

in. double floats ; the mean velocities with 1-in. ti

rods generally, and with i -in. wood rods In depi

than t ft. As the ordinate spacing required clodi

nates where the change of veIocit>- was more ra|

transversals were divided into lengths or spaces,

I each of which the sub-spacing was equal ; the arran|

I being symmetrical to the centre line of the bed 11

case. The mode and order of the field work and

were similar to those already described, so a]

arrangement in sets and series. The average 1

I observations were finally plotted as rough curves \

I transversal, as also the resulting means of die p

Ivclocitics, at surface, mid-depth and bed, a

isectional. The notation here used is: A=any

icfacc breadth ; ii = hydraulic radius; B=

Jdepth ; B=wet border; S=surface slope; a

lvalues of these are given with the trans\-ersc •»

Burves for each site. The causes and conditions

panying local peculiarides in these cur^-es ai

entered into ; but the principal deductions mat

the whole set of curves arc the following :

LAkGE CANALS, 1

%. That like curves are similar under similar external
QniJitiaiu. 3 That like curves with equal mean velocity
oK.ceUns paribus, equally flat-on the whole, 3. Curves
i' low velocity are flatter than those of like kind ofhigh
I'indty. 4. The flatness of a curve depends more on the
ntan velocity than on the general depth, as shown by
mparing low -water and high-water cur\-cs. 5. Wide
■:.[es give flatter curves thoughout. 6. Sloping or
^'-ppcd banks give rise to sharp curvature. 7. Vertical
"ink* give rise to curvature also, but this is less than
Mth the former. 8. In comparing unlikecurves; ofun-
iii.ccur\-cs under thesame external conditions at the same
;■■: of rectangular section, the mid-depth curve is usually
iM outer, Uic mean velocity curve intermediate, and the
>d curve the inner. The mean velocity curve is one of
iir !l&tiest and the surface curve the most rounded, so
^udi sot tliat near tlie banks the surface curve becomes
-nc of the innermost 9. The figure of a transverse
^loclty curve can be determined with equal precision at
=1' pins excepting near the edge. 10. Edge velocity is
JSiumcd to be zero, but not plotted.

The attempt to arrive at a geometric figure for a
'r«»i-crse velocity curve generally was eventually given
''I' is hopeJcss ; but the sort of curve most nearly pos-
•^^g the required properties is the elliptic curve of the
'I'l* represented by the equation

a)-™(i)-='

The' following were also general conclusions:

I. The figure of the transverse velocity curves is for

E'lM external conditions determined by the figure of

'^ehed.

i The velocity (v) should be expressed not only as

198 ON FIELD OPERATIONS AND GAUGING. CBft

a function of the abscissa (y) but also of the depth (2f) ;
so that the equation should be of the form v-l- F=/(y,^,
&c.) ; it may also be a function of the average effective
distance from the wet border.

/;/ the caladation of discharges^ the mode and nota-
tion adopted were as follows. The data used were :

A system of depth ordinates H^ in the cross-sectioo.

A system of velocity ordinates v^ in the velocity
cur\'es.

A system of curve areas D^^H^ u^ with the same
abscissae ± y ; i.^,, at the same points of the transversal

The quantities D^^H^ u^ were prepared by multi-
plying separately every rod velocity Uy by the average
depth Hy along the float course. These so-called super-
ficial discharges D^ past the several verticals whose
abscissae are y are then equally spaced quantities used
in ordinary approximation formulae, of which the pris-
moidal formula is one, to obtain the total or cubic dis-
charge. The following were the four formulae used ; the
quantities a, a,, a,, at equal spacing 6 to right or left o*
the centre line being distinctively dashed thus— a', ^ »
tt/, a/', &c.

1. Simson's

2. Cubic

3. Weddle's.

^6{(a,"+o,"+a,+o,'+a,') + 5«'+«.+a,')}

4. Simson's modified.

where q a missing quantity =i (if +^ is between two

. : scent quantities M B, these and e being all alike at
. lii spacing. This last was convenient for such cases.
With a rectangular cross-section the total discharge
= f',i/; D^ being the superficial discharge past the
man «!ocity transversal, or area of mean velocity curve.
Tbc conclusions arrived at with regard to total or
cubic discharge were : That it is sensibly constant from
iniUnt to instant, but tliat at any site it increases and
il'weascs rapidly with the rise and fall of water-level,
II is liable to increase or deficiency from a cross wind
filtwing toH-ards or from the gauge. Moseley's dis-
:Htr|;e formula meets with very strong condemnation,
*!iii its fauttiness is clearly proved in a most lucid
niinner. For comparison of discharges at successive
''i«, iJie field work should be cither simultaneous or in
ih<; amc body of water at all the sites ; and for those
f''".m successive observation at the same site, immediate
'Uccc^sion is desirable. The discordance between suc-
ccMiive comparable results under similar favourable
Conditions may be expected to be seldom over 3 per
ctnL

Wiik regard to mean velocity, the following also arc
"» conclusions of Captain Cunningham.

I. That the arithmetic mean of velocities past neigh-
'"uring points on a transversal is not the mid-distance
"'^lodly, but errs in defect

i The mean velocity past a transversal and the mean

^ttional velocity arc less variable from instant to instant

n most of the individual velocities, but the former

s scnubly.

I. The mean sectional velocity is constant from

u)t to instant, and more so than the discharge.

y The chief source of variability in successive mean

*W ON FIELD OPERATIOSS AND GAUGING, ciur.

velocity-measurements is that each single result b ii
perfect, and this is due to unsteady motion.

S- The mean surface and central surface velocitJf
Pg, v^ and also the mean sectional, central mea
central surface velocities (F„, U, t'J, and the quanlit
VRS increase and decrease with either R or S.

6. In high up or down -stream wind, surface velocit
observations are liable to be under or over-estimatGi
and are quite unsuitable for computation of discha^
but mean-velocity observation is but little affected b
wind of any sort, and error is then attributable toai
abnormal gauge reading.

7. The ratio c= K-f-P^ gereralty increases wJlh in
crease of depth, and probably with decrease of velodt
or surface slope ; but its variation is obscure, pcrlu[
owing to the effect of wind on (J^

8. For rapid approximation to mean velocity a gw)
average central mean velocity observation is at prtsti
the most reliable mode,

9. Theratio c= 7-7-100 v'fliSincreascs anddeciws
generally with increase and decrease of R, depends
some complex manner on S, and also on the nature
the bed and banks at the site.

This last conclusion is obviously of the h^i
importance in Its bearing on calailated velocity /orwmi

In a careful examination of these latter, Capt)
Cunningham states that these are all, with the 5
exception of that of Herr Kutter, quite untntstworti
and that Bazin's relation c,= 100C-f-(100 C+ 25-34)
fundamentally incorrect as a relation between «= F-f
andO.

The rejected formulse among the really old one* 1
those of Dubuat, 1786 ; Girard, 1803 ; Dc Prooy, l&

■■^^ aV LARG& CANALS.

ling, l8o3 ; Dupuit. 1848 ; St Venant, 1851 ; Ellet.
vi ; and among newer ones, tliose of Bomemann,
! i;^(^n, Gauckler, Mississippi, and Gordon.

i*hc only two formulae of sufficient value to merit
.'.ended discussion were those of Bazin and Kuttcr.
' 'le results of their examination are :

1, That the form of the value of C in the Bazia
'Tmulais defective.

This was also Herr Kutter's conclusioa

-■ Tliat making K a constant in the expression :

• "ot just, and A' varies from 22-4 to 99 in 61 cases,
''' from 170 to 107 in 43 selected cases g^ven by
■ ■'•'in,

3- The effect of applying Bazin's coefficient <^ to
'Ural surface velocities v^ is to produce too low values
' mean velocity.

4. Baj;in's ratio c, increases with R, whereas the ex-
i'^rioiental values of, show no signs of this.

J. For earthen channels Bazin's ratio c is so low as to
** of little use.

Next, regarding Kutter's coefficients {0^ ;
I. The formula, though complex and laborious, is the
''ot empirical formula yet proposed for calculated mean
Velocity (and hence for discharge).

I. When the surface slope measurement is a good
i^vcr^gc, done in calm air on both banks on a canal in
'"'1 train, t7» will give results whose error will probably
i'li.>ra exceed 7^ per cent in large canals.

201 O.V FIELD OPERATIONS A.VD GAVGTNC. i

3. The coefficient of rugpsity must be cxpcrin
tally determined for each site.

It may be here noticed that the books of the ant
were employed by Captain Cunningham to obtain vs
on the Kutter system suited to Flngtish purposes, and
referred to repeatedly ; and that with reference to
liability to error of 7^ per cent, in these quantities,
clear that as discharges under favourable circumsta
of experiment are allowed to be liable to 3 per cen
error, the former being about double, this pro\-cs i
degree of exactitude for a mere calculated w
formula, and practically justifies the claim adviil
in those books to an accuracy within about S per cei

The above constitute the principal results of Caj
Cunningham's experiments.

In addition, much care and experiment were del
to fan current meters, Moore's and R^vy's and B
proving them by separating the recording portions
the fans ; but from uncertainty of oriculation, of d
of gearing, and of non-measurement of forward veW
their employment was eventually considered si
useless, A series of observations on the effect of a
suited in the following conclusions, that, 1. There
obvious connection between the velocity and I
density of different parts of a site ; the silt density 1
from instant to instant at one and the same poin
The silt density and silt discharge do not appc
depend sensibly cither on the depth or the xtlocity
site, but in the Ganges Canal they depend chiefly 0
silt admitted with the supply.

The observations on evaporation produced th
lowing conclusions : I. The evaporation from a fk
cvaporameter on a lai^c stilJ-watcr surface or ri

MJTA'J 0!f GAUCim

kis than from a small vessel on land. 2. The
j^-oration from Uic Ganges Canal at Rurkhi averages
III jV inch daily out of the rainy season ; and the
. by c\-aporation is about jj-cth part of the full supply
'lie canal, or about ten minutes' full supply daily.
The main result of the whole may be expressed in a
words, ' That most of such hydraulic results as were
iousiy accepted by only the few have now been so
iiU-d on a lai^e scale as to command their acceptation
■he many.'

12. — Gener.\l Remarks on Systems ok
Gauging.

The foregoing brief accounts of the modes adopted

'^■■•■arious hydraulicians in carrying out field operations

^ a far better guide to the engineer about to under-

.■-!■ the execution of gauging operations than any

'■'^trary advice, or set of rules, could possibly be ; the

';'liiir may, however, be permitted to make a few rc-

■ iiks in conclusion. It is, of course, assumed that the

most advisable mode of proceeding in one case might

not be applicable to another, and that the method of

I ffuiging should be suited to tiio general object, the

e,and the circumstances. When the object is of an

mmcnta] nature, having scientific results in view,

t experimentalist himself is the best judge of the

.e most suited to his object Most gauging opera-

i. however, have for their purpose the determination

• the discharge of a river, or of a canal, with as little

l*hnur and expense and in as short a time, as anything

■fEToaching to a^uracy of result will admit ; in these

ao4 ON FIELD OPEKATIONS AND GAUGISG. a

cases the amount of predetermtned accuracy g
affects the choice among modes to be adc^ted.

I. The most rapid and least accurate mode of
mining the discharge of a river or canal at a c
place and time is that which dispenses with vt
observations, and makes use of a calculated vdi
formula as a substitute. The dimensions of two
sections of a straight reach of the channel arc mea
the inclination of the water surface between the
levelled, and the nature and quality of the bed
banks are noted ; these data enable tlie discharge
calculated by the aid of the most modem and
correct formula with a certain amount of approxil
trutli. The point now to be considered is what
of exactness may be reasonably expected from,
practical application of this method.

The general formula for mean velocity of di
and for discharge in open channels,

F=cxI00v'fl^; andQ=JK;
where

seem theoretically to leave nothing more to be d(
except perhaps a sim pi ili cation of form not attai
in the present state of hydraulic science. It is;
table to channels of all dimensions, from the sir
distributary or rigole to that of the Mississippi
can be applied to channels of any matcrisi,
wced-co\'cred earthen beds to cut stone and
planed plank, the data on which it is most cai
based being those of numerous cxpcrimcntalista
functions or terms involved are only three, fl, &, i

REMARKS ON GAUCmC.

aoS

fI which the iw-o former can m most cases be readily
v.A i-uflficiently exactly observed in practice ; the great
r.ty, however, lies in the determination of the third
■n. An examination of the {jeneral and the local
> of «, given in Working Table No. XII., will
lin this. Among the general values suitable to
['f special construction, from well-planed plank to

' '■?. the \-aIue of n ranges from 0009 to 0017 ; and
:.;radations of roughness or quality of surface are
y marked by the corresponding values of «, the

.tcit gap being the difference between 0013 for
ir and 0017 for rubble, a difference that can be
; worked up to in practice without any likelihood

iiijwrtant error. It would hence appear that there

iM be no difficulty in practice of determining dis-
jos with fair accuracy by means of the above calcu-
i velocity formula for channels constructed in such
"cial materials. It is, however, in the cases more
ii in practice, namely, in those ot canals having

* ii;[i beds and banks, and in natural river channels,

- ilic values of n offer so wide a range of choice, that
calculated discharge might involve serious error as
H-iult of the adoption of an unsuitable coefficient.

■ rarthcn canals tlie values of n range from 0020 to
ij. the gradations of which are far from being yet

';^-ii:nily definitely marked ; and for local values the
■'■:.'. is about the same. It would seem, therefore,

't in these cases it would be necessary to determine
ulocity measurement tlie discharge of the river or

'iJ at the site under consideration, and thence deduce
ilucof 71 suitable to it before the above method could
• applied for obtaining its discharge at any time or

■i« with sufficient accuracy ; or, in other words, a

O.V FIELD OPERATIQXS AS'D GAUGING. «i*. i

small amount of actual gauging must be done bcf<^
this mode of procedure can be adopted. In the fu;;;;r
we shall probably have the values of this function ow'
definitely laid down, and we shall then be able to mJ^''
use of this method more readily, and with greater Aju
fidence in the results ; now we have only the present
amount of information to guide us, and are hence un-
avoidably forced into a certain amount of wlodi}'
measurement as a means of correctly gauging atiJ^-
and river channels in earth.

2. Assuming, therefore, that velocity measurcmcri-
is absolutely unavoidable, the question next arises, nhv
is the least amount of it necessary in determinrrii; ■
discharge ? The results of Bazin, determining the reii
tiort between the maximum velocity in a section and it
mean \-etocity of discharge, give the readiest solution ui
this problem for small canals. His formula

where F,= the maximum velocity, and y_= the
velocity of discharge ; and it is evident that by
bining with this formula the more modem coeSit
of Kutter, we can, with the aid of only a few otfiervs
of maximum velocity, arrive at a mean dischat^
rapidity and a fair amount of accuracy, and may be
wards able to determine a discharge at any time unt^'
the same local conditions by means of the ordin.
calculated velocity formula and the Kutter coefHt
already mentioned, without the need of more v(
observation. The reduction of these equations
French measures is given at page 38. Chapter I.
It is extremely probntle that this mode of
will be more universally adopted in future, and

I

KA'S ON GAUGING. aoj

J scries of observations will throw more light on
fRlation of the maximum velocity to the mean
Tciocit)' of discharge, and enable it to be determined
;i greater accuracy than is at present possible. Ob-
-~.K5 arc therefore recommended to keep in view in
■' a*"fi™g5 conducted on this principle, not only the
-lional position of the maximum velocity in a section
t-idi may be confined to a single point either in the
rrnJdle of the channel at the surface, or at a few feet
'•'.low it, around which the velocities may diminish in
-i-iioo ratlier suddenly, or may extend with but little
i-rninution over an important portion of the section), but
;>o the locus of maximum velocity, or its depth below
Tic water surface, which may vary sensibly in a long
■idiof river. This inclination of the locus, as well as
■■■- amount of section of very high velocity, arc data
njt will probably aid eventually in determining the
'itio of maximum to mean velocity of discharge with
itcater precision than BazJn's formula now affords,

J. The next mode of gauging that seems most
•iriplicable to ordinary rivers is one of the modes recom-
roffldcd by Captains Humphreys and Abbot This,
ti'^e^'cr, Involves a greater amount of velocity obser-
vation, and at the same time requires the velocities to
^ 'jbseried at a greater depth, for which all descriptions
if current-meters are not applicable.

The velocities are all observed at a uniform depth
'*ia»i to half the hydraulic radius of the section, and
*t equal distances judiciously chosen across the line of
w^ion; and llie mean of these velocities (J, is taken ;

¥

r~thc mean velocity of discharge, V^, is then obtained in

HHr formula,

ao8 ON FIELD OPERATIONS AMD GAUGING. CBAKS

\

T

\ = [^1-08 U,_ + 0-0026) _ 0-045 ^/ft] '

1*69
where 6= 1 ; and r is the hydraulic radius.

(r+1-5)* "^

This mode should, however, be limited to very large
rivers ; in fact, the application of any of the Mississippi
data or formulae to artificial channels or small streams
cannot be recommended.

The defect of the above method in assuming the
relation ?7=0*93Fm is sufficiently evident, so also is that
of assuming the parameter of the parabolic curvature
of mean verticalic velocity ; but when these quantities
are predetermined for any case under consideration, the
same principles may be applied in gauging small
streams or canals with quite as much success as in
gauging the Mississippi.

4. If we accept the conclusions of Captain Cunning*
ham, given at pp. 91 to 93, Section 8, Chapter I.; ^
may gauge any rectangular or approximately rect-
angular section of flow by single velocities taken at
equal distances on a transversal ; the depth of observa-
tion being | the total depth generally, and -^ the total
depth at the points near the margins ; these velocities
will then be representative elementary mean velocities
in their own portions of channel, from which the mean
velocity for the whole section may be deduced with some
degree of general correctness. Further correctness may
be obtained by taking two velocity-observations on each
vertical from which to deduce each mean verticalic
velocity ; the formula recommended for this is (see

p. 87), ^ . N

SEMAKKS ON CACCmC »9

\ to say, the sorface-vekxitty znd the tdocity it |
epiK, are sufficient

c defect in the«e methods is erident ; it ooosuts in
g the parabolic curv-ature dependcot on one point
i two points, whereas three points are the least
If, however, we apply the three-point
) (see p. 86) and obtain values of T oa each
I through three synchroooos observitioas oa it.
lake

jF deduce a mean sectional velocity that is theo-
y almost unimpeachable, though based oa a very
nie amount of vclocitj'-ohservatioa.
J The next furtber attempt at accoracy in mer
! involves a complete invest^tion of the whole
k velocities in the channel sectkxi ; die velodty at
Ipotnt in the cross-section should be Vnown and
d on a diagram, they can then be grouped into
Ms of the section by vertical and horizontal lines
[[ which the variation of velocity is not impottaitt :
n velocit)- for each division is calculated and nml'
^ by the area of that division to obtain its di*- .
Wk ; the sum of these discharges is the diKJiaifje '
I whole section. There are, however, two or three
ids of treating and observing the velocities. Wheo
these fluctuate locally to a very small degree within a I
ibort space of time, any velocities observed at the «aine i
cite within a day or even within a we«k may be grouped \
logethcr to serve as a basis of calculation ; limilartjr |
~ "hen there is very little local variation of vdodty^ I
L, mean velocities observed over a portion of \
r from 50 to 200 feet in length will reprcsencJ

aio O.V FIELD OPERATIONS AXIi ^.-.. ^-.V^. ...»

mean velocities at the middle of that length. M
both such advantages happen to be combined, the w
of the observation is much simplified, as the velocities I
must not then be necessarily confined to an exact «-
tional site, and need not be perfectly synchronous.

Preliminary observation is therefore necessary to
determine the conditions under which the velocity-ob- ,
scrvations will yield correct results.

When the local variation of velocitj- along a (tiii
is important, either a sufficiently favourable reach tnost
be found, or the method of using loaded tubes and floats
must be discarded in favour of other appliances ifu'
actually afford velocities at points of observation, or yii
vertical lines, at a single transverse section.

When velocities vary much at the same spot within
a short time, synchronous or exactly simuIianeou>
velocity observations at the given transverse section ac^
absolutely necessary, and appliances must be used thj'
will obtain these Among them may be mentioned iH'
d'Arcy gauge tube, and the author's current- meter.

Such detailed observations when carried out on "!'
extended scale involve a large amount of labour, caf
and skilled personal superintendence, but at the Mt^
time afford results not only valuable as regards li
determination of the discharges of the river spcciili)
under consideration, but also as records of bydn
experiment aiding in the progress of s>

ON UQDULRS

CHAPTER III.

PARAGRAPHS OM VARIOUS HYDRAULIC
SUBJECTS.

"«Koihil(t a. The Conliol of Floods. 3, TowigB. 4. On Various
II^UladfDunic Fonnube. 5. The Watering of Land. 6. Cuiat
fiik 7. The Thicknes of Pipei. S. Field £>iainage. 9. The
BBin of Canal*, la On waici-metets.

\. On Modules or Water-Regulators.

'"DRAULIC engineers not having yet arrived at a per-
't module for regulating the amount of water drawn
'■' in an open channel for irrigation or town,supply
""H an open canal or reservoir under a varj-ing head
'' pressure, it is a matter of some interest to examine
i" older types of design of modules that have been
'^at various times, and in various countries, before
'ing on to those of more modem form. Such designs
■ iig necessarily simple, they will be found perfectly
fprehcnsiblc by means of description without the aid
' :iriwings or diagrams.

Piedmont appears to have been the birthplace of
'''wlulcs, for although irrigation is essentially Oriental
'" origin, owing to its extreme reproductive power in
oot climates, and though it was introduced into Europe
F &e Moors, we do not (ind, either in India or in Spain,
: portions of these works still exist, anything

Mb

aia MISCELLANEOUS PARAGRAPHS.

approaching to a module. The systems employ
carrying out irrigation almost prove that they hai
such a thing at all. In India the practice s
have been to turn water on to a field until eitha
landowner or the tumer-on of water was satisfii
perhaps rather until the landowner was satisfied th
could get no more. No doubt this was the best
to start with, as the object of irrigation was to
the fields sufficiently ; and the landowner being thi
judge as regards how much water was required fo
crop, this mode insured the observation of the (
persons. This plan was, however, open to one
serious objection ; when the landowners discoverec
an extra amount of water beyond that strictly nece
for the crop was in some cases capable of increasin
amount of produce to a small degree, they would'
more water, either by stealth or otherwise ; the 3I
of perpetual squabbling on this subject would then
been very large, had it not been for the fact t
Oriental countries irrigation works were made by 1
emperors, or chiefs, whose despotic rule and c
institutions supplied a very practical limit in sui
ters — moral or physical force.

In Spain, under Moorish rule, it is probable
this useful substitute for modules was also in
but in the huertas or irrigated lands of Spain,
modem times and under Christian rule, the water
the joint property of several villages that combii
keep the works in order, and legislated for tliet
about the distribution of the water, the first grcai
the just division of the water on a large scale zmo)
several villages, had to be regularly carried out.
canals being comparatively small, a proportjonal d

Oy MODCISS.

led by equalising the size of » t
pf outlets Croro the main canal iolD tfee
' channels, one vUtage tlu*» tddog a SmbA
of the total v-olume of water p

idmont the oondhioos were

•ing hilly, and the water I

Its havir^ a considerable &I1, «

Y used for driving coni nuUi. It if |

I were a few vatcr-dmcB con onlfe hcA ia

in Spain, but there >udi xaaB^wodA be patSc
s, the mitlcf being aserrantof theoosMnMCy,
living on a fixed inocune, or ytaAf fay, fiwai
kind or in money by all tbe mif^hammg
ing the mill In Piedmont tbe laBt wot. ibe
>pcrty of individuals, as tbey an at dKfMaeM
rope ; hence it was there that the fint wut of
surement was arrived at — tbe aawyaUrf wamr
I drive a com mill, whkh i

of about tbe same sixe and
int of water then aasumed a tedwial nane,
facqua; the same thii^ 'm Loatbwdjr bcias
rodigint. in Modcna a madma, mA ia tbe
■ mouian — the same circanstanoei io rafioW
bding to the adoptifia cf a ■inifaf' Miit <4
pnt. whkh was naturally ntber vafteMc In
the amount was generally abotrt 13 onbic feet
9, and was supplied by aa ootletaboM i-(a
t, the water issuing free from pfcaattrc at dw
rcl The next step was tbe tntroductioo <4 a
lit of mcasucemcot for parpoves of im^fOMM
rges under prcsnre, tbe Piedmuileac i/>uia ;
I a fcctangtUar outlet o'43 ft. bread, crjA ft

MlSCELLjnrSOVS PARAGRAPHS.

hfgh. having a head of water 028 ft. abow the upp
edge of the outlet ; its dischai^ Vfas 0-85 cubic feci pi
second, and this was the immediate parent of d
Picdmontesc module, and, 3s far as we know, tl
ancestor of all modules.

PiedmonUse Modules. — These, the most perfect tj
of which is that of the Sardinian code, were designcdd
intended to fuI6l the following conditions : thai the w
should issue from the outlet by simple pressure, ll
this pressure should be maintained practically consQ
that the outlet should be made square in
having vertical sides, that the issuing water should h;
a free fall, unimpeded by any back-water, and that d
water of the canal of supply should rest with its surfaif
free against the thin wall or stone slab in which lli=
outlet was formed. The following is a description ul
the general type. The water is admitted through i
sluice of masonry, having a wooden shutter working
vertically, into a chamber in which the water is siipi>a!«i
to lose all its velocity and is kept to a iixed level mark
by raising or lowering tlie shutter ; the chamber is of
masonry and has its pa\'emcnt on the same level as d
sill of the sluice, the regulating outlet from this c
being an orifice 065 feet square, having its upper e
fixed at 0-65 feet belon' the fixed water-level mark o
chamber. Its discharge is 204 cubic feel pcrs
If a larger discharge at one spot be required, thebrcJ
of the outlet is doubled or trebled, the other dimei
remaining imaliered. Such are the sole unalteni
conditions or data of this module ; all its others s«
have varied very greatly ; its sill is sometimes at th:
level of the bed of the canal of supply, sometimes abov

^■nd sometimes below it, in which case a slight
^■onty incline was made from the bed down to it ; the
H[lh and breadth of the chamber vary greatly, the
Hber from 1 5 ft. to 35 ft,, its form being circular, oval.
^1 pear-shaped ; the side walls splaying outwards
^■tetimes close up to the sluice, sometimes not till near
^B regulating outlet, the object being to destroy the
^■idty of the water within the chamber. The lower
^■e of the regulating outlet is generally, but not always,
^■erd at <y82 feet above the floor of the chamber. The
|ped floor of the chamber is in many cases, but not in
■ill. continued at the same level beyond the outlet

The practical advantages of this type of module
consist, therefore, in having a chamber in which the
*»fcr can be kept to a constant level, and from which
the mater can issue under a constant head of pressure
tiifough a regulating oritice of fixed dimensions.

MUanese Modules. — The modulo magistrale of Milan

B the most improved type of Lombard modules, the

'e of Cremona and the quadretto of Brescia being

nfcrior to it in design, its principal advantage

' the Picdmontese module being tlie fixity of

nsion of almost all its parts ; in other respects it

) it very much, the principal differences being

water chamber is always rectangular and

I with slabs, and is hence called the covered

r, that its flooring has a reverse slope in order to

n velocity, and that the masonry channel beyond

ulating outlet has fixed dimensions also, a portion

t being called the outer chamber. In its general

Hipmwit, the sluice of supply has its sill invariably

'level with the bottom of the main canal, tvhich \i

116 mSCELLA.VEOtrS PAKaGRAPHS.

paved with slabs near it ; the breadth of the sluioe is d
same as that of the r^ulating or measuring outlet ;
sluice gate is worked by lock and level, being fixed a)
locked at any required height by catch lock and fc
As to dimensions, the covered chamber is 20 ft. IwgJ
flooring having a rise of 015 feet in that length, and i
breadth is 1'64 ft. more than that of the sluice
that is. 82 ft more on each side ; the lower surfaccof^
covering of slabs or planks is fixed at 0'33 feet a
the upper edge of the r^ulating outlet, which \:
height to which the water must be kept to secure!
fixed dischai^e. In order to gauge the water in I
chamber, a groove is made in the masonry so as to alio
a gauge rod to be introduced within at the sill of t
sluice, which will read 229 feet of water abore the 9
when the proper head of pressure exists ; should It n
more or less, the sluice gate must be raised or low
The outer chamber is 066 feet wider than the roeasur
or regulating outlet, its total length 1779 fL ;
walls, which like those of the covered chamber
vertical, have a splay outwards, so that the width at
farther end is 098 feet greater than at the outlet C
that is to say, it is there equal in width to the cow
chamber. To insure a free fall, the flooring of the o
chamber is 015 feet below the lower edge of the o
and has besides a fall of 0'i5 feet in its length
1772 ft.

The total length (./ the module is nearly 3771
but its breadth is variable, according to the amoi
discharge required. If intended to discharge a Mitai
oncia viagistraU, tlie Milanese unit, uhich varies f
V2\ to 164 cubic feet per second according to diffo
computations, averaging 15 cubic feet per second.

O.V StODULES.

ill

outlet is 066 feet high and O^JS feet broad,

a constant head of pressure of 033 feet ; the

of the covered chamber being 213 feet and the

of the open chamber 115 feet and 213 feet.

essentia] to the effective operation of the

iting sluice that the difference of level between the

in the canai and that in the module be at least

feet ; and as the height of water in the latter must

feet, the depth of water in the canal must never

\aa than about 3 feel, in order to allow the

i!c to work properly. The following are the relative

fcwls of the parts of the module referred to the bottom

of the main canal as a datum :

Who uifface id Ue interior oflhe modtile
Vppu edge of ibe meuuiing outlet .

Upper eni] of flooiing of open chamber
Lower cul of ibc utme ....

Such is the type of the Milanese modules, the
tensions being suitable for a discharge of 15 cubic
fwi per second ; unfortunately, in point of fact, the type
ItJ been rarely adhered to rigidly, and thus its
'-^^■ait^es as a universal, or even as a local water
Jiidani have been comparatively thrown away in
■■ctice. Its use, however, established a discovery that
^■^^ it that time very important, viz., that larger outlets
"p i ^aler dischaige than that due to the proportion
' ihdf section for small ones ; it was therefore deter-
"Unl that no single outlet of a module should bo made
' 8 discharge of more than eight oncia or 12 cubic
'"' pei second ; and when a greater discharge was
"iui-td, two or more separate outlets were to be used
' 1" by side. A gauge post was also found to be

ai8 M/SCELLMA'EOt'S PARAGRAPHS ois. :

necessary in order to enable the water guardian:- >
adjust the sluice accurately.

The principal defect of the Milanese modules is i\..:-
owing to the rush of water from the canal, it is rcsi
impracticable to keep a constant head of pressure on li-
measuring outlet ; besides this, sand and fine silt viliaic
the accuracy of amount of discharge.

Such are the comparatively ancient modnles, tic
Milanese modulo magistrale being the most imprt"'ol
one of them. Their type has been very much adhered
to in modem times ; that of Messrs. Higgin \
Hi^nson on the Henarcs Canal may be considcrB
the greatest improvement that can be made on fl
without departing from that type. In this modui
entrance by a sluice into a chamber for destid
velocity has been preserved, but the exit is an o
and hence more susceptible of exact mcasuremel
discharge ; the means applied to deaden the vcloc
entrance are again different

The entrance into the channel through a wall \'-
passage 1-96 feet ('6 m^tre) square, regulated by a "■
fitting cast-iron door raised by a screw ; the chambt'
rectangular, io'37 fL long, by 7'20 ft. wide below. --

I ft. abo\-e. the side walls having a batter of i in 6.
bottom of the chamber is horizontal and at a Ic^t 1
feet below the sill of the entrance sluice. To dcT'
the action of the water.a partition of masonry graiii]
built across the chamber at a distance of 4 ft. from itit
wall, and 5 fL from tlie overfall wall of exit, it t
broad, and has eight slits or vertical passages not ^
barred, each slit being 045 feet wide. The water h

J been deprived of all action by passing through t!il!

Ii^angcment, enters the second portion of the chamber

from lilt
ot^l

O.V MODULES.

jd then passes over a weir ha^Hng an iron edge 656 ft.
! metres) long, fixed nearly on a level with the top of
■ ntrance sluice, or 2 (t. above its sill. The discharge
'i?d for irrigation being never to exceed 176 Hires
: cubic feet per second, the depth on the weir sill
:h.ereforc never exceed 0'5 feet, the sluice opening
; 1 97 fL square.

1 licre are two small side walls having a batter from
(J on either side of the sJuice entrance, these walls
■iting into the main canal, in order to protect the
"iTTCe and pre^'ent silt from accumulating there, which
nise, and perhaps even in any case, would have to
i.ig out occasion.ally. In order to keep the chamber
:>per working order, a keeper must be employed,
I gauge post erected in the canal, by reference to
1 he lowers or raises the sluice, and keeps the water
■ 'ak chamber always at a fixed level.

It ii evident that the changes may be rung on this

ipKies of module to a great extent without effecting

""■■A\ improvement, by increasing the number and

ing the positions of the sluices and overfalls, and

.lying the arrangement for deadening the action of

This has been done in many cases without

BtcsuU: it is hence not worth while to bring

1 other examples of this type,

though some of these are complicated in form, as

• much varied in detail, the types are exceedingly

fc; they al! require tlie occasional attendance of a

y for adjusting them according to the variation of

B ; they are made of brickwork and masonry, and

of a series of open passages and covered

3 connecting orifices and overfalls. It is quite

t that, except under special circumstances, such

aio MISCELLANEOUS PARAGRAPHS.

modules are far behind the wants of ar
economises labour, attendance, and supervision when
possible.

Self-acting Modules. — A module to be of muchfl
now must in the first place be self-acting. Nor, in^
is this all. A large number of self-acting apparatd
regulating tlie supply or flow of water have |
designed and used, but three-quarters of tliem dcH
answer all the purposes required of them at pra
Some are large, some expensive, others involve a I
expenditure in protective or additional lai^e chain
others arc complicated and liable to get out ofd
and others involve a great loss of head, which, \\
case of their application to irrigation canals of smal
is an insurmountable objection. The worst ofthen^
be said to be those that fail in their main objefl
producing practical invariability of discharge. Win
these objections to deal with, it will not be nec<
do more than make passing comments on the |
number of them, and the principles involved i
design and construction.

We will, however, first mention the requin
of a good module. The fir.it consideration i
under ail ordinary circumstances the discharge I
practically constant and correct, that is. should r
liable to vary more than 5 per cent. ; secondly, i
should be very simple in construction and appli(
thirdly, that it should not be liable to deranj
fourthly, that it be portable, easily applied and n
from any portion of tlie canal without invr>Mng J
waste or loss ; fifthly, that it should not involve d
loss of head, and that it should be able to 1

I ON MODULES. ii\

laiul or basin of supply, down to a le\-el of one
shove its bed, and deliver water if need be as high
1^ within one foot of full level in the canal ; sixthly,
hn it be inexpensive, not costing in England more than
ibout lo/., and more than 5/. additional for its attach-
ncnls, slabs, cisterns, or chambers, and setting it in
place in working order.

There are perhaps only three modules yet designed

' tnay be said to fulfil these conditions ; these we

iV.r the present term portable modules, and defer

.iing with them until after commenting on the others,

Dr ordinary self acting modules, some of which have

lulvaotagcs or disadvantages worthy of notice, or have

itiractcd special attention in any way.

Tntil recently, the power of flotation was the sole
Ti-: adopted in self acting modules for obtaining an
.1 discharge under varying heads in the canal or
11 of supply. The simplest manner of applying this
■ ihaps in attaching or fixing the pipe or pipes of
I'ly to the float itself, thus insuring a fixed head of
•ure on their entrance, however much the surface
i in the supplying basin may vary. So far as this,
modules depending on this principle appear excel-
'. but unfortunately all of these seem defective- on
■uiitof other considerations. For instance, in 'the
"■nded opening' where the water enters through two
■'.mial pipes into the body of the Boat itself {which
^ pt submerged to a sufficient depth by weights) and
■ '^ out of it through a vertical pipe fixed on to the
'-' side of it, the vertical pipe has to slide up and
■n in a species of stuffing-box in a masonry platform
^iw, so as to discharge itself clear of the water in the
■"•iJn canal, and prevent the latter from leaking through

I.

a« AtrSCElLANEOUS PARACRAFUS.

into the well below (he platform, from which the mod
water alone should be drauTi ofT This is plaii
contri\-ance that n.'ould be defective for purposa
irrigation ; should the vertical pipe not slide e
the stuffing-box, the power of Rotation may be e
neutralised ; should it be too easy, there will be lea
and perhaps to a serious amount ; the loss of lev
seriously great, the delivery level never being \
than I ft. above the bed level of the canal. Modifier
of this contrivance, having in view the abolition c
loss of head, ha^-e been made by using syphons c
erect or in^^rted, instead of the sliding vertical pplT
Thc>' certainly attain that object, but introduce tie* 1
defects sufficient to render them less useful for purpose |
of irrigitioD than the original suspended opening ; they 1
are expensive, and difficult to man^c, the action of the '
syphons is liable to be stopped by accumulation of a
and their discharge is not only practically low in cor'
parison with their theoretical calculated dischat^, t'
also is variable, as they arc verj' liable to foul ; tl'
adjuncts, chambers around and attached, arc expen-iv
The \'crtical pipe arrangement of the suspended opmun^
is the principle on which many so-called watcr-o
used by water companies for discharging water in ]
quantities, ha\'e been constructed.

The same principle has been adapted to pury
irrigarion in the module of M. Monrichcr, on the 1
seilles Canal, constructed between 1 839 and i?so ;
intended to supply irrigation channels having disc
of from I "oo to 434 cubic ft. (30 to 1 20 lilrcs) per a
as a constant supplj-. The details of oonstnictii
as follows: A masonrj-rcsen'oir 1115 ft. by I4'7J
having its bottom at a level approximately 3 fL I

i of the canal, is connected with it by a rect-
r niasonr>' passage having a horizontal masonry
mg at the le\'e! of low-water surface in the canal ;
isveise masonry wall stops the action of the water,
i enters the reservoir afterwards by two passages,

■ on cither side, the wall and passages taking up a
tlon of the reservoir space, lieyond two pairs of

ives for putting in stop-planks for shutting off the
r entirely during repair, there is no other sluice or
c to the free flow of the water. In the centre of
)t rectangular reservoir is a cylinder of masonry, having
holemal diameter of 2'30 ft., being roo ft. thick, the
I of it being approximately 2'00 ft. below the
tom of the reservoir, and its top edge about 200 ft.
r low*water canal surface. An iron cylinder is
idc to 6t the internal masonry closely, and to slide
pand down it, and to hang by a rod and adjusting
trcw to a wooden bar supported by two wooden floats
pUced clear of the masonrj', each of which is 1 '64 ft,
deep, 1*31 ft. broad, and 534 ft. long. There arc also
two vertical bars in the reservoir outside the floats, up
imi down which the bar slides on rings. The adjusting
• TCw enables the iron cylinder, which is about 5-8 ft.
n|j, to be placed so that its upper edge may be set at
1 i_v depth below the water surface, so as to produce
v required discharge. This, when once fixed and

■ ixkcd, is never altered. The whole is inclosed in a
ickcd building.

The water of the reservoir therefore enters the iron
cj'iinder above, and flows out below ; the lower water
being divided from the rest of the reservoir above by
masonry partitions. It rises through the masonry passage
thai made into the masoniy water-course or irrigation

an iflSCELLANEOl/S PAKAGRAPm.

channel, the bottom of which is not more than
below that of the bed of the main canal ; the <
section is 200 ft. by 1-31 ft,, having a small c
ment 338 ft. square at the commencement of the'
nel, Plans and details of the module here des
are given in MoncrieiTs ' Irrigation in Southern E
In this module, therefore, the section of ootfc
that of tlie iron cylinder, is constant ; the edge (
cylinder rises and falls by flotation ; the loss of li
as small as can be conveniently obtained in roodu
this principle of design, and if the cylinder coult^
out much care or superintendence, be made I
well in the masonry without leakage or friction I
detrimental e.xtent, as stated by the engineers
Marseilles canal, the amount of inaccuracy of diS(
cannot be great. It would doubtless be an im
ment were some arrangement applied to this 1
for preventing silt from entering tlie reservoir,
must be liable to interfere with the working 1
cylinder, and produce a greater deteriorating c ^
this module than in many others. Theroasonryj
of the module would require good workman^
tlie putting together of the whole In good woiicing
considerable care. It is. therefore, rather exp(
and certainly has not the element of portability.

The suspmded plug \&, like the suspended op<
principle that has been adopted for modules and
in a very large variety of ways, some of which
complexity of parts and details. Its main princ
probably slightly more modem than that of the
both arc decidedly old, but as the-ie old contri
are perpetually being rc-invented, a brief

ON MODVLES. =25

principles may be of use to some, while comments
'■'. ilKm may ticter others from wasting their energies
^^Udca that appears to have been fully worked out.
^^Bfc simplest case of the suspended plug is this. A
^Btr Dftficc \s 6xed tn a floor at the level of the bed
'" '" ttom of the canal or reservoir, and a plug of vary-
Lcliwn is suspended in it, being attached to a float
tlul rises and falls with the surface of the water; the
ff water passage thus left open is made to dis-
Hjual quantities under varjing heads by propor-
I the section of the plug throughout its length;
B erf" the annular opening being in inverse pro-
El to the velocitj' of dischai^a To insure a free
c is a well below the floor into which the water
ha depth equal to that of the depth of the floor
i-watcr level of the canal. The depth of the
i tU attachment to the plug prevent its acting
li of water of less than one foot in the canal.
1 points, which are serious objections to the
n of this module on irrigation canals, have been
podiflod in the more complicated modules con-
il on this principle, which will hereafter be men-
As to the plug itself, it is either a conoid hung
ular orifice, or a fiat-sided conoid of equal thick-
ionc direction hung in an orifice which is rectan-
Bterally and of circular curvature transversely ;
r case a fixed area is left open on the flat
If the plug which has to be allowed for in the
ms for the section of the plug. The diameter
plug in the case of the conoid Is obtained by
[ the areas required to pass the required dis-
T viuious heads of water, as, from I to 10 ft.
' three inches, and deducting these from the

MISCELLANEOUS PARAGRAPHS.

fixed area of the orifice, the remainders are then|
areas of the circular sections of the plug for those d
from which the diameters are obtained. The fiat o
can be made of the same lateral section for all discha^
(he tJiickncss of the flat sides being increased ia i
proportion.

The following is an example of a module dcsifl
on the suspended plug principle, and is perhaps!
simplest application of it in actual practice. It «
signed by Don Juan de Ribera. projector of the I
canal, or canal of Isabella Segunda, and is used ond
canal with good effect

It is so arranged that the size of the outlet diminU
when the head of water increases. The module jtsi
a long tapering bronze plug, 0524 ft. in diameter al
lower end. and is attached to a circular brass HoataJ
which floats freely in the water of a masonry well ,V3^
by 3'94 (*■ square and 416 ft. deep ; at the bottom '■'-
this well, which is on a level with the bottom of W:
main canal and the rectangular masonry pasMgec:
nccting Ihem. is a circular orifice 156 ft. in dianic:n
within which the lower end of the module is made 1
work vertically, the plug and plate being of bron'-
to prevent rust. Below this well again is a second on'
into which the water falls after having passed throutb
the ring between the orifice and the plug. The entmr. ■
of the rectangular passage leading from the canal, whiri
is only about 3 ft. long, is protected from silt by an ir :
grating, and is covered in at the top by slabs to the fu'
level in the canal ; the well is also covered in by a locV^'
iron trap-door. In this module friction is reduced I"
minimum ; the module hangs freely from the centn; '■
the float, and can be slightly raised or lowered in orii'i

Oy MODULES. ii7

r increase ihe discharge passing through the

ir^ or space between the edge of the orifice and the

.: . but when a constant discharge is required it is

y properly adjusted, and then entirely left alone.

(loat is about 2 ft in diameter, having a thickness

■V' middle of about 09 ft., and at the edges of 06 ft.

This mixlule discharges one cubic m^trc C35'3i(36

I ii. feet) per hour, and is hence styled an horametie,

(ii'ichargc being 2777 litres, or '0098 cubic feet per

rui The curve oflhe module or bronze plug is such,

-■ !he rooU of the vertical abscissie vary inversely as

Ihc ilitTerences between the squares of the radius of the

Oniicc and of the horizontal co-ordinate. Hence, if the

requited discharge is given with a head of water of one

-rr, when the diameters of tlie orifice and plug are

"itivcly '20 and "1653 mHres, then, if the head of

■r be reduced to 81 metres, the diameter of the

' at (he level of the orifice must be 1610 metres.

^'\ : VSl ::(20)'-(-1610)»: (■20}'-(-1653)'.

Vngths corresponding to the different diameters of
1 ipcr of the plug will, for a constant diameter of

Me of '20, be as follows :—

i'n from water surface 10 12 -ifi '41 77

I'-'tm of plug -00 -0585 'ogia -1211 -1J74

\i from water surface I yfi 190 271 371
■.:m of plug -1480 1554 ifiio -i^Si

principle being that the velocity of discharge
!,;h an orifice varies with the square foot of the head
■Iter ; thus, taking Rr to represent the radii of the
"ficeand plug respectively, the discharge per second

J

228 MISCELLANEOUS PARAGRAPHS. CHAP.tt

H being the head of water, the value of the experimental
coefficient, o, being for this case deduced, from a series of
experiments of Don Juan de Ribera, to be '63, in accord-
ance with similar results obtained in ordinary practice
in parallel cases. This is probably the module in most
perfect accordance with theory yet designed ; it is,
however, of small dimensions, and hence likely to be
much affected by even the very small proportion of silt
that would pass through the grating. Its principal de-
fect is, that the loss of level necessarily involved in it in
order to obtain a free fall would render it inapplicable
in a ver}' great number of cases, where even a few inches
of fall are of extreme importance.

The modifications of this type of module consist in
putting the float in a separate chamber, which thus be-
comes a silt trap, and relieves the orifice from being
affected by silt, the connection between the float and
the cone being either a chain passing over two runners
or a lever : in these cases the plug is reversed, having its
broader end upwards ; the friction involved affects the
working of the module and its accuracy of dischargCi
and, in the case of levers, the lengths of the arms modify
the quantities employed in the calculations of sections of
discharge. In some cases the form of the lower well
assumes various forms, having for their object the re-
duction of the loss of level existing in the more simple
type. It is extremely doubtful whether any of these
modifications can be considered advantageous on the
whole.

Rising and Falling Shutters, — Contrivances of this
type are generally suited for large quantities of water
where great accuracy is not required. The falling shutter,

A on canals in England or Scotland, is an ofaliqoe
r hinged below, and raised or lowered in front cf
tning in the side of the caiu] by two floats in re-
L the water passing over the Upper ed^ of the
' [n a tolerably unifoTin volume. The ti^og
r is a vertical shatter in front of an opcnii^ in
\de of and dou-n to the bonom of the canal ; it is
I or lowered t^ means of a float attached to it by
D passing over a runner, the float being in a sepa-
lamber, and having trunnions and friciion rollers
; in cur%'ed grooves or recesses on each side of
mber ; these cun-es require *-ery accurate con-
in order that the discharges may not tary
} different heads. Shutters of this description
t pressure on one side only are very liable to stick,
: out of order ; they are hence ver>' inferior in
Ce, although new ones under favourable conditions
k made to work very accurately,
e above three t>-pes comprise the whole of the non-
He self-acting modules that have been much used
ticc to good effect,

e Stif-aeliHg Modules. — In this class we com-

I modules as could be removed or replaced

: much difficulty or loss. There arc three such

s that have attracted attention, though there are

bly others not so well known.

■oils Module. — The first is that of Lieutenant

1, of the Royal Engineers ; its principle is exactly

i the well-known draught regulator : the pressure of

Btcr is made to regulate the opening in the one

. the same way as an increased draught of air is

I

*JO

WSCELLAffEOl/S rAnAGS.iPtlS.

made to partially dose the opening in the other ; and thf
application of the principle is excellent for the intendL'l
purpose — it car> be made almost entirely of iron, :
simple, effective, and admits of removal without causi";'
much loss or expense. Drawings of this module are
given in the Rurkhi Professional Papers.

Andersons Moduli. — The second is a modJficatioTi of
the hydraulic lift regulator. in\'entcd by the late N''-
Appold, used to regulate the descent of hydraulic p.v-
senger-lifts under a variable load ; it has been applied (■
its new object by Mr. W. Anderson, of the firm ofEa-
tons and Anderson, and in some respects resembles ihi^
module of Lieutenant Carroll ; the velocity through ihi.'
pipe of discharge is, however, in this case made to mrm
a suspended plate of curved form, in front of an opeimv
also fixed inside the pipe, and the opening is therefur'^
reduced by increase of velocity.

In December 1866 some experiments were maJ^
with a 6-inch Appold regulator at the request of C-
Smith, consulting engineer to the Madras Irrigali'
Company, and of Mr. Clark, hydraulic engineer to tl ■
Municipality of Calcutta.

In one experiment, in which the regulator was us<^'
to discharge water from a tank / 7" square internal ' ^
during 13 minutes, the surface of the water in the tai ■
sank as follows, in one-minute intervals : ^'-^^ %\, j -
3i. 3. 3A. 3i. 3. 3,St. 3. l-h' 3i. 38" ;-tlie total quantit ,'
discharged in 13 minutes was ^^|

= 7' 7" X 7'7" X 3' 5i" = 1 97-22 cubic feet, ^f

or about t; cubic feet per minute.

In the second experiment, the surface of the wHer in

ON MODULES.

aji

: : lanlt sank as foIIo\ra, in one-minute intervals : 3"^,
:■ % 3i. 3A. 3i}. 3|. 3|, 33. 3. 3^. 3i. 3A 3i. 3i,
V' Jn- 3H* 3ft> 3 'ft ' *^* *^**^ quantity discharged in

- : minutes was

= 7' 7" X r 77" X 5' 8"= 323 cubic feet.

about 1613 cubic feet per minute.
In the latter case the heads at the beginning and the
•::il of the discharge over the centre or the pipe were

:S feet and 1224 feet.

In each case the same regulator or module was
■ ■^A ; its square aperture on the delivery side was 5"4J
'■jn.and 3"}^ broad, or a section of 2o""35 ; the swinger
' -' J"i wide, nearly touching at top and bottom ; the

i-c 5i wide, and the area for water passage 8|'j"x ig"
= ii"77 in section.

Two of these Appold's modules are it is believed in
' "on the Tumbaddra canals of the Madras Irrigation
' Linpany. From the convenience of form that this

i-iiule possesses, being self-contained, and externally a

wpie iron tube, with an enlargement like a box in the
iiiJiilc of it, that admits of being attached or detached

" ni an orifice very rapidly, it would appear to be
'"cfcrablc to that of Lieut Carroll, and less liable to

'-'mage in transit

7ht equUibrium moduU. — The third portable self-
"^'ing module is the design of the author of this work,
'"'lis named the Equilibrium Module. It consists in
'■I'^Etst place of a box or chamber, having an entrance
'■fl an exit orifice, and one or two air-holes above ;
n this box is the pipe leading horizontally from the
ince orifice for a short distance and then turning

MISCEILAKEOI'S rASAGJfAPm. iv.\i 1

vertically opwanis; this is terminated b>' a dead n
but has two or foor slits or narrow vertical openings
the sides, through ubidi die water passes when t
module is open and working. There is at all tiit
enough water within the chamber to rise above the 1e
of these openings, and to worfc a float above them ; li
Boat, worldng %-erticaJly, raises or lowers the captl
slides o\'cr tlie bead of the pipe, and gradually openi
closes the slits in accordance with the ^'sriation of I
level of water in the chamber ; which is below the lo
water surface of the canal or tank of supply. The fo
of construction adopted reduces to a minimum the Ae\
from the water-level within the chamber to the openia
which discharge above the sliding collar, and thus cam
the loss of head to be unimportant.

This is also a small module, possibly only aquat
larger than the Appold module before mentioned,]
equally con\-enient as rcganis portabtlitj' ; it is sim
in design, being actually little more tlian one nf the
upcs of equilibrium steam valve applied as a moduls
a chamber under pressure : it could, however, be
of any siie, the adjustment of the sizes of the orifice*
entrance, of exit, and of the slit-openings being
only important points of variation. It. might also,
rough purposes, be made generallj' of stone-ware, i
the pipe would then be square in section and have c
two slits, the other two sides forming part of the li
This module slightly resembles the old c>-linder sin
which is also a modification of a double beat steam va!
the latter, however, is not so simple, being far more lil
to choke or get out of order, one of its valves wari
witiiin the pipe, and it is therefore not so effectiv
constant use as any of the three already mcniioncd.

■odulcs have been here treated as principally in-

i for regulating irrigation ; the reason of this is

■lie requirements are then more stringent in many

eulari, A module for water supply of other kind?.

faent!)- termed a water-meter, although possessing

Bting power) generally acts under greater head and

□ Eroni silt, and may hence be of coarser design.

2. The Control of Floods.

The prevention of the submergence of land by inun-
'^(mi from overcharged rivers, and the drainage from
'irvhcs and submerged land of the water that has been
' iwed to accumulate over it, are kindred engineering
■'iblcms that appear at first sight to present but little
■Acuity. Their theoretical solution, when merely on a
-ill scale, is ready and simple ; on a larger one, how-
'T, the practical details brought into these problems
-■ici.-t thcin to such a degree, that, although the prin-
;'« involved cannot be said to be subverted, their
'•~nt\g out is forced into a comparatively new form.

Litid liable to submergence from a river is lower
' in ihe extreme Rood-icvel, and in open communication
ill it ; the remedies consist, therefore, cither in lower-
'■'] Itic extreme Hood-level in the channel by providing
'"cr passages for the water, partially diverting it, or
"iljtng out a deeper channel, or by warping up the
■'^1^1 liable to submergence, or by cutting off possible
'"imwiication in flood stages between the river and the
''<! by tncana of embankments. Submerged land, again.
■i»inf in that condition for want of sufficient natural
-ifall; an outfall has, therefore, to be cut. tunnelled

134 mSCELLANEOUS PARAGRAfm. CUA

dredged, or enlarged to a sufficient extent to l
gravity alone to do the work, should that be {
or economically sufficient ; in other cases pumps art
dispensable.

Imagining, then, the case to be one of an arcai
few hundred acres, liable to inundation from a river
a moderate declivity, the application of these prind
involves generally but little difficulty as regards engin
ing, and becomes a local economic question, rather t
an engineering practical problem. Putting the cai
on a large scale, a vast tract submerged by the fi
a river having a very small decli\'ity — the usual cM
tion when large areas are submerged— the dimcnsi
entering into the worlcs that would be neccssaij
adhering rigidly to the above principles become so li
that their complete execution is positively impossiU
most cases. Let us adduce the embankments of
Ganges, the Mahanaddi, the Po, and the lev^ of
Mississippi, which are not and never can be comj
and sufficiently developed to insure, by means of tl
selves alone, the absoliite protection of all the land
their banks from the devastating effects of exU
floods.

To this it might, though perh.ips rather thoi
lessly, be replied, that very extensive works may b
costly as to be impossible, but that the application a
principles need not vary. It is, however, in point a
also a matter of modification of the applicatioo of
ciple.

The case of a comparatively small river s
the ffood, very nearly, and in most cases totaUy, !
the con .side rat ion of the flood to its principal poin
extreme flood-level ; the catchment area of 3 wfwll

iJfTXOl OF FLOODS. xjS^

\g tolerably uniform supplied throughout the rain-
its upper portions do not require very special con-
sideration ; the declivity of the small river being tolerably
'"■ipid, the condition of the lower ranges of the river does
Hilt affect the matter to any very important degree.
lotc local conditions being comparatively disregarded,
being possible to cope with the flood at the
ircd point both successfully and economically, the

involved are necessarily small.
On a large scale, on the contrary, the extreme flood
!, tbc nature, causes, and duration of the flood may
be greatly affected by any of the physical conditions of
the entire catchment area of the region watered by the
river and its tributaries, from the loftiest hill on the
watershed down to the currents of the ocean, miles be-
yond the river's mouth ; and as these physical and
irological conditions vary greatly throughout large
itrics. a perfect knowledge of them as regards the
itry under consideration is absolutely necessary in
Order to arrive at sufficient information to enable one to
propose measures for the mitigation of the effects of the
flood. In other words, the natural drainage of the whole
ngion under any state or circumstances, as well as every-
"^ ig that practically affects it in any way, must be
ighly known in detail.
It will be unnecessary to dilate on the physical laws
and conditions of our sphere, matters best understood
from studj'ing the larger works on physical gcc^aphy
t« be found in any good library : and a knowledge of
these will hence be assumed. The detailed knowledge,
ho»'ever, of the special physical conditions and rainfall
' the region under consideration, may possibly not be
> btainablc from any book whatever. It is not sufficient

Hijnetcoi

^■Bnntr
|kutr

236 MI.SCELLAA'EOUS PARACkAFUS.

to possess meteorological statistics of observations H
at a few towns in the valley of the river, andatoneor
points or villages on the hills; it is needful tok
definitely what is the greatest amount of rain that
falls in the region, the greatest area in it o
rain falls at any one time, and which portions of the
they are likely to be at any time ; or generally
much water, when, and where, so that it may be p
cally accounted for. Detailed obaen-ations takcfl
many years at a very large number of metcorolq
stations are therefore requisite, and it is almost ps
to reflect in how very few instances arc even a modec
small number forthcoming. As a notable exceptio
this apparent apathy, may be noticed the lai^ numl
meteorological stations in the United States of Am
and the large sum annually spent by their Go%"cni
in obtaining such information. Besides ihe i
logical data, a correct detailed topographical and hj
graphical knowledge of the whole of the catchmd
the river, based on engineering surveys and vd
observations, is necessary in order to determine the
charge and the flood level of the river at any time,
under any possible meteorological condition.
all this information we are enabled at any time to
what will be the results in rise and amount of disc
of the river, corresponding to and resulting froil
special rainfall lasting for any usual or unusiu
over an area, or detached portions of area with
catchment basin, and the evils to be contended w
then fully knoun before commencing to deal «
and attempting to mitigate thejr ill effects by mti
engineering works of any sort.

To this it may be replied, that the expense

TUB CONTROL OF FLOODS. 2yj

W these data, and especially those of a hydro-

cal and topographical nature, which cannot be

t by skilled hydraulic engineers, must neces-

ry large ; and if after all this it should be

J that under any circumstances no engineering

i remove the evils, or even moderate them to

tant extent, the expense would have been use-

hcurred.

itircly so. Even should no works be attempted,

mation can be made use of in the protection of

, and in thus mitigating the fearful effects

, by sudden and devastating floods. The

land liable to submergence under certain

«js of rainfall in any part of the country being

a practical certainty, the telegraph can be

d to warn the inhabitants of an impending flood,

' them to save at least their own lives, and

salso that of their cattle and movable valuables.

Y be urged that the terrible catastrophes resulting

e loss of life generally commence with the bursting

mbankment, which happens before the flood over-

; doubtless it is so, but it would be an important

the topographical knowledge to ascertain to

"liat height of flood these embankments, which, when

^'Jiind condition, are in most cases only sufficient

' '^LCtion against ver^- moderate floods, are practically

Timely warning could, therefore, be afforded in

case, and Uje inhabitants would be spared the

~ble infliction, in case of flood, of watching the waters

I?, and not knowing either how much higher they

,iit rise, or la what height of flood their dams might

But to proceed to the main object, the protection of

I

I I

/

i
■ I

the . "'^^' and
- so the flood levp/ ^^

« flood under"^!:/"' "^ fi

THE CONTROL OF FLOODS. 239

uon, h&3 set in tolerably mildly ; the river swells,

r.niascs in depth and velocity, and is discoloured at

■ , this afterwards passes away, and the water then

itcadily, tolerably clear. The rain increases in the

I ., and tlie sky gives prospects of a heavy storm in

lifcction of the uplands of the river. Let us watch

.[Tect The rainfall of the plains, in fact the down-

' ail around us, increases the depth and the velocity

'.'J river, but its colour is unchanged, in fact it seems

:'.>■ pure. Suddenly a roaring of waters, like that

■nv an overtopped mill weir, is heard, and up stream

w notice a white line of foam approaching ; three or

l»t minutes, and a flood sweeps by on the surface of

ihc rii-er, like a wall of water 3 or 4 feet in height ; all

water is muddy and dark with detritus. The

Ti after this again rise still higher for twenty-four

t^, but arc yet muddy ; the low-lying lands near the

" are submerged. We learn afterwards tliat a con-

-ublc fall of rain has taken place in the uplands of

ik liver, and that towns and villages in the plains have

■i^Enundated.

Hwch is the flood, its subsidence Is a matter of less
Witent : and such is the type of flood to which those
Musing serious catastrophes generally belong. In this
ftisc we fully satisfy ourselves of the rationale of the
flood ; the lowland water rises steadily and clear, going
pfrtiaps one mile an hour ; the upland water comes
'I'Mi'B with a velocity of nearly six miles an hour and
tihifged with silt — for where else is this velocity and
^i' silt to come from except from its course in the
Itiilif— and tops the lowland water ; the combination of
s gradually decreasing in speed spread themselves
r the land in the first locality, where the form of

*-!□ MISCELLANEOUS PARACRAPHS.

channel and banks admit of it, and perhaps in more t
OBe, extending even for miles beyond the natural b
the river.

How is such a flood to be controlled ? Apart
the Dutch principle, already shown to be fallacious
large scale, there are only two methods, either or t
of which can be adopted. The first, the improvcme
the whole of the natural drainage lines of the counti
such an extent that the velocity of the waters
under such circumstances be increased throughout
whole course of the river, and a little beyond it, into
sea or next large river, and so that tlic natural bed,
improved, may be sufficiently large to carry off
previously known flood, without being exceeded.
second, any means of separating the upland from the
land waters, holding or retarding either the one o
other, or portions of either one or the other, and provf
for their discharge cither separately in different c<
at different times in the same watercourse.

Let us first indicate the nature of the works
quiring execution, when the former principle alo
adopted : the perfecting of the natural lines of dn

The ultimate free delivery of the water into t
or any way entirely free of the river, is pcrhap
most important point of all, the low-lying lands <
loxver ranges of the river being there more extc
than elsewhere ; to insure a free delivery, ihe
outlet of the river should be carried out to deep i
protected on both sides by banks or jetties, a
shore currents, and so directed as to avoid as mi
possible the retarding influence of sea storms ;
the delta, also, a single direct cbanDcl of pn
determined dimensions should be made i

tHB CONTKOL OF FLOODS.

pibankmcnts ; by these means the mass of water

n forcing its way in this course to the sea, scour for

'' 3 deeper bed at the outfall and throughout the

■n ranges of the river, and carry off floods more

Hy, improving the river continually. A further

ige from confining the river to one channel is

tf the reclamation of a large amount of land

jsly occupied by marshes, as well as by the

iDus old channels of the delta.

the middle ranges of the river the works to be

ire all such as will promote a more rapid

: the enlargement of the bed wherever it is
rtcd or narrowed ; the removal of obstacles, rocks,
islands, silt deposits, shoals, or anything that

velocity ; the straightening of the course
rer it can be done to good effect ; the prevention
I deposit of silt in such places as would be
onable ; the deef)ening or dredging of the bed in
juisite places : the whole course to be put under a

that would remain constant generally, and
I continue to improve itself by scouring in contra-
tiun to its former habits of silting up and causing
i levels to rise,

iie uplands, at! the works which should be con ■
1 arc those that have for their object the control
detritus washed down, and the prevention of its
; at unfavourable spots. If the silt could by any
be entirely prevented from being carried down
C middle ranges of the river, or into the plains, it
be X great achievement ; but this being hardly
e, palliative measures are perhaps all that can be
|L Besides this, the hills might be covered with
plantations, which, catching the rainfall, would

^__

■A. .

-Jt <

— -^

■-— *:

' ii : •■

• •*.

n ' ^a'

■*'/•.!'! .r,-.'ir' fK' ;i/!'I;':or;ai idvar.tac^s rfrerfect
?r.r;.-': rjr;iiri*i;y '/f th'; '.ountr>-, ar.i cf ha-.-Ir.^ ;
k-aTr- ijr/r*lv for irri:';ilion

Towage.

: adoption of the tvo prindplcs thus described^

I insure a perfeci remedy and an efiectfre ccwiirol '

~' blinds tinder any practicable dnnimstanccs. Tlial

.'ii woiks would necessarily be expensiiie there b no

' ibi whatet'cr, but ibey would still be less costly i

n: effective than the continuoBs lines of embanki

i^Ticd on the fallacioas principles before quoted :

ilis again would improve the nt'cis instead ofdete

■'■ng with lapse of time, and the gain b>- reclamation

I irrigaticn n-ould, apart fn>m other collateral ad%-an*

iimt, yield a profitable retura.

jHcccnt experiments show that the pull on the tow-

wpe of a barge is, within practical limits, proportional

iKc square of the speed, and that it varies widely ac-

: Jing the form of the barge ; assuming then a general

R = bT V

B is the resistance in lbs.,

T = the displacement of the barge in tons,

Y = the velocity through the water in miles per

hour.
5 a coefficient depending on the form of the barge.

I has been found that for the small and bluff barges

t 70 tons employed on the Thames.and for limits

I not exceeding 5 miles an hour, the coefficient

[, or generally about 0*369 ; and that for welt-

s of medium si/e.

"5F^

rAMAGMAFBS,

lOtO-irO:

I kaises with good lines^Si
e wvc-iopc sj'stem, whiis
E 13^^ tnes dtctr beaic, and aic

-orevsafly aboot 0-109.

IteteftaTipaed far A^ ril be about lo tniles a
tM«. Md fcgiwl Ask bib Hk resistaace & wDOld
«rr vili Ac faiKlh powr of F; but wittim M
issu=»fi '— '-s. ^^:i!sl>:cs Eij- be made on the abfftT

r^ rir^ns: :c bcrses recuired to draw a train of
;i.-^^ Ti^j bno: be r^iiHy dei jced. The best perform-
i.T'^-s :c 1 irxa^t-bccfe anxking S hours a day, is
--.-^rr-ri i" Sr i; oe ^peed ot' jj miles per hour, when
--; V ;.\rr; i^ i-.-sn^ pi^ of about i2o lbs. ; substi-
;»r.*^ ti-- -.il^a; ir. lie iboi^e fomiuia, we obtain for the
:,-r-ii7? izii: -oe bcrie will pull at the speed of !'5

1*0

iri:

= 113 tons.

Ir i -.^rrTfr:. tr:^^ rcfistanct or the pull upon the toi^
.-.-c »■-" :Tv;^i:?e a? the square of the speed through llJ
xtjirrr. bi;: ihs h-x^^e in this instance moving over ttl
s^v^nd is jTv^iT^fT at a less speed than that of the boC
:hr,M;i:h the nawr ; ar.d this is an important distinction
w hkJi mus; not be overlooked in estimating the effect C
A ourrfnt. The mode in which the necessary correctiol
ci\U»t be eiievtcd will be best illustrated by an examplC'

■ Kcfcrring to the la^t example, let as assume that the

: nf 113 tons' displacement encounters an advene

Tcnt of I mile an hour, and it is required to know the

niccd speed at which the horse n-ill then go, assuming

B to be performing the same average work per hour,

I In the last case, the said work in mtle-pounds u-as

X 15 = 300 mile- pounds per hour; in the present

c the pull upon the rope will be proportional to the

i of the velocity through the water ( T), and the

B the horse is capable of pulling will be inversely pro-

ttional to the velocity at which he is travelling (v) ;

I the diflcrence between these two t'elocities will be

ErXpecd of the current (v,) ; we have therefore

V = v+v^ where f,= I mile per hour

Ind Rv = 300 mile-pounds per hour

V'(r+ V,) = 15-4
Hice « = 1 9-4 r». and V - V*= 15-4.

'living which we obtain V = 286 miles per hour, the
■'^cj of the boat through the water; and the speed
--■'. land, or rate at which the horse is going, will be
-Sfi_i = 186 miles an hour.

It n-ill be obser\ed from this example that the in-

tficc of the current is relatively less important when

r^es are employed, than when steam-tugs, either paddic

: screw, arc used, the reason being that in the latter

-.-L- the reaction operates upon the moving current,

Whilst in Ihc first case against the immovable tow-path.

*liu3 in the present example, if the power, instead of

being an animal moving on the tow-path, had been a

1 horse in a tug, the speed through the water would

c smc, whether the water was still, or ever so rapid

14* afISCELLAN£OUS PARAGRAFBS.

a current In this instance 25 miles an hour the
past the land, which is the useful result, would be n
to I s miles an hour in the case of the tug, instead
1-86 when horses are used.

The difference of conditions will be more si
marked if we assume the current to be 25 mites a
because then it is obvious that the steam tug. caps
moving through still water at that rate, would:
simply maintain its position tf it encountered such
rent ; and although the paddlc-wheels or screw
be revolving at the same rate as before, the only
of their effects, namely, the maintenance of posit
the boat, would be equally attained if she dr
anchor ; in short, the whole power exerted woi
thrown away. In the instance of the bar^e tow
horses, on the other hand, the whole power \
would be utilised ; and it may be shown by thf
reasoning as in the last example, thai the 1 13 ton
would be towed by one horse against a current
miles an hour, at the rate of 1 \ miles an hour,

Obviously the same reasoning would apply, w
the motive power on the tow-path were horse
locomotive, or whether the tow-path were dis(
with, and a rope were laid down in the bed of the
and coiled round a drum in a steam-barge in the a
now generally admitted to be the most economica!
of conducting heavy traffic at a slow speed in r
rapid current and on still-water canals.

From the above we may conclude that, in 0
tabulate for the effect of a current on the dirolnu
increase of speed of a horse, we have to calcut
increased or diminished value of F, the velocity tl
the water, and apply it in the general fonnulaF^^
R = ht K»

ing (JifTcrcnt values Tor the constant 5, which lie
en 'I09 and 369, according to the form of the

In the above case R = 120 lbs. for a draught horse ;
for other animals corresponding values of R. witli
: to their best continuous speed, can be applied.
Assuming a case of a current of 3 miles an hour.and
the ordinary limits for the speed of the horse in
tg a toad with and against stream, are 4 and 1 mile
»lir respectively, the velocity through the water
;ps I and 4 miles an hour, and the loads 706 and
fis, the horse performing the same average work-,
Bxeeuting the average pull of 75 lbs. with stream, and
■gainst it

values required are given for the limits in the
(wing form,

For barges having 113 tons' displacement, and a co-
Hit & = 0"I7, the results are as follows: —

1:

^■3

..

In Mill Mllir

to 2-5

3'<»

L

(88
4-38

3-2

2-S

3'S6 3-66
1-86 116

3 '97
■97

1

S-oo

3 '5

IS

1-5 0

-o-S

Icre f, is the velocity of the current, whether
irable or adverse.

V is the velocity of the barge through the water.

V is the speed of the horse.
V, is the velocity through the water for the case

ifch a steam-barge is used, and is given to illustrate
jomparison. The foregoing formula on towayc

i«»

MrsCELLAlfEOUS PARAGRAFHS.

were denounced by a reviewer in ' The Engineer]
apparently the critic had confounded formula for mi
ance with those for horse-power ; yet a reply forwird
to the denunciation was not published in the pa;
referred to. A more important paper would have b(
great enough to acknowledge a blunder : the attenif
to shelve it has not succeeded.

4. On Various Hvdrodvnamic FormuIjE

The results of the various formulse given for dcU
mining dischai^cs, according to various authors, vl
very greatly ; and it is hence interesting to exatnt
them in a tabulated form in comparison with meuoii
discharges.

The following data of comparison are given by 1
David Ste\'enson, and by Captains Humphrey's 1
Abbot ; they apply to four cases of river dischu
from a small stream up to the Mississippi ; tiius tn(
ding all limits within which such formulae are requin

I. For a small stream of 24 cubic feet per sea
Mr. David Stevenson made careful measurements,
velocity obser^'ations, and compared the deduced
suits with the results of formula, thus :

I. Deduced discharge *K^%

J. By Dubuat's formula . ,

3. By Robinson's formula . . . ■ 96^

4. By Ellet's formula .... 40'4»

5. By Beardmore's tables .... 33'9>

6. By Downing's formula, coefficieiit foo
;. By Leslie's formula, coefficient 0'6S .

2. For a r

of 2424 cubic feet per second.

tWnced dischai^e .

Sy Dabual's fonnula

Sy Robinson's formula

By Ellet's formula .

By Beardniore's tabular fonnula

By Downing's fomiuli, coefficient i

By Leslie's formula, coefficient o'6a

^DRODYNAHIC FORMULM.

Stevenson and Dr. Anderson made velocity
on the Tay, at Perth, and the comparisons

S4»3
2987
1560
2033

2769
"83

t unfortunate that in these two cases the hydraulic
would enable us to extend the comparison
» rnrmulae. are not given.

ir a large river of 31 864 cubic feet per second ;
aof the Great Nevka, measured by Mr, Destrem
I follows:

of section 15 SS4 sq. feet ; width 881 feet

31 864 c. feet ; perimeter 893 „
I velocity 2-0486 ft. per sec. ; max. depth 2 1 „
aulic slope oocx) 014 87 :
! following are the results due to these data ca!-
by various formulx and compared with the
^schar^e :

. Deduced discharge

k Young's coefficient .

\ Ejielwcin's coefficient
f Downing's coefficient
J. Dubuat's formula
i. Gitard's formula
J. De Prony's canal formula
L Young's formula

k Uupuit's formula .

31864
»3 3S9

•9 777
'3 4Sfi

msC£LLANF.OUS PARAGKAfUS.

•, St, V'enant's formula
. Eilet's foTtnub

. Humphreys' fonniila

■ 13807
• 3393*

4. For a ver>' large river, the Mississippi at CaiTolti
the measured data at high water in 1851, were.

Area of section 193 gSS sq, ft, ; width 26336
discharge i 149 948 c. ft. ; perimeter 2693 ,

mean velocity S^gaSS ; maximum depth 136 .
hydraulic slope oooo 020 51 ;

and the corresponding results, which are kept in t«ni! '
of mean velocity to lessen the figures, were^

, Deduced mean velocity .
. Young's coefficient .
, Eytelwdn's coefficient .
. Downing's coefficient
. Dubuat's formula ,
. Girard's formula .
. De Prony's Canal fomiula
. Young's formula .
. Dupuii's formula .
. St Vcnanl's fonnula
. Eilet's formula
, Humphreys' formula

5 '9288 feet per second
3:1400 „

38434
27468
4'8i48
3717'

3'»74"
48753

3'49°7
3 045'
S%03

\

A careful examination of these results in fourcasC'
of rivers cannot fail to be instructive.

In the fourth case, a very lai^e river, Humphiq
formula is by far the most correct, and then coB
in order of correctness, Dupuit, Girard, and Dowi
while Ellet and Dubuat are again the worst In t
third case, Downing is most correct, then Dupuit, afteij
wards Humphreys' formula, and Ellct and Dubi
agaiii the worst In tiie second case Ellet and Dubv

^^ftODY.VAMIC FORAfUL/E.

vforst, and the best are Robinson, Beard-
Downing. In the first case Leslie and

; best, and Downing worst
c understood that the formula mentioned as
being more familiar to many under that

ally that of d'Aubuisson, applied to English

vilhout any modification.

Ing the results, the formulie may be thus

WamKatmulx

B«t Fi^muf.

> *4

Downing

Leslie alul Dubual

3434

EUcI «nd Dubmil

Robinson, HciiJinor
Downing

31 »♦

Ellrt «.<! Dubaat

Downine, thipuil,
Humphreys

1149948

Ellel and Dubuat

Humphreys, D
Girard, and Dow

ivitable conclusion from all these comparisons
one of tliese formulae is correctly applicable
r different sizes, nor holds its own equally as
rrectness throughout For the few and special
lich the (Uschai^e of an extremely large river
i, the Humphreys formula might be used
lusly, in spile of its form being rather un-
id in the same way Dupuit's formula for a
t. But for ordinary general purposes the
the practical hydraulic engineer require.s is a
>lcrably well suited to all cases and of a
n, so as to admit of easy rapid calculation.
simple formula having a fi.\cd coefficient is
iwning or d'Aubuisson, which gives for mean
' discharge

K = 100 (fl5)*
where fi = mean hydraulic radius
and S = mean hydraulic slope ;

«S"

MlSCELLjysOUS PARAGRAPHS.

and this, Xoa. is the formula shown to have been ge
ally the most correct throughout all the compart
and discrepancies, failing only in tlie ver>'
streams, and evidently worse according as the s
or discharge is less. This then is the best basic foil
for general purposes, though it requires mo(]i6cadc«
experimental coefficients to answer ordinary i
ments in canals or canalised rivers.

The formulae of Young, Eytelwein, Bcardn
Steicnson, and Leslie, all belong to this tj'pe. mc
using other lixed numerical coefficients instead of ttH

Putting the basic formula into the general form

r = c X loo (fl sf
where c = l according to Downing,

the values of e, according to the other formulx of
same type are thus :

Young, for large streams
Neiille, rivers, velocity<i'5 fiset
., >i"5 feet
Ejlelwein, generally
Beardmore. open channels .
Stevenson, for rivers of 30 cubic feet
„ „ 1500 cubic feet

Leslie, small streams
„ large streams
Downing, Taylor, d'.Auhuisson, for open channels

By comparing results through formula contaS
thesccoefficicnts.wemay then tabulate a scries of vi
values oi c that will be practically correct, when
ably applied into the general formula. The con
before mentioned show that Downing's coefficient

VtODVNAMIC FORMULAE.

»S3

mall results in cases when the area exceeds
c feet, with a mean velocity of 2'5 ft, or a
if 17 500 cubic feet per second, and too large
cases of smaller data ; that the Eytelwein
'934 in the same w^y is too small above and
clow discharges of about 2000 cubic feet per

a& the Young cocfficteiit 843 is incorrect for

J above 900 cubic feet per second ; also that

itreams of 25 cubic feet per second, a coefficient

Soo is tolerably correct

rident then that with a very large number of
.refully measured discharge, this principle of
J practical coefficients in relation to approxi-
le or velocity might be carried out to further
allowances for irregularities, lateral bends,

►rth, being either comprised in or made inde-

f this coefficient

's coefficients comprise all such allowances,
ucc a subsidiary variable coefficient of rugosity,

pplied in the general formula, to canals and

iveiy sort

ithor's coefficients (c) are analogous to Kuttcr'.s,
indent on fixed surface-rugosity coefficients

ted differently, but do not comprise irregu-
bends ; they apply to canals and are not

for rivers.

the above was written, the large hydraulic
its of Captain Allan Cunningham on the
tnal have also indisputably demonstrated that
of the old hydraulic formuljc, including the
nt formula of Bazin, utterly fail in general
I. The variable coefficients, adopted with the

Dodifications in the author's Canal Tables.

*S4 MISCELLANEOUS PARAGRAPHS. ciur U

are declared to be the sole coefficients of general v^
cability. yielding results within y\ per cent, of quuitiCiB
determined by experiment ; while these latter are ut
mittedly liable to an error of 3 per cent, in the castso
the Ganges Canal. The errors due to the old formula
above proved to amount to 50 per cent, and even more
will, it is hoped, not find now any supporters.

To apply the same method of comparison to di*-
charges through pipes, taking the same general formol*,

F= c X roo(ffS)*.

This formula being more convenient in practice in tenni
of the diameter of the pipe (d), it becomes for M

cyh'ndrical pipes, where A'= jJ ; K=c kM \dSy .

And again as the actual discharge is the quantity most
often wanted, this is

Q = .dti = c X 0-7854 d»x 50 (5 tZ)' = cx 39-27 {S^j\

'($)'■

Taking an example to compare the results of ^^
various formula, let Q = \S-57 cubic feet per seco"'*'
when S= 1 in 1276 ; the results then are for diaraete* '-

[. By Duhuat's fomiula

3374

2. By Neville coefficient -318

36-80

3. By the above formula, ccefficient o-jj

37 I*

4, Young's modification of Eytelwein .

37'7

5. Beardmore, coefficient -235

37-9»

6. Hawksley (in Box's tables)

39 59

7. De Prony and d'Arry .

47 ^i

8. De Prony's modification of Dubuat .

48-16

9. Gerney

4884

r tVATBRIS'G OF LAKD. 455

"Qiese, there are very many authors that
e results for diameter ver>' much below that
; it appears also that none of these formulie
lally well to both high and low velocities of
, although it is unfortunate that a sufficiently
ibcr of data are not forthcoming to determine
the limits at which it would be advisable to
le coefficient,

lx>ve comparisons, while showing the merits of
IS formula in certain cases, also point to the
lent conclusion that a variable coefficient of
is necessary for rivers, canals, and pipes ;
it must be suitable both to the dimensions, the
lie fall, and conditions of irregularity of each
case. The best mode now known of doing this
(f canals, artificial channels, culverts, and pipes,
1 in Chapter I. of this Manual. With rivers,
some velocity -observation is indispensable.

5. The Watering of Land.

allowing is the usual mode of classifying crops
rd to their special treatment under irrigation.
meadows, or natural meadows of gramineic. 3
I crops or cereals. 3. I.^guminous crops. 4
ps. 5. Those specially requiring more water
^o, tobacco, sugar, bamboo, water-nuts. 6
r fruit crops. 7. New plantations, and trees.
iarities of climate, soil, and water will generally
! amount of water required for irrigation pro-
tban the species of crop. In England
of grass land, or Italian rye-grass, are those

as* U/SCELlAyEQDS PAKAGSAPtrS.

ihat generally profit mosi from irrigation. The
u^ual plan is to keep the land flooded to a depth of'
two inches during the months of October, Nciv-ember^
December, and January', for twent>- daj-s at a time, aoi
then to let the water drain off from it for five da)\
before putting it again under »-ater. In frosty we»llw
howe\-er, the field should alwaj's remain fioodnl. In
February and March the fields are flooded for cigtil
da>-s at a time at night only : at the end of March ^
land is left dry ; and in May the grass-crop is cat
Irrigating fields in England in the hot weather is liablt
to produce rot in sheep, but does not harm cattle.

There are tw-o methods of laying out the coimesn
channels in English fields :

1, The bedwork system, applicable to fiat land.

2. The catchwater system, applicable to steepo
coantry.

According to the former, the land is made into a seiicf
of very flat ridges, having a genera! direction ncafljrd
right angles to the channel of supply, and being mntf
more than 70 yards long and about 40 feet wide, itx
inclination of the ridge itself having a fall of about 1 ii
500, and the inclinations of the sides of the flat ridgo
varying with the retentive power of the soil, fnim I in
100 to I in 1000 ; the crown of the ridges ts not ikw-
sarily. therefore, in the middle of the breadth of the b;
of the ridge. The feeding and drainage channels J. '
generally from 20 inches wide at their junctions t>i '■
inches at their ends.

The catchwater system used in On'onshirc •' -
Somersetshire consists of a series of ridges made ao'
the general course of the water, which bold the w.v

THE WATERINC OF LAND. 257

tain it over successive long strips, the water
wly round the end of one ridge to tiie lower
the next ridge, and so on. This is neces-
licapcr than the other system — about half, and
ricd out at the cost of about 5ve pounds an

{hout the world generally, there may be said
y four methods of distributing water on or
surfaces, of which all others are mere
5. In all cases it is best that the land
one general slope throughout, the irrigation
mning along the head of this slope, the main
drain along the bottom.

method is that to which the English

tyslcm bclong.s' the field being prepared in

ridges alternately from the head •to the foot

either in the direction of the fall or making

with it, according as the quality of the soil

leral slope of the land may require; tliese

being from 10 feet to 50 feet wide and only

es in depth, receive the water from the

channel, which will then cover tiie land nearly

crests of the ridges, or in fact entirely if

snd method is very similar to the first, but
instead of flowing in the furrows, runs in little
It along the crests of the ridges, overflows the
IS the slopes, and drains off in the furrows
ic main catchment drain. The ridges used in
are generally wider than those of the first
id have a greater lateral inclination.
i[rd e» commonest method for applying water
scale is to distribute the water in little

atfi MISCELLANEOUS FARAGRAPHS. char in-

trenches around smalt squares and rectangles of line!,
allowing it to permeate througbout the surface iiKknH,
which must be very nearly level with the »-atcr in lb;
trenches.

The fourth method, most commonly adopted in
Spain, Portugal, and India, in cases where it is rcquir«l
that a large quantity of water should remain on ihc
land for some time (as on rice-crops, and sevrra! grain
and other crops in their early stages, that could n^i
thrive on hard baked soil), consists in levelling dielanJ
into a number of nearly flat squares and rcctan^!
divided from each other by small ridges or dwarf m
walls, to hold the water on them. The number of «
angles depends on the fall of the ground ; the »
allowed to flow in at some corner or temporary bra
and flow out in the same way on to the next rectai
when it has remained suflficiently long.

As to soil : — For the surface, the most permeaUfrfl
best, being most easily warmed, and allowing the «
to arrive at the roots of the grass most quickly;^
retentive surface-soil causes evaporation, and cools 4
land, which is generally a disadvantage, though r
under some circumstances ;— a subsoil of clay,
retentive, is an advantage in very dry climates, .
cconomiseswater. In hot climates the nature of tbefl
is of inferior importance to tlie quality of the )
transported and dc[)09ited.

As to the quantity of water required for irrlgatii
certain area: — In Piedmont and Lombard/ one e
foot per second waters 50 to 100 acres of mardt^
grass-land, or only 40 acres of rice i in England \
amount required is generally also 1 cubic foot per »
[cr so to 100 acres ; in the Madras Prcsidcnty a

TUB WATER im

North-West Provinces i cubic foot per second
ordinary seasons loo acres of rice, or other
Wet cultivation, but in Mzry dry seasons the duty
i low as so' acres. Taking all the crops watered
ighout. counting single waterings in all, the duty
cubic foot per second is 200 acres both in Northern
Central India ; - the highest duty actually
led being about 270, In Northern India one
abicfoot per second waters 4i lo Sj acres for 24 hours.
But details as to amount necessary in Spain, Italy,
France, for Orissa, the Panjab, and India generally, will
be found in the Hydraulic Statistics.

As to quality : — Pure water is bad for rice cultivation,
»nd i» always far inferior to that which brings fertilising
particles with it. The best water for irrigating land
Bay be said to be that which brings with it a fertilising
"Utter most suitable to the improvement of the land
"Oder irrigation. As a rule, water containing much
l>}>drous oxide of iron is very bad ; so also the water that
'Wtes from forest or peat-moss is inferior. The water
'■'^1 Kimes from a granite formation, holding potash, is
'"J ; so also is water that comes from pure carbonate
' ''me ; if the water is brackish, it is no objection ; salt-
"cr meadows are highly productive, A good method
■ f'irctclling the effects of the water is by observing the
■''ural products of the irrigating water, such as the
'^■l^^es and plants that grow on its borders.
With regard to the temperature of the water, very
'■'M spring-water is not generally good, and crops
""juire careful preservation from the effects of frost in
*'ntcr. Warmed water is generally advantageous, and
"Sitscs rapid growth ; it is partly for this reason that
^aicr that has been long exposed to air, soil, and sun is

i6a MlSCEl^ANEOUS PARAGRAPHS.

more fertilising than it was in its previous coo
Morning and evening are the best times for wa
The long exposure of the water is much affected
inclination of the land ; the inclination of the
channels in Lombardy is about I in 3600, hi P
1 in 1600. in Provence 1 in looo, in Tyrol i ii
I in 300, in Northern India it is generally kept
I in 1000 and i in 2000. In India generally it ia
so to arrange tlie inclinations that the resulting
velocity of current may never exceed three ft
second.

In connection with the watering of the
management of its drainage is a matter of the
consequence. Modes and stj'les
necessarily varied, according to local circumstances
they all have one main object, to keep the circttlat
the water and the air through the soil under {
command, so that the periods of intermission m
so managed as to suit the soil, the crop, aft
circumstances. Any want of good management 0
point is liable to cause most deplorable results ; si
tion, causing decomposition and malarious edccts
neighbourhood, and even, in the case of sewage
making the very crops grown to be useless as I
man or beast

For the healthy support of crops, a certain
of water and of stimulant may be used advani
{see Hydraulic Statistics : Watering of Cropis in Fi
beyond this, any addition is worse than a loss-
positive source of injury — clogging the soil,
preventing it from fulfilling its necessary
With regard to the period of intermission
probably varies greatly ; recent experience io

THE WATERiKC OF LAND. »«?■

fcould, however, seem to show that equal intervals of
mng, and of draining off, for twelve hours at a time,

Hbrd the most rapid way of utilising in irrigation as
h sewage as possible : further experience, however,

^perhaps likely to show that this is not by any means

1 rule to be followed generally in all soils and
I COnilitions.

Asicism€ntof JVaUr-ra /^.—Thcvc are three principles
"" which water-rate may be levied on land.
J. By fixed outlet, or by module.
Tile small channel of supply being constantly full
"'''^ of a certain section, the rate may be charged at so
''"'ch ]xr square inch or square foot of section, indc-
,- ndcntly of the amount of pressure, for a certain time,
' by the hour or day of 24 hours, This has been
'•^[Mct! in Italy, but has not been found to act well.

A further development of this method is to regulate

' niodute all the water when distributed ; a mode more

^*iIyto be adopted at present, now that modules arc

■"•s expensive and more effective than formerly.

2. By area of land irrigated, or by crop.

This has the following disadvantages ; the land to

^ irrigated is alivays varying in amount, and this

^**inoi be watched in detail continually, nor can the

'■ n^owncrs be trusted to state truthfully the amount of

ricigc over which water has been distributed. The

' ■"'? can also be varied, .so as to use more or less water,

■'^'J the payment by crop also would be useless against

^eating. Again, in a good rainy season the cultivator

'^icht try under these circumstances to do without the

^*na.\ water, tlius causing the water-rate to be precarious.

} Water distribution by rotation.

Af/SCELLANEOUS PARAGRAPHS. cmr ii

An irrigating channel of fixed dimension, giving .
constant fixed discharge, passes through the lands o:
several proprietors ; a period of rotation is fixed for this
channel, from 6 to i6 days according; to the crops, the
former for rice and the latter for meadow land, as, for
instance, in Italy. Each landowner can then have tiie
whole volume of the channel turned on to his land ooce
in the total period of rotation for a certain numbcrs£
hours, as from two to forty or fifty according to i
amount of land he owns,

For example. Let ten days be the period of n
and let him require twelve hours' supply once in ll
period. His name is placed on the list, say sixth, t
he gets his supply turned on at a fixed hour and tufw
oft at a fixed hour also. If the channel gives twenty
cubic feet per second, his amount of water is equivalent
,20x12

second. In this way intermittent supplies adtiutfl
mutual comparison.

Last with regard to the cultivators thcrasdvesfl
Whether on the Continent, or in England, the fat
generally a grumbler under any state of afTairs. ;
India the cultivator invariably complains, although!
assessment is very small by comparison with the b
circumstances ; if he grow two very moderately {
crops in the year, it would only amount to about I
and a haif per cent, per annum on the value of 1
produce, and he can therefore well aCTbrd to payfl
water-rates, especially since both the yield and I
number of crops produced on irrigated lajid is d«
and the highest water-rate is small in compwison J
the expense of making wells and raising the !

- !

THE WATERING OF LAND.

afij

imounl of water bj- ajiimal power throughout the year ;
lie enjoys also the advantage of living under a tenure
'::.it itmits the land assessment, and distributes food
: i:ii in years of famine, while not demanding more
asmcnt in years of plenty. If the water-rate is in
5nmc just proportion to the increase of produce and
saWng of expense resulting from the irrigation, it
matters not how high per acre the rate may appear to
be. If the irrigation is applied to suitable land in such
sway that the natural drainage of the country is not
interfered with, there can be no detriment to the health
of Hie cultivator ; this can, however, be rarely carried to
perfection in actual fact To this it can be replied, that
Ibe population will thrive on the whole and increase
ii'^ly, which may be considered as a set-off on that
I '.mmt, and that landowners who prefer going away

■ I" always do so and part with their land at a premium ;
■-'il always commanding a ready sale. A compulsory

■ la-rate nn land that is under water command cannot
' considered a hardship by any one that considers the
:aj«t in a fair, unprejudiced manner ; the privilege of

■ -ing able to obtain water should be paid for, and since
'■■ same principle has always been applied to towa
H'ply of water, for which every inhabitant has to pay
irthcr he uses it or not, there is no reason for leaving

"'■'- payments of water-rate in the country to be optional.
*' iicthcr both the landowner and the occupier should '
i> *cparatc]y for the advantages they both receive is a
int dependent on the local tenure of land; under
"iioary circumstances they doubtless should do so, the
cupicr being benefited by increase of produce, the

mcr by increase of rent ; but i
e of the advantages should be paid for.

any t

; the

MlSCSlLAlfEOl'S PAKACRAPIIS.

6. Canal Falls.

That a fall of water at the headworks, or at s
part of a canal, should be allowed to remain unutilii
appears, in these days of expensive fuel and eo!
motive power, to be a very painful waste of a valoa
advantage One's natural tendency is to devise mc
and ways of using everything, and to imagine thattfa
could hardly exist circumstances under which it wa
be necessary to arrange for the destruction of the po»
and velocity generated by a fall of water. Grindi
com, pressing sugar, or extracting oil, are requireniei
even in semibarbarous countries, by which such mot
power could be easily utilised, even if it were availal
for only four months in the year. In spile of this, ho
ever, it seems rattier frequently to occur, that in disti
countries the engineer has fo devise means for destro^
the effect of a fall of water ; this occurs, generally, dt
at the headworks of a canal, where the water cnte
the canal in flood seasons has a great head of [
or at certain points in a canal where, owing to
inclination of the country being steeper than that ■
to a convenient velocity of canal current, it has tM
found necessary to concentrate the superabundant G
the Ganges Canal and the Bari Doab Canals have ml
such examples. In either case, as the fall is indcpcnd
of navigation of any sort, which has to be conducted
a special channel of d^our, the problem is one
economy. The natural means would be to break
the force of the water by both lateral and vert
breaks and angular obstacles, and to oppose the rem
of the velocity by a pierced breakwater, beyond wl

CAKAL FALLS. 265

ic water w-ouki issue with so small a current as not
) be nblc to cause any damage to the bed and sides of
- -anal, or to cause any prejudicial effect to naviga-

Ihc breakwater, involving an enlargement of the
1 of the channel, and, if a rock foundation be not
;b!c, requiring artificial and carefully made founda-
carricd to some depth, is necessarily expensive,
IS hence generally dispensed with, except under
irablc circumstances.

ihc fail itself is generally a modification of one of
wr following tjpes : —

I, A uniform, or a broken general incline.
, A vertical fall with gratings,
[ 3, A vertical fall with a water-cushion,
f 4. An incline or fall with a talus of boulders, S;c.

b most primitive mode of managing such falls of
s lo conduct it down ^n incline, made as gradual

psibtc, and break up the velocity by a series of
A long reach of rocky bed offers a convenient
opportunity for such a construction, which could be
liewn in the solid rock. In otlier cases, where it would
require building on artificial foundations, the expense
'•ould be ^-ery great ; and, even if the incline were so
Hade that the resulting velocity were not high, the
edges of the treads of the steps, even in good stonework,
•oold soon wear, and the maintenance of the fall would
■Inbcctimc an important item of expense. Apart from
[hoc objections also, this type is unsatisfactory. Al-
Uioagh the treads of the steps may be set with a correct

I inclination, so as to oppose more directly the
I direction of motion of the momentum of the

366 M/ACELLANEOVS PARAGRAPHS

water ; and, although a further improvement mijf
made in giving a more considerable reverse inclini
to the treads, and by allowing a large pro[>ortion of,
water to run ofT laterally and wind down the steps;
under all circumstances the inherent defects rcmainj
steps cannot accommodate themselves to the varil
of the quantity of water passing down the fall ; tf
steps are small, tbey fail to receive effectively the I
falling water when the amount increases, and bet
then comparatively valueless ; if the steps arc veryli
the rise and tread of each step causes the stk
acquired from each step {which, it must be rcmeml*
increases in the ratio of the square of the height of
step) to be very much increased, and to become
destructive to the stonework,

The next improvement on the inclined type C
is the ogival fall used on the canals of Northern II
in this the general slope of descent from the h«
the foot of the double curve is from one to six 1
in nine; the upper one-third of the slope bcin|[
chord of the upper or convex curve, which is tangcml
to the surface of the water in the upper reach ; and thi
lower two-thirds of the slope being the chord of ih
concave curve, which is tangential to the convex I
above, and tangential to the horizontal line at itsfl
extremity. The height and tcngtli of the fall appUf
to any special case is determined by equating t
charge of the open channel abo\'e with the (
over a weir. The principle which this form of D
tion asserts is that the water at the foot of the c
being deprived of all vertical action and dcliv
zontally, will not cause any damage to the 1
channel in the lower reach.

CANAL FALLS.

j67

In canals where it is required that the discharge

'iild remain perfectly uniform and unaffected by its

' : down the weir or incUne, an ogival fall must neccs-

■i!\- have its siil raised above the level of the channel-

■1 of the upper reach ; as would also a fall of uniform

■■pc.

Curves on more carefully eliminated principles have

(I been tried with the object of effecting some im-

"vcmcnt, but the advantages resulting appear com-

r.ilively small. These curves generally effect, no

"'ubt, some saving of masonry in comparison with that

' r a single uniform slope, and probably deliver the

iter with less destructive result than the latter ; they

-t, however, stili expensive, and the action of the water

ii'''<:red is rather concentrated, and hence destructive.

^" attempt at economy on such falls has been made by

■'smiwing the fall, and thus diminishing the amount of

masonry ; but the results, caused by the increase of

action as well as irregularity of effect of the water,

f'-inire greater expenditure in repair ; they present also

'■'-'^ ■idditional disadvantage that during repair the whole

' ■'! instead of a part has to be stopped.

In the above cases of inclined falls it is supposed
■' ^t it has been found convenient to concentrate the
'I in a comparatively short length ; in other cases,

Ie it is spread over a long reach, it is usual to
ipt to annihilate the velocity resulting at the foot
e incline by introducing a reach of canal having a
ie slope ; and in cases where a greater length still
be allowed for the incline, to break it up into
MS of descent, each followed by a portion with a
'^'ctfe (lope and then a short horizontal length, thua
I'l'osing the accelerating effect in detail without allow-

268 MISCELLANEOUS FARAGRAPllS.

ing its results to accumulate. In such work Ihe I
tlie channel must necessarily be paved ; ir tl)c vela*
do not exceed 1 o feet or 1 2 feet per second, large n
convex boulders, laid dry. form the most suitable pavl
and even up to 15 feet per second the same t
may be adopted if ver>- large boulders atone are u
beyond that velocity the boulder work requires packi)^
with shingle and pebbles, and grouting with good b
draulic mortar.

While the above arrangements may destroy a i
deal of the velocity, there is perhaps almost alvn
certain amount of it still remaining at the foot «
incline, and should the channel at this place hapj
be in soft soil, further arrangements, tail-w^l^b
wood spurs, or piles, are also necessary.

The Ban Doab Canal tail-walls offer an <
illustrating such a case, the arrangement beinggi
as follows : At the foot of the incline the bed C
channel is made horizontal for some distance,]
banks are then splayed outwards in a curved form d
the top width of the channel at water level is <
wider tlian before : this, giving additional wata-4
reduces the velocity ; the channel is then nar
nearly its normal width by walls of dry bouldt
each side, which project fnto the stream at an tncUi
of I to 5, and slope longitudinally with a fall of t u
from their commencement, where their height is D
full supply-level, down to the level of the bed :
are, of course, totally submerged at full supply, I
produce the effect of concentrating and directuif
current to the middle of the chaimcl. The objec
raised to these tail-walls as employed on the Ban E
Canal is that the}' do not appear to answer thdr |

CANAL FALLS. 269

<^Pficicnt!y completely, and it is supposed that by
■■ I the ift-hole arrangement, both the enlat^ement
'.he reduction of section, a greater length, it would
answer all purposes ; this, however, would add
•;y to the expense.

'■ '•■rtUal fiiUs with grating^s. — This is one of the most

oinic and convenient modes of dealing with a

r'.-falL The sill of the fall is not raised above the

1: of the upper channel and the whole section of

iv-agc U hence unimpeded by reduction ; the grating,

Mch may be placed at any slope from r in 3 to t in

ptcseiits a large perforated surface to the action of

iiatcr, thus keeping the upper water up to its proper

I, and distributing the effect of the falling water

ing through it on a long portion of the bed,

inishcs the action to such an extent as to render

:iirmless. The gratings are supported on cross

iiL'r*, which again rest on masonry piers or iron

iJiions, erected at about 10 feet intervals along the

.? of the fall or weir. The higher a fall of this

ription is. the more truly the water falls and the

' w manageable it is. These gratings require clearing

liJonally, and hence necessitate the attendance of a

■ : but as frequently there is a lockman to attend to

-neighbouring lock, for tlic navigation passage near

f-ill, there is no additional expense incurred on this

um, as one man can attend to both. This type of

" admits of comparatively little variation in design.

VertUai fails tvith waUr-cushioiis. — This is ihe form

'^niUy adopted by nature in discharging water down

! 'il ; the action of the water scours for itself a basin,

' i;h fills and forms a natural water-cushion, the scour

■I'mumg until an equilibrium is established beiwcen

t;o MISCELLANEOUS PARAGRAPHS.

the force of the descending water and the res
offered by the depth of water in the basin. T
itself has a tendency to approximate to the ^
the force of wind and spray from the falling «
making it slightly overhanging, and in some c
causing a retrogression of fall, and coincidently al
retrogression of water- cushion, thus giving it sn d
gated form ; the scoured silt, or debris, is deposits
the bed of the stream lower down.

The most natural mode of designing a vertici
with water-cushion for a canal would perhaps (
on a consideration of what sort of fall nature i
make for herself under the special circumstancetl
conditions of the case, and what improvement!
modifications of that would be necessary. The c
tions to allowing nature to make her own !
water-cushion are these : — first, it requires ti;
this, in some, though not in all cases, is an objcctJc
itself ; second, any want of horoogeneity of the s
rock would result in an irregular form of basin, wl
might become almost unmanageable ; third, the \
and silt deposited in the channel below would 1
serious injury to it ; fourthly, the retrogression <
fall might eventually undermine the weir or t
cause its entire destruction. But this ktter obj
might be very easily counteracted by pro
measures.

In cases, then, where these four objections c
removed or are unimportant in result, there is no it
why a natural or a slightly modified natur^ fa|] )
not be adopted. When the soil is firm or of b
gencous rock, a great deal of the objection i
a certain amount of excavation and trimming <

CAlfAl FALLS.

made as to aid in the natural action, and lateral

.ichmcnt may be easily provided against ; a tolerably

. IT basin can tlien be economically made.

A? to the form of basin beat suited for a water-

I'^n. the breadth in plan should be rather wider than

L \trcme breadth of the falling water, as the wind

. L-:af the latter considerably to one side ; the length,

r , will probably vary from l^ to s times the breadth,

ugb it would hardly be advisable to make it quite

ngular in form, as the comers would be filled with

u^eics* water ; the pear ahape, therefore, is perhaps the

beK. and is certainly that moat generally met with

under natural conditions of homogeneity of soil. There

jIJ probably be no advantage, even if it were

i.mic, lo make the basin longer; the full or

L-ii-: depth may be terminated by a reverse slope

ICC, the deflected velocity thus obtained producing

r'Mter degree of stillness than the passive effect of a

,-r continued full depth.

The main point, however, is to determine what depth
ateir is necessary in a water-cushion. The velocity
ii-Uvery is evidently dependent on the depth on the
■ lill or fall above, and the height of fall down to
•urface water in the basin ; the resistance is the
!h of water in the basin, and the quality of the
!'rial of which its bottom is composed. If, then,
- depth be calculated by equating the forces for a
'iiii producing equilibrium just clear of the bottom,
■iQlain an expression, involving also an assumption
'■ tlie bottom is perfectly indestructible. It seems
"rfotc, impossible at present to determine absolutely
' actual depth necessary ; and hence the practice is to
-■mvt an approximate calculated depth, and see how

17* MIXCELLASSOUS FAKAGJiAPHS.

this answers its putpose, altering or adding
until it appears to be satisfactoiy.

The formula generally used for this purpose oo
canals of Northern India is —

d ■ the depth of water in the basin ;
Ai =the total height of fall, including A,;
A, = the depth or head on the weir sill.

This is probably very limited in its range of applicatn
for, in applying it to the well-known case of the projoc
Mahsur reservoir dam, designed by the engineers of
Madras Irrigation Company, it yields results t
small in comparison to tliat allowed by the cn^DM
thus, for values of A| = 43'5 and A, = 6 feet,
calculated value of d, suitable to a brick bottom,
about 1 8 feet, while the engineers have allowed loi
hard rock bottom a depth of water-cushion of 33
in this instance.

In a second instance of the same case, the foro
gives for values of A, = 16-81, A,= 8-5G, ii= 12-34, <rf
is very much less than that allowed, 16'ig feet; tbit
^so in hard rock.

Major Mullins, the Consulting Engineer to
Madras Irrigation Company, when commenting on A
cases in the Proceedings of the P. W. D,, for April ll
refers also to a well-known natural fall as an illustnl
of the insufficiency of the above formula. The Hi
Fall at Gairsappa, with values of A,=h29 and ^■
feet, would, according to that formula, require a it
of water-cushion of only loS feet for brickwork,ar
for stone, a depth nearly a half less than the
depth, 130 feet.

CANAL FALLS, >73

b a smaller natur^ case, in hills in Berar, coming
f the observation of the author, for values /i, =26
UmIA,= 1, the depth, according to the above formula;,
would be for a brickwork bottom 765 feet, and for stone
S4 feci ; whereas, in the soundest of basalt, the actual
depth was as much as 8 feet, or more than a quarter
niwe than that calculated.

It would, therefore, appear that the above formula,
J^Hrt from its varied coefficients for brickwork and
stone, is generally defective, and that, until a very much
IT range of experiments and observations is made, it
d be more advisable to approximate to such depths
I obtained under natural conditions, than to follow
mula for determining the depth of a basin serving
rater-cushion.

I practice it would rarely be necessary to construct

er-cushion of very great depth, the fall, if over a

eing generally easily broken into three or four

, and it being advantageous to do so, as the

lels are convenient for affording a supply at

IS levels ; probably, therefore, the above-mentioned

I 43'5 feet of artificial fall may be considered as

e for which a water-cushion would be required.

^ future, too, the waste of such a large amount of

\ motive power will be deemed a barbarism, an

tfial reason that there is not much probability of

c ease being exceeded.
tUnes and falls with a talus of large blocks. — Under
circumstances it is not advisable to terminate an
fc with a long reach of ogival tail-walls, or a basin,
kapply any of the foregoing methods to the foot of
I foil. The velocity of tlic water having to be
ctcd, presuming that it cannot be utilised, an

'U

MlSCEllAKEOL-S PARAGKAPHS.

alternative method is to allow the velocity to <l
itself by impinging on a lar|;e number of huge b
and masses of stone of considerable weight This a
was tliat adopted by Messrs. Fowler and Baker inl
improvement of the Nile Barrage ; a most unforla|
dam constructed by the French at an immense cx]
which failed to effect its purpose, otherwise 1
serve as a bridge, until it was entirely remodelled
English engineers.

7. The Usual Thickness of Water-pipes

The thickness of a water-pipe is a matter dept
on practical considerations, being comparatively I
affected by the theoretical determination of wU
should be in order to resist the pressure brought c
and is, like a very large number of the so-called c
tions of the engineer, made almost entirely d
on prescribed custom. The following notes 1
formulae in vogue are. hence, not given so mDch I
the object of elucidating the principles as that f
formulae themselves, valueless as they seem, should be I
available for reference.

The largest scale on which a watcr-ptpe to r
extreme internal pressure is made is that ofthecyltDden \
of hydraulic presses : in these the extreme wotVir;
pressure is limited to 4 tons per square inch, the cjttn r-
permanent strain allowed in actual working being t^i"/
one half of that ; and the thickness of the <
pipe is determined by the formula of Barlow—

(=

TffJS TUlCKyESS OF PtPES.

*T5

And r arc the thickness and internal radius of
•icr or pipe,

IS the cohesive strength of the material, and
IS the internal pressure, both being in tons :

,.( ral principle asserted In this mnde of calculation
ihat the strain on the material is greatest at the
.'. surface, and less beyond, the extension varj'ing
•J square of the distance from the centre.
. I example of the application of this formula, to a
'i cast-iron water-pipe, is given in Box's ' Hydrau-
■ le results of which are as follows : —
, .uming the cohesive strength of cast iron to be 7
3(u pcT sciuarc inch breaking weight ; the extension E,
k the inside ring at the moment of rupture, for a
Si»Eth=l,

■■=■000 165 IF+'OOOOIOS ]f»xi=0OI 659 7;

:ii>: extension at any distance from the centre is in
i!:o of the square of that distance to that of the

ring.
'. .le strain, at any distance from the centre, is then
''uincd from the extension by the formula —

V.-000 010 3xZ

f 64-16

:)-.

■01

iijc mean strain on each theoretical concentric ring

i-.taJ is the average between that at its external and

'lis internal circumference; the bursting pressure has

ben the same ratio to the mean strain as the thickness

»pe has to its radius ; and tabulating these for

i cast'tron pipe, they are ; —

■

»76 MISCELLANSOUS PARAGRAPHS. (^H

^ss-"

Sloin«.lheMcDa

I

M... Mm. M<«i

70 5*6 6-130
7-0 4-09 S-40!l
7-0 y^ 4-8*7
7-0 a-6s 4-359
7-0 j-io 397»
7-0 1-8S 3-647
70 i-to 3373
7-0 1-37 3'37
7-0 119 a-93i
70 1-05 3-749

The

given for

ivhere ff
of the pip

are calcu
Thetl
a water-p
of process
on the top
ron wate
ir have a
diameter,
md inexa
The c
Mr. Bate
Engh'sh s
Jce thinn
•estrictior
Jrauh'c E
n accord

■

practical empirical rule, however, that is
the thickness of water-pipes is —

s the head of pressure, and rf is the d

le, and it is according to this that mos

ated.

fieoretical mode of arriving at the Ihid

pe is, therefore, about the most unsati
es ; and it w-ould probably be useless to

r-pipes arc about those given by this
thickness of one-fifth the square roo
and a little more to allow for defects in
clitude of bore.

Imensions of the pipes used at GU:
man (sec Appendix) have been h*
andards for some time. In Continent

1

er large pipes are used ; those dcsjgne
s by the author for Rio de Janeiro, wl
gineer in charge of the waterworks, wei
nee with such practice. See Appeodi

fVB TmcjexBss ofi pipes.

aM

die in the case of cast-iron pipes of all soits,

\ has always been a tendency to theorise, and to

I thickness on the laws of pressure, and extension ]

Ltcrial : in stoneware pipes, this has been almost J

fely disregarded, and a thickness is generally giveaj

I that is established entirely on practice or usual .1

I, and often varies according to the caprice of the ■

■ or manufacturer. This is generally accounted

|f saying that earthenware or stoneware is a very

ible material as regards strength, while cast iron is

cneous, and is very much alike in substance : a

le reflection, however, will show that this is hardly a

idcnt reason. Carefully- made stoneware, after a

y careful selection, may be, and often is, exceedingly

Uble, while the variety of qualities of cast iron —

X especially since its high price has brought such a

le amount of very inferior material into use — is now

y marked ; some cast iron being known occasionally

P&U to pieces from its own weight. In spite of this,

p manufacturers of stoneware pipes still consider them

QStiiled to the discharge of water under pressure, or

t drainage in cases where the outlet is liable to be

d ; and although they can make pipes that will

y bear a head of 40 feet, yet do not recommend

Q. alleging that the joints cannot be made to stand

I' pressure at all. There is, however, no reason to

lot that under skilled superintendence and manage-

'■, stoneware and fire-clay pipes, as well as their

Pots, may be well enough made to serve most efficiently

r the distribution and drainage of water under tow

s,and that a considerable saving of expense may

■■fleeted by dispensing with iron in such cases.

mSCElLANEOUS FAfiAGSAFtlS.

8. FiEiD Drainage.

The drainage of the surface water of a field,
part of the general drainage of the valley or cj
in which it is situated, is necessarily partly d
on the conditions of that general drainage, th^
sions and fall of the watercourses, ditches, chani
rivers, their straightness. and dtstribudon of
also on the position of the field with reference
land in the same catchment, the drainage fn
may pass over or tlirough it in various ways.

In the second place, the drainage of a singly
dependent on the geological formation at the
distribution and superposition of pervious ani
\-ious strata, their undulations, configuration,
lentive qualities.

Any interference with the general dralnag
country by proposed works of improvement is i
requiring the professional aid of the hydraulic i
while in the same way any intended alteratia
subterranean flow and conditions of moisture
operations of marsh, bog, or spring drainage as
strata, boring, intercepting deep drains, small
&c., require that the hydraulic engineer sliould
a hydro-geologist.

The drainage of any single field may be aa-
altered or modified by works or operations
kinds, that any special drainage or series of di
the field itself may be entirely unnecessary, ai
may be thus rendered thoroughly fit for all the
of the agriculturist

Treating far the present all engineering »i

TfSLD DKAINACE.

■ Ini-gculogical operations as external matters, which
v-4\.\\ be cither impracticable, not beneficial, or exces-
«ire!y costly, and supposing that the actual state of the
Etncral drainage and hydro- geological condition is
n^crately good, and incapable of much improvement,
. -nay yet happen that a particular field may suffer

■■-■■\ insuRicient drainage, or may be improved by local
lif-iiiiage, or simple field-drainage.

The totidition of good cultivable soiL^As the object
of ioch drainage is to put the cultivable soil in the best
p1^^ible condition, the first consideration is the quality

'iicsoil. Should the soil be exceedingly porous and

M, it may be deficient in retentive power and require
'.Linsolidation, top-dressings of clay or marl and careful
nwtllgemcnt ; under such circumstance* drainage would
f« hurtful, and deep -ploughing should be avoided, unless

'h the special object of subsoiling, or improving the
by admixture with the subsoil turned up. Such

I ! benefits by irrigation, and the accompanying infil-
'f»!ion of clayey particles, and liquid manure in the
*^iL If on the contrary the soil should be exceedingly
ftttntive and clayey, water or rain lodges in the soil,
thills und binds it, rendering it unfertile and hard to
'Ditivatc: Such a soil would benefit greatly from field-
[jaim and deep-ploughing, admixture of porous soil or

V-

e are the two extremes of condition of cultivable

profiting least from drainage and most

I, the other most from drainage. Apart

: composition of the soil itself, the climatic

ions, and the amount of r^nfall, snow, dew, and

ihoic moisture affect the greater or less demand

I

»

ano MISCELLANEOUS PARACRAFi

In a hot diy country, a retentive soil is fa
to the growth of rice and many wet crops that
in a semi-marshy state, and require very slow di
in a moist chilly climate the same soil would
the most thorough drainage in order to grow
roots, or pulses. Between the extremes both of
of soil and of local moisture there is an infinite
in degree, and the agriculturist has therefore
his requirements as regards drainage in accon
the conditions and the crops he wishes to g
lute stagnation is invariably fatal to crops,
rice crops in India, rot will result ; a certain d^
circulation is necessary everywhere. In Englsni
Is a large amount of land that is, either natui
through repealed deep -ploughing, sufHciently c
admit of full permeation of rain-water to a great
and thus capable of growing the ordinary crops!
country without special drainage ; the greater {
the land, however, is less favourable, allowing w
lodge in it within a few feet of the surface, aij
necessitating field -drains.

The condition of soil aimed at is an imititfiotl
which is naturally most fertile ; the r^entiot
moderate amount of moisture, a free permen
irrigation -water or of rain -water downwards
sufficient depth in wet weather, and a corrcsfi
free capillary upward movement of moisture
weather or in the periods when irrigation is susp
the dispersion throughout the soil of air, m
volatile gas, and the soluble ingredients of acconi{
fertilising manure, whether natural, chemical (
ficial.

Depth ofactivt toil and of kumus. — Such be

PISLD DRAINAGE, SSV

ral condition requisite, the first and most natural
stion arises, how deep should such a soil be, and ta
I depth is drainage advantageous ?
The depth of active aerated kumus that will support
advantageously is a most variable unit ; it is
nerally believed that the greater the depth, the more
tile the land, that crops augment in yield by every
Iditional inch and foot of humus. It may be so ; but,
ilcing an extreme case coming under my personal
rvation in a province entrusted to my chaise, a
spth of from eighty to ninety feet of soil on the banks
f the Puma in Berar did not yield markedly better
I oops than in other places where the depth was half of
o in other cases, frequently noticed by myself
in the earlier days of my experience in irrigation as
exceptional, but afterwards considered very common-
place— where cereals were grown under irrigation on
pure sand, and on very nearly pure sand. A lai^e extent
•tf such land is irrigated, and at the end of the year, a thin
surflce crust of half-formed humus is formed ; the crop
^that year is zero in one respect, usually consisting of
©*SB seeds, &c, that on growing form a spongy layer of
'**<*t!and verdure, useful in arresting and binding the
■'Unius. But in the second year, under the powerful sun
**'^ India, and by the aid of careful irrigation and good
°**tiagemcnt, a very inferior first crop of cereals may be
^*^Wn. In the third year a moderately bad crop is the
'**'>lt. and afterwards excellent crops of wheat and of
'*"'er kinds of produce, that can exist without throwing
"^'y deep roots.

In such cases, the depth of humus and spongy crust
^^B'ither can hardly exceed three inches or perhaps four ;
''^ splendid crops are grown.

l^^^^fc

At Danzig on the sewage farm, excellent crop^
vegetables were grown under rather similar condition
it is not necessary to mention many such well-kn" •
cases on English sewage farms, Aldcrshot, Edinbiir
&c. It may hence be considered that world -wi*^ -
experience has disproved the old theory about def
humus being the main source of fertility. It is i
therefore, only one of the sources, and its imp«
is frequently outweighed by otiier conditions, :
especially by the depth of active soil

In England moderate crops may be grown i
inches of soil on stiff land, but for really good i
depth of three times that, or eighteen inches, of t
aerated soil may be considered a suitable miniJ
The maximum may be determined by the exl
depth to which roots of grass and grain crops axe (
to penetrate, about seven feet in thoroughly-dri
active soil.

Defili of JUld-draim. — Taking the two extreni
eighteen inches, and seven feet, as suitable to fim
in England generally ; the minimum depth for {
drains, out of reach of the plough and not anectina
crop, by reducing the productive area, should be 2M
and in strong clay lands four feet. It may be nol
that water does not permeate truly horizontally, \
lateral direction from the bottom of the active soil fi
field-drain ; but in perfect drainage should desfc^
slightly in its lateral movement to the bottom of ''
field-drain ; hence the necessity for placing the dra;..
lower than the bottom of tlie active soil. Li'
conditions, depth of soil and subsoil, and econt"!
considerations form the guide to determining i
greatest depth at which field-drains might be |'i-i

W.IUELD DRAW AGE.

apart from diem it would be diflficult to say what would
be the extreme depth that could not be advantageously
«c«dcd under special circumstances.

Vny strong clay-lands, with drains cut in the subsoil,
ivould certainly be worse for having them very deep ;
I lut, keeping in view future improvement of the suD-soil
■ ly disintegration — as well as economy of labour, it
ipfcsri seldom necessary to drain beyond five or six
Let in depth unless in boggy retentive land, and even
* ii^n a few extra deep drains may be cut without inter-
I'.ing with the ordinary field-drains. The limits thus
'between 2\ and six feet. Such general limits can,
l'0*ei'er, constitute merely a rough guide in connection
"iihthe special objects to be achieved, and the local
"jcumstanccs. Drainage pure and simple has for its
nain object the removal of sub-surface water down to
'ume or any practicable depth ; but another object is
i^tn blended with it, the further improvement of the
ubsoil, and the increase of depth of active soil, in the
"^aycy and stiflf lands to which drainage is most fre-
iwntly applied. Some stiff subsoils are so impervious
wd hard as not to admit of improvement by drainage ;
Ti such cases the field drains are perhaps best placed
■■ i'h their bottom just on the subsoil. Much good clay
-iitaoil will, however, under drainage, alternately wash
i-id contract, and gradually break up ; a most desirable
-^ngc that may be much aided by extra deep
'^i^ching with steam-power ; in such cases the field-
'fain-solcs may be sunk to a foot and a half in the
"Jli»il, or even more when accompanied with subsoiling
''iteration*.

Diitanas betu/een field-drains.— "Xht: closeness of the
^il-dmns to each other must be determined so as tu

MISCELLAXEOUS FASACRAFUS,

afford sufficient active permeation of moisture t1
out the whole of the intervening breadth of land ; tl
will depend on the qualities of the soil and ■
down to the level of the sole of the field-drain, t
drains being closer in stiff soil and under conditions \
heavy local rainfall and further apart in more open s
and a drier climate. In England the distances betwt^
the parallel lines of field drains usually adopted i
from fifteen to forty feet ; in any special <
tance should be based either on the evidence affotdl
by actual drainage in the neighbourhood under simOl
conditions, or on partial experiment on the spot
size or dimensions of the field-drains may be detcrn
in the same way, but this is naturally dependent tol
certain extent on the sort of field-drain adopted.

Tlie alignment and length of fidd-draitts.—K fi
may consist of several planes, or several fields mayfl
in one general plane or nearly uniform slope; 1
under all circumstances the field-drains, being set I
some certain depth either below the surface, or I
subsoil surface, lie in a plane or planes nearly pati
to those of the fields. Each plane has therefore to I
treated separately as regards the alignment of the fiet
drains. The main drains, into which the fie!d-dnt:r
run, are necessary at the bottoms or lower edges n
these planes, and afterwards unite and run failo
some watercourse or general drainage-line of the
country, at a point sut^cicntly low to secure suffident ii
outfall.

There are three modes of aligning ficld-druins,w
under all circumstances are arranged in paralld lin
each separate plane, and besides at uniform or i
mstely uniform inclinations. The r^ularity of i

^^B|r in rather steep ground be attained by setting out

^^H soles of tlie field-drains witti the aid of boning

^^HIks, the A level, or some rough spirit-level ; but on

^^Hght inclines a small Gravatt level is absolutely neces-

^^puy. The first and most common mode of alignment

^P is to direct them on the lines of greatest slope from the

H lop of a plane to the bottom ; such lines maybe long

I even as much as 300 yards, while the distances apart

■ way be from fifteen to forty feet as before mentioned

I in accordance with the soil and conditions : the drainage-

' iclion is then entirely lateral and works by permeation

i'lloihe field-drains, which transport the filtered water

liiiu the main drains. The second mode is termed cross-

irTiinagc, the parallel field-drains running across the lines

■f greatest slope, that is being nearly horizontal, having

I flight fall towards the main drains : in this case the

■vmcalion is aided by gravity, and may be more rapid ;

■ ■; licld-drains intercept the filtered water, and conduct

if> the main drains at a comparatively slow velocity.

': ic third mode, generally preferable to either, is the

i^htly oblique method ; the field-drains are only slightly

i;!ined to the direction of greatest slope, that is from

iL-n tr> twenty degrees, and are supplemented at long

intcr\a!s, of about one hundred feet, by cross -drain 5 that

arc nearly level. In this case both the preceding modes

Bdniinage-action are employed ; gravity assists both in
t lateral and in the transverse permeation, and inter-
pK>on< b adopted to a small extent.
In comparing these three methods, it may be noticed
that the first is that most usually adopted in England,
and is generally far preferable to the second. The
permeation is, no doubt, the least rapid part of drainage
action ; the filtered water nn arriving at the field-drain.

386 AirSCELLANEOUS PARAGRAPHS. CIUI u

when in good order, rapidly runs into them ihroti^ th:
joints, and still more rapidl)' is conveyed away. Kocpmg
this in view, any check in the permeation due to any
accidental circumstance or shortcoming wiU evidently
produce a check in the drainage of a whole plot F''
instance, the distance between the drains may be sligh'lv
too great, the depth may be slightly in excess, the «"'
may in certain places be less permeable than in othfr%
a drain may become rather clogged. Now when tht
first method is adopted, the plots are very long nami'^
strips, half of the water from each strip going Utersllv
into each field-drain, one on either side of it ; and should
the permeation be accidentally retarded, a middle por-
tion, perhaps flie middle third, of the strip remains in an
inactive condition. The length of the strip may be
long (zoo or 300 yards) that permeation, aided
gravity in the direction of the main drain, is almost
of the question ; and here lies the defect
method.

The second method has no drains along the di
of greatest slope, but places the whole of thefield-di
as intcrceptcrs, but putting them at the same disi
apart as in the first method. Il is true that with
method gravity aids the permeation, but as the pei
tinn in each strip has to act over the whole
breadth of each plot, instead of over half of it each
nothing is gained ; in fact it is rather the reverse
action of gravity is an aid, but not a very lar^
from many observations we may see permeation
successfully against gravity, as in the lines of damp
sides of ditches, the rise of damp in walls based
damp foundations, &c.

In order to make this method as cfHcacious

1

Mcr. S FIELD DRAINAGE. ,g^

•; as the former, the distance between the field-drains
iild be reduced by about one-third, and this means
Laving half as many drains again, and adding one half
more to the cost of the drainage.

Experience has proved not only the truth of this
deduction, but also that, even when the field-drains arc
placed still closer, the drainage efifected has not always
been thorough, and re-drain^e on the first or longitu-
dinal method had to be substituted in the end after the
dearly -bought experience.

Cross-drainage on this generally unfortunate method
is, however, specially applicable and advantageous when
. the upper strata contain much water and either crop out
across the line of greatest slope, or discharge their water
in natural furrows existing on the surface of the sub-
soil ; in that case thecross-field-draina actas intercepters
to the fullest extent, and collect water readily as it comes
forth, although not perhaps setting up a draining per-
fneation in the strict sense, as their influence on per-
meation in the subsoil cannot be very lai^e

The slightly -oblique metliod preserves the advan-
tages of the longitudinal method as regards lateral
permeation, and remedies its defect in longitudinal
[lermcation by the obliquity, which also aids in intercep-
tion ; the occasional cross-drains at about loo feet apart
still further aid the longitudinal permeation, and assist in
rendering the whole action complete and effective even
under the incidental shortcomings that may occur any-
where and in anything.

Tht t^riaus sorts of fUld-drains. — The object, the
disposition, and the depth of field-drains has been dealt
the preceding paragraphs, independently of
[f actual form, sort, or construction, under the piemisc

aSS msCELLANEOUS PARAGRAPHS, atx

that they are sufficiently large, porous, and well-
structed to carry off any effluent drainage, or filt
water, that may arrive and enter into them. The
of drain adopted is necessarily in accordance with I
circumstances and economy.

The oldest method was one of simple ridge
furrows, for carrying off surface-water, subseqm
deepened to carry it off from a lower depth, and I
with porous soil or porous material. Such shi
drains interfered with ploughing, and reduced the el
tive cultivable area. Deeper sub-surface drains, cov
with good soil, and leaving a flat surface equally
ductive everywhere, have long supplanted the
method. More latterly, porous cylindrical drain-p
from 2 to 6 inches in diameter, with collars, have I
usually adopted, in preference to other means ; and tl
placed at the required depth, and covered to a si
height with porous soil, and finally with a good top
have been considered the most effective ordinary xat
This may therefore be considered the tj-pica!
method for many years past, though not the
modern one. It is well suited to clayey lands in
land, and to the condition that the pipes can be cb
made or bought, and the clay dug out of the drains
be profitably burnt to form manure, or nude i
locally.

Previous to the general adoption of cylindrical p
pipes, large drain-tiles, horse-shoe shaped in sccti
inches high by 3 wide, with flanges, sometimes re-itii
separate tile-soles about 5 inches wide, and
merely on the clayey bottom of tlie trench, were \
monly used; this arrangement developed into the
bottomed cylinders made in one piece, that arestiU 1

FIELD DRAINAGE. iS^a

iotne places, tiles of dried compressed peat may be
ffective in field-drains, but the peat must be tough
lus to resist the action of water. In others,
^ and brushwood form a field-drain of an economical
I fen'IaiHla, where the materia! is cheap, and the
a water is slow.

B drains, of rough stone, so arranged as to give
e interstices below, and filled up above or covered
Jlstnaller stones above, are also economical in some
s ; but the method is inferior, and the damage to
ii by carting stone over it forms a strong objection^
> slow drainage, cinders, gravel, or other porous
trials are far preferable, from being more effective
Bl longer time and from being lighter to transport.
I Many of these modes, though lacking permanence, are
Ih'c for a considerable time, and, being inexpensive,
it of renewal after a few years without prejudice to
my. One of the most important considerations is
^txtent to which they become deleterious or hurtful
\ becoming inclTective in lapse of time. Such inert
3 broken tiles, stones, &c., cannot be of any ad-
; in cultivable soil ; originally they are perhaps
1 in the clayey or stiff subsoil ; but if effective
draiiugc and deep ploughing and subsoiling be adopted,
lie iubsoti becomes disintegrated, and the active soil
•My then reach down to near the level of the field drain ;
tettones and inert matter are then out of place.

Stiff soils being those to which drainage and subsoil
iiJiprovcmcnt is most applicable, the most modern mode
"feffccting drainage, by the deep drain-plough, is also
'>Kt suited to them. Thcdrain-ploughcuts a mere gash
'n llic surface of ground, but forms a cylindrical burrow
: drain in the clay four feet below the surface. In less
U

M/SC£LLMV£OCS PARACHAPI/S.

Stiff soil, drain-pipes can be laid in the passage to li
it permanently open ; ihe whole being efTbcUd (
machinery in lengths of about loo feet at a time.

The drain made, being parallel to the ground-surfKl
will not be on a regular incline in undulating g
the process is hence more adapted to level and eve
inclined land. The advantages of this method a
great ; drainage becomes a more ordinar}' agricultu
operation, the surface of the ground is not seriously s
terfered with, the process is inexpensive, and may b
renewed every five or six years, and finally in stiff st
no inert matter, stones, or old pipes, are necessary, ar.i!
hence are not allowed to accumulate.

Tk£ tnaitt'drains. — The system of field-drains, hofl
ever constructed, constitutes the principal and cfieftivc
portion of the drains ; they draw off sub-surfiicc waict.
increase the depth of active aerated soil, put it into ;i
condition for assimilating manure, and for supplyir^C
sustenance to the crops through their roots, at sny
moderate depth ; thus causing wannth in the soil and
an intermittent hygromctric action beneficial both tr
the crop, shown by augmented produce, and to the
husbandmen by diminution of heavy labour. Them
drains are mere collecting drains supplied from I
extremities of the field-drains and conveying the d
water into the arterial watercourses of the country.

There is generally but little choice as i
alignment and length of the main-drains ; theynmil
the lowest tines in any field, or along water-course li
at the bottoms of tlie various planes making \
field, and through any hollows that may exist
are made as straight as the lowest edges of the fi
and of the planes, or as the directions of the water

■ will conveniently admit When several fields to

rained happen to be in one plane, and intervening

5 can be removed, one main-drain may be made to

E for all, though enlarged to do so efficienlly. The

iDval of needless fences is very advantageous, not

f for convenience in draining, but also from saving

jfiil land ; irregular fences and crooked boundaries

f be straightened with similar good effect. Main-

is arc generally covered so as to protect the ends of

I field-drains from injury ; their fall or inclinations

d not necessarily be very regular, although these as

B as the sections should be sufficient to convey away

Tkily all water that may arrive under extreme condi-

s, as aAer heavy rainfall, when the watercourses of

■country are in flood.

mt/ti/isafuia of the effluent. — The various modes of"
Bing the water are necessarily dependent on its amount,
[imlable fall, and the local circumstances ; it may be
mcd, stored, and used either as a cattle pond, for
lotion, or as the motive power for preparing food for
, thrashing com, or other operations connected
|i husbandry.

IVhen sufficient ready outfall is not available, as in
I fien-Iands, or on the banks of watercourses and
pms of small fall, a long channel may have to be
c to conduct the effluent parallel to the watercourse
a sufficient fall is obtained ; and its discharge may
\ require tide-valves, to protect it from return-water

\ floods.

ET/w and expense. — The most favourable time for

rainage is when the land is unoccupied and during

F'Weather; in England during autumn and winter,

r the cutting of a white crop, or a clover crop, or

MJSCEltAIfEOm PAX-AGKAPffS.

whea tbe land b in pastore or in stubble, and immr
S^atif bdbre a stunraer rallou- or a green crop. Tl:.
■ofk bas aeccaarily to be suspended during severe
frast ; bat any intervals of sJigbtly wet weather m'
s opportunities for diain-ploughing or dnji>
r in stiff clay. The expenses of onlinai>- fid-
dnmage in Engtxad vaiy from about iL to 20/. per ic-^
at even owce^ jpi. to 40^ The justifiable cost will iii
any case be considered in its ratio to the e\'entual valu'
of ihc yieiA per acre, or cnlianced yield after tlionHi.,^
drvnage b completed. The expenses will neccssani'
baiv to be bome \ty an additional rent-charge an iaj
land for se\'ml years until the itnprov-ement elTcctel •-
eomparAtiixty exhausted. In some cases the expen^^:-
aic repaid in jridd in two or three years, as the increj-^
of vtiglu of wheat groMn per acre may amount to &c<i:i
I again up to nearty double, and the ^airi'
■ ptrtato oops. Perfijct draining, accompanied b)
management and follovrcd by good culture,
ev-er, general)}- nccessarj- for such achievements.
Wet lands in England, that really require drai
and will not repay the cost of thorough drainage,
geoenlty be considered hardly worth the expenses
mere cultii-atioa.

The drvnage of irrigated fields is a nutter most
quently distinct from ordinary field -drainage, and hcDce
usually treated in connection with irrigation. The
drainage of marshes and bc^ and the diversion wA
control of springs is also a separate branch of draii
requirir^ hydro-geological knowledge and special !:
mcnt, before ordinary 5eldKlrainage can be convenif
applied to the land aflcnranls available for oiltiv^c

irc, is
heoari

r RUIN OF CANALS.

The Ruin and Deterioration of Canals
OF Irrigation.

1 purely intended for navigation, the velocity
c water has to be kepi below a Sxed maximum ;
w that it may be anything down to still-water without
g serious harm ; but in irrigation canals, which are
tenuallyrcceivingfreshsuppliesof water, and distribu-
ter the land through minor channels, the velo-
VoftJte water must be regulated with extreme nicety
Icarc. in order to avoid many evils ; the twoextremes
Irhich result either in making the cnaal utterly un-
from not carrying sufficient water for
of irrigation, or in the eventual ruin and
m. from deterioration, of the canal itself Such
s cannot be maintained like roads, by merely re-
{ and trimming worn places ; they also require
\ [heir suitable velocities should be perpetually
i and regulated, even in the case that the in-
I velocities were originally correctly determined.
; designs and works made in accordance with

One of the most important causes of ruin to works of
"figaiion is that tlie velocities were never originally well
ilearained, but were faulty and unsuitable, if not
"iroughout the whole of the works, then at least in por-
■i"!!* of them, the result of which eventually affects the
"liolc. This is the case with a great many Indian
t^waU, and is likely to be so on many others, as the
"witcr of hydraulic vclocitiesis one on which knowledge
'i4s been very deficient

The next cause in point of importance is faulty

«74 msCELLANEOVS FAKAGRAPHS.

engineering design and defective construction of
works themselves, but this admits of remedy, «ilhi
going in most cases to such an enorinous expense
the former class of error entails. Even under this be
tlie apportionment of the velocities at intakes, outl
bridges, and such works, is of extreme importance

Thirdly, even if we assume the comparatively i
usual case of the original intended velociiies and'
works themselves having been correctly designed in i
abstract, and of the works having been constructed
perfection, the canal itself may yet follow the s
course to ruin. For whenever rain falls on the canal,
freshets or floods occur in any of the streams, riven,;
sources of supply, which then increase the supply of
canal, the depth of water in the canal is increased
certain places ; and besides, the hydraulic gradietl
increased, thus causing a very lar^e increase of velo<
taken in proportion to the adjustable correct lit!
Under the same circumstances, too, a certain araoun
siit is washed into the canal from its banks, and stit-t
ing water mayalso, from want of early precautions, e
from the streams of supply. A high wind m«y
increase these evils; while, again, the velocity of
canal water may again be increased by the augmea
velocity of the water entering the canal.

The practical adjustment of the velocity, or its reg
tion, becomes, under such circumstances, a matte
extreme care and refinement, even with the aid of all
hydraulic science the world now affords, and the ■
ance of good instruments and appliances for determii
velocities ; while without both of these aids it is i
impossible in most instances.

Setting aside the extreme cases in which the c

THE RUIS OF CANM

r water admitted may be so large that it becomes
ar)' to let it out over the country by breaking
D a bank, and assuming the very moderate one of
velocity being increased by only one-fifth, this alone
b imply suiTicieat to cause scour and erosion of bed and
banks to a \-ery appreciable extent ; and if this recurs
X riiny seasons for years, it becomes positive ruin, not
Ttly on account of the erosion itself, but because also
« Kourcd matter is transported by the water in the
n of nit and deposited at other parts of the canal,
le whole regimen of the entire canal thus gets out of
', the velocities are redistributed unsuitably or in
U proportion ; such errors augment very rapidly, and
ft partly worn and partly silted-up canal is the result,
is is ruin, which cannot be set right except by extra-
ilinary repairs costing half as much as the original
t of the canal ; and this is the principal cause of
win on works of the very best design.

Other causes of deterioration are the admission of
■It-bearing water at intakes, neglect of petty repairs,
Ind non-removal of such an average amount of sedi-
»it as may be deposited in the canal and channels
t>m causes apart from the preceding. It may also be
"Mentioned that neglect of repair in one year is not
"■•^ftipcn sated for by double the amount in the next,
"'•tier similar circumstances ; but that all such results
"'"e cumulative, from increase of interference with the
^ftci regimen of the canal, and its suitably apportioned
^ *ilocitics in various parts of its course.

The consideration of these causes, and more
^*pccially of the principal ones, leads to the inevitable
I Conclusion that a careful adjustment, measurement, and
pilaiion of the vclociiies of the water in canals and

196 JUISCEU.A.VEOUS FARACRAPHS.

works of irrigation is the basis of almost all i
for preventing or deferring eventual niin.

That considerable refinement is necessary is c
from the fact that the maximmn velodtaes [
in canals are : —

25 feet per second for \«ry sandy soil.

27s „ „ sandy soil,

3' n i> loam.

4- „ „ gravel and very firm soiL

While with low velocities of v% and 175 feet per scoMl
any suspended silt may be deposited, and vcgetatioti
springs up— the other source of extreme damage. Tkl
interval between the extremes b comparatively l
and very easily overstepped.

Our present knowledge of velocities, their calculatiiA I
determination, and measurement is extremely coarse ^1
present (not long ago it was altogether erroneous), heiKt
the necessity for more knowledge and greater refine-
ment which should be based on extremely careful ex-
periments, carried out under the most advant^eoQ^
circumstances, with all the aid that improved inst
ments and appliances of every sort can give and civi
assistance can furnish. The results of greater r
ment in dealing with velocities may therefore, if c
made use of and applied, prevent the lamentable ndn I
canals which is illustrated by so many nearly oblMl
rated ancient works in several formerly welUirr
countries.

The causes of deterioration, and the remedy I
them, having been previously explained, the next \
to be considered is whether it is worth white lo \
to the expense involved in applying a more 1

t RUIN OF CANALS.

pledge of h>-draulic velocities, and in the methods

ing with them. The amount actually invested

idia in canals and works of irrigation, including

ration done at all times, is certainly not less

itwenty millions of capital, clear of all working ex-

(For figures in detail, see ' Hydraulic Statistics,'

I, 1875.)

I Mow in dealing with statistics of this description, for

s of argument, it is absolutely necessary that no

eptional case, rates, or figures should be used ; this

tewill therefore be rigidly adhered to, and instead of

iog with any special case of canal, a theoretical

tl under conditions that average well among actual

rtics will be dealt with. Let us suppose a com-

lely dewloped irrigation canal to have cost one

Son pounds, the irrigated area to be half a million

i annually, and the net annual profit to per cent.

w the capital. (The Eastern Jumna Canal yields 22,

thtWcstcm Jumna Canal 31, and the Kalerun 24 per

ttnt, and these are the three completely developed

on^s of India, while it is evident that half-deveioped

onals do not afford a fair basis of calculation, any more

ffisn partly opened lines of railway.) Now although

'induration of a canal, or its lifetime, cannot be actually

,:iJ!y estimated, it is perfectly fair to assume that a

"111 relieved from the wear and tear of excessive vc-

"itics and from lai^e deposits of silt, retrogression of

"ds, and so forth, which are all solely due to the

'iiws previously explained, will last for a duration

'-'filing by a quarter the period that a less carefully

■■"laged canal will last ; in other words, let us assume

ih.it if such a canal in one case will last fifty years, in

^ other it will only last forty years with the same

1-Liting rse

dint cmfy'at to- cIwibh. Ae tacd pnofiB is oAb
w{Q be n pRipaftiEM to tbe

rtte aetaal tancwben Ac topcr
dwTiBifcw dowa tr> bdbw tan, or tfie caoal is intii
lilac B caOed a loa^ is a AfcRnc mm nwiih^ fi

of*

Total profia dsnng » centBiy

a, Im at ^ mart rafid wwi.
oper ceoc fcr 4oyem .

% „

4000000

4S0000
3>oooo
160000

8000a

I,oM during 13 yean to be deduoed

at I pci cent .... 1 30 000
Total profits during a century . . 5 560 000

The difference of total profits, apart from cither ril
or compound interest on them, is about one million

■t^ TJIS RUIN OF CANALS. S99

half pounds sterling, or half as much again as the
riginal capital expended on one canal. Taking twenty
ich completed canals to represent the capital invested
I India or twenty millions sterling, the loss due to the
Wre rapid deterioration becomes thirty millions sterling.
r half as much ^ain as the capita! invested, if ex-
ended over a full century in each case. Over half a
entury the loss is simply equal to the value of the
■liitil invested, and this seems a probable and fair
! of the anticipated loss in that period, or
e done

To this estimated loss, or to something very near to
It, there is only one alternative, and that is, the expen-
diture of the same amount in ejctraordinary repairs ;
■riifeh might be set down in the returns either as added
to rtie capital account, or as included in the ordinary
tepairs. But, however accounts may be managed, the
aznount estimated must cither be lost, or spent in making
head against the destruction occurring more rapidly in
one case than in the other.

It is useless to ignore that there is a lifetime to

evtrything ; the principles of dilapidation cannot be

controverted. It may, however, be asserted that under

any circumstances instructions may be given that the

canals shall be kxpt in perfect repair, that every care

'*al! be taken, and so forth. This is the very point ;

the care cannot be taken to prevent such damage unless

» higher knowledge of velocities enables a more refined

' ■■"- ;ind a real prevention to be exercised. No doubt

damage, instead of being allowed to accumulate

■-'■ so many >'cai5 into absolute ruin, may be stopped

iicurring more expense annually ; but this is merely

ruling the bill for damage over a number of years,

300 MISCELLAASOUS PARAGRAPIIS.

the expense is not prevented in that case, bill i
divided ; and if this fonn of account be prcfd
Instead of dealing with a total loss of twenty ratlliaT
fifly years, it becomes a waste, loss, or combinali^
both, of 4C».ooo/. yearly over the whole of the ifr^
canals and work's of distribution of India, wbifl
simply due to the coarseness of our knowledge I
velocides. Comparing this annua] waste, or cwn til
a quarter, or a tenth of it, with the relatively small
of a thoroughly well-conducted series of hydi
experiments, we may easily see whether the latte
worth while from a financial point of view, as a ji
remunerative investment or expenditure on
works.

The principle involved cannot be avoided by d

any analogy between canals and railways. All ir
modes and principles, and increased knowledge, (
mcnts, and so forth, on railway's, may have cost 1
nothing. As railways in their perfection weicl
required in England where they are still being impT
at the expense of skill, money, and thought, olll
ideas may be borrowed gratuitously. But there a
large irrigation canals in England, and India
necessarily work out its own improvements in I

branch at its own expense, and effect permanent c

mies for itself, if at all ; although it may, and periu}"
should, bring to bear on them the highest English -•
available in every respect, and make use of it both •■■
home and in India.

In following up, or copying in practice, any clear!
defined thoroughly- worked -out principles, as thoN."
roads, railways, and navigable canals, a routine *ysi'"
of the marionette tj'pe may be sufficient for ihepUTp-:--

ON tVATER-METEXS. joi

1 practical improvement has to be gained by
xperimcnt, and skill, such a system is in-
Iblc without further aid.

Ir method hitherto adopted of following up and

Hie hydraulic experience and formulas devised in

uice and Germany, and of applying their errors as

■fell as their principles on a very magnified scale, thus

KaviT^ expense in experiments, has had the most

^itastrous effect on the irrigation works of India ; this

point hardly requires exemplification. Latterly the

'■■-: scale experiments of Captain Allan Cunningham

■- demonstrated the immense amount of error involved

; ing the French and American formula; and have

'td out the correct method. This, however, is not

ih.it is required; the correct principles must be

■;'.d in practice. Any dispensing with the application

"iproved knowledge in a branch of science that pre-

i.L-ntly affects the permanent benefit of large and

:.-vibive works of irrigation seems therefore perfectly

indefensible either on financial or on any other

grounds,

k; term water-meter being frequently used with little
inatiori, it becomes necessary to notice briefly the
"iiKinction between water-meters and modules or water-
•'pilalors. A module actually regulates the supply of
*ster passing into a channel or into a pipe, or makes it
Prwiically constant, although both the amount of water
*'«I tile pressure in the main canal, main pipe, or reser-
""ir, supplying the branch canal or pipe, maybe variable.
A vstcr-mctcr does not regulate supply it simply

10. Ok Water-Meters.

3M MISCELLANEOUS PARAGRAPHS. cjwp i

measures or registers supply under corresponding i:
cuinstances. Such is the broad distinction ; yet w* >
companies frequently use modules for regulatmjj :;
supplies, when in large quantities, and call ihcm wj
meters ; also real \vater-meters have sometimes auxi'i
regulating appliances attached to them. In the foi"
case there is an habitual blunder in language ; iii '
latter there is a constructive difficulty, apparcTV
affecting the term used.

A module is undoubtedly the more perfect appHn.
as it both regulates and enables the amount of u
passing in any time to be arrived at by calculatioai
is to say, It also answers the purpose of a water-id
A registering or chronograph ic apparatus
attached to a module, but it still remains a t
A simple water-meter or registering machine dw
regulate supply with practical exactitude (or if it d
it then is really a module) ; but, if it has an am
regulator, this merely controls either pressure ord
tity, or both, between two limits, convenient to the ■
of the mechanism, and tlie machine still remains a %
meter from the fact of its not possessing thccoi^
qualities of a module.

The notion that all such appliances may be d

I guished as regulators or meters, according

attached to reservoirs and canals or to pipes of si

is erroneous.

For various types of module, sec the |
devoted to that subject.

As to water-meters, nominally so-called, we v-'
expect to find that some of them are really modules-

Trough-meters. — The earliest of the English wbI'
meters dates from the time when iron pipes c;

ON WATERIUBTKRS. 30J

Qse in England for conducting water, and was

as Crosiey's water-meter. [It is aaid that

nel Clcgg, a mechanical engineer in charge of some

ps at Liverpool, in 1802, was the inventor of a

Bitter (See William Matthews's ' Hydraulia," of April

, and of the stand-pipe, and that his ideas gave

to the water-meter, but Uiere is much doubt about

Samuel Crosiey's first liquid-meter was a rotat-

lirum inclosed in an air-tight vessel, and certainly

the converse of a gas-meter, as regards action,

ley's second liquid-meter was a rotating trough, in

I very like the first. (Sec p. 304, Matthews's

draulia.') This latter is the common one, and is well

rn to this day ; it has been re-invented several

\ and is sometimes known as Parkinson's, on account

bme error (in the Minutes of Proceedings of the

(tution of Civil Engineers, January 1851) having in-

lonally or undesignedly conveyed that this meter

his invention. But in this case neither favouritism,

llh, nor combination have sufficed to obscure the

Crosiey's liquid-meter is a good one, as regards

titude of measurement ; one of its defects is the loss

II pressure at points beyond it, or after the water has

led through it ; hence, when applied to the supply of

Iglc house, it must be placed at the top or at the

n^iest level in that house where water is required. It

:: a balUvalvc regulator for maintaining a constant level

. ihe supply-trough

Piston-meltrs. — Brunton's meter (see copy of paient

rtory of Arts,' &c., for July 1829) was a piston-

e water passed through a cylinder with packed

1 rod, noz2le, and valve, or cock ; its principle

[ in appl)'tng the static fluid pressure on the

304 UISCELLA.VEOLS PARAGRAPHS. cnA». ill

piston to move it with sufficient force to raise a weight
on an inclined plane during the whole range of irapulsc ,
tlie power generated is, at the termination of the impuk
capable of moving the \'alves or four-way cocic, anl
reversing the pressure on the piston, by which the Hfi),'tit
is again raised ; the motion is therefore continuous and
expresses the quantity of discharge, which is rcgistcird
by wheelworii attached to the machine. This mct«
has been re-invented, with more or less improvement, by
Kennedy (sec ■ Proc. Inst C. E.' for 1856). The defrffi
of meters of this type are, that the reversals of pressure
cause shocks in the mains, and allow some water to pjs'
unregistered ; also either the packed piston, the reversing
cock, or the balance may be seriously alfected b)' friction,
so much so as to gel Jammed,

Frost's meter is also a piston meter, hardly preferable
to the other two ; its reciprocating mechanism is H"'
better, though it has a tliree-way valve moving an aus-
iliary piston and working another three-way cxhiii^i
valve ; its piston moves leather buckets within ll«
cylinder, and the whole is liable to stick. (For di
see ' Proc. Inst. C E.' for 1857.)

Among the modem pision-meters is GalaiTe's
two cylinders and two slide-valves, working in ciW
action, thus neutralising much defect, or rather pethi^
keeping it out of view. It is much used in Belgium, tn^
is perhaps the beat piston-meter now well known.
compensation of defect that it afibrd-s must not,
make us lose sight of its inherent qualities. Rii
water-meter is the most recent piston-meter, and
some advantages in simplicity ; it ace
development of the gss-metcr of the same in'
All piston-mctcrs appear to require supcrviaioti,

the I

%

<; generally unsmtcd to low speeds and small

] ..rgcs.

■urbtMe-taeUrs. — Water-meters on this principle are

'aps older than those of the preceding two classes,
iijjh it is impracticable to assign definite dates to

;r introduction. Their applied object is to register
velocity of supply through a fixed opening, but, as

-v: friction must exist, they actually record a less
aty, and, when very defective from wear or rust,
"me utterly untrustworthy. There have been turbine-

vrs of several kinds, the modem form is the reaction

■ 'ine in common use ; Siemens' turbine-meter is one

:;iL-st The peculiarity of this meter consists in the

<-boards attached to the rotating drum, which ensure
' iis velocity shall not exceed that of the water at

. lime, and thus within certain limits maintaining a

: Mnt speed of revolution under a supply that does
.ary in amount ; in other words, the effect of slight
Uion in the velocity of the water of supply is entirely

■ uiicd. This is a marked advantage, but the appli-
suffers from the be fore- mentioned defects, insepar-

' from its class of water-meter.
! im-meters. — These light fans, constructed with the
it that the effect of all passing water shall be regis-
d, are the water-meters of the most modem sort. They
Ti uch used in Germany, Russia, Italy, and France, but
not popular in England. Siemens' fan-meter has
plates to moderate velocity, as in his tqrbine-meter,

'■ ihese constitute its chief advantage.
'iylor's fan-meter (described in a paper read before
^institution of Mechanical Engineers) has the same
c as Siemens' : its wheel is of indiarubber, its
8 for entrance-water are well arranged, it is not

■"306

MISCELLANBQVS PASAGXAFHS.

easily choked by sediment at the points of exit, and \-
generally a much-improved fan-meter. A special in:
provcment in it is an appliance for regulating ihespL :
of the fan by a counler-current of water, so arrange :
that it is adjustable from the outside of the case. Th:
is of great convenience in testing, as any error in rcg-
tration due to long use or accident can be rcmerfii i
without taking the meter to pieces. On the whole, i!:
Tylor's fan-meter is perhaps the best of its kind ; it h-;
been thoroughly tested by Mr. Anderson, who has a hi^ii
opinion of it, and it is much used already in i^^
Colonies,

The objections to fan-meters, or their defects, coI1^:;!
in allowing unregistered water to pass, in slowncsj iri
getting into motion at starting, and in spinning on ailsi
the supply has been cut off ; these defects do rot compe:.
sate each other, but they may be tnuch rcduccil t>
management and care.

General Remarks. — In order to arrive at a just aii
full compfrchcnsion of any particular meter or mwlul'
the thing itself should be inspected or examined ilwi'
action under various conditions ; illustrations fail '
convey the information that may be obtained io ui
manner.

It maybe noticed that house-meters for registtir
small supplies of water must necessarily be more delii.-.
in many respects than the large supply-meters of *a'j "
companies ; they should demand little or no supcniss
and be so arranged as not to permit of beinR ci'
tampered with, either by the consumer or by the ws'
officials or agents. Probably some type of mnluu:.
ensuring constant head during action,
graphic apparatus, admitting of independent c

itb a ch^H
lent ched^H

''eft WATER-METERS.

JO?

, would best answer such purposes (see Modules.

, Chapter III.).

' For exact measurement of supply through pipes

■ variable pressure, a good pressure-gauge and a

)hic apparatus are necessary ; besides this,

t outlet must be free, and a considerable length of the

; must be made of some exact diameter, less than

B ordinary* varying diameters above the point of ob-

ration : all the conditions require much precision and

mpeteot management.

J.,...

f"

i..«-- ■,■■

1(^1-

HYDRAULIC
WORKING TABLES.

VII. Channels and Canals.
Vni. Pipes and Culverts.
IX. Bends and Obstructions.
X. Sluices and Weirs.
XI. Maximum Velocities.
XII. HvDKAUUc Co-efficients.

. Additiomal and Miscellaneous Tables.

Wean be used either mth tr.jdesmen's tmiti or with the units of
the English dedmai iclmtifif series.

Tabli I.— gravity.
CAX^cmj^TKD Values of tkb Forci of Gbavitt in Fizt at

I>IFF«R»NT LdtTITUDES AND ElXVATIONS, BBINO A TaBU-

LATBD Application of the rotMVLX

/-M-1S9B (l-0«>384 cot SZ) (l--)-

GRAVITY. '

4

Vaiue

ofthejorct of gravity m/eam/^M

Eleva.

IN FEET

LATITI'DE ^H

0°

6°

10'

^

0

3»'078i

3* -0795

33^1836

3»'09^

too

3= -0778

32f79a

32-0833

31 ^:..

200

3S-077S

32-07K9

32-0830

3i-c.-. ■

300

32-0772

j.-orS6

32-0S27

j/^-

m

32-0769

J=^7S3

32Tfii4

yv.< J

BOO

33-0766

32-0780

3»-oSll

321^'^o

eoo

32-076J

3»-0777

3*-o8i8

ji-c^^i.

TOO

32-0760

32-0774

Ji^iS

32■c^■.

eoo

33-0757

32-07;!

32T>8.,

J2-C.V.'

wo

32'i'7S4

32-07^8

3«-oSo9

JI-OS

tooo

3J'07Si

31-0-65

32-0806

32 w; -

MOO

32-071 r

3»-orjs

3* -0775

3i-:.V:-.

3000

31-0690

3»-07o4

32-0745

3«"-i;

4O0O

32-0660

32-0674

32-0715

31 -c;:'

6000

32-0630

32-0644

32-0685

31---^

Elbva-

Latitudb

40"

45'

60°

E6'

0

J3-'536

32;i69S

32-1854

31-wrf

100

32-1533

32-1851

32-2O0S

200

3215J0

32-1848

32-*0M

300

32'i528

33-1845

321^

400

3a-iS'4

321683

32-1842

31- IC'

£00

3»-:S2i

321680

31 1839

JIT).

GOO

311S18

32-1677

32 1835

32 f' ■

700

3''5'S

32-1674

31-I8JJ

31 !':■■'

SOO

3»'5"

32-1671

32-1839

31-1'--

SOO

3I-IS09

32-166S

j2-rS

32 1 ■■

1000

32-1506

32-ie6s

32-1823

31.V

3000

3»-'473

3^1633

3a-l7<>3

J2-V.I

3000

3a ■144"

3»-i603

32-1 7iia

JJ'.^-:.

*000

3a-(4n

32-157*

32-1 731

32-1 '.>■

SOOQ

32t3S»

3*'lS4>

3»-i7«»

J2 1*.,

■

1.

,

J

■

■

■

■

^^^^

n

Latitude

ao°

»•

30°

38=

3»i599S

32-1108

32-1238

3»'f383

33-0991

32-1 10s

321235

32-1380

3*0989

32- 1102

32 ■1131

32-1377

3i'098ti

32- 1099

32 1139

32-1374

3*-o9«J

32-1096

31 '1226

32-1371

3jQ9»o

321093

32-1223

32-1368

jj-og??

321090
J2-I0S7

32-1120

32-1364

31-0974

32-1217

321361

33^71

32-10S4

31-12.4

32-1358

32-0968

32-1081

32-1211

3^1355

31-096S

31-1077

32-1208

321352

32-0934

3J-iai7

32-1177

321322

3J-0904

3S-:oi7

32-1146

32-1291

32^74

33-0986

32 HIS

32-1260

^B^

3"-oS43

33-09SS

32 -.0*4

32-1229

Latitude

60*

70°

80"

80"

3J"S^

32-2395

31-2554

33-2609

322149

312393

32-2551

32-1605

^■2:46

31-2389

32-2548

33 '2603

3* -1143

32-2386

32-2545

31-2600

32 -J 140

32-2381

32-2541

33-2596

33-2>3(>

32-2379

32-2538

32-2593

3*»'33

32-2376

32-2535

32-2590

)2-»l30

32-2373

32-2532

321587

312117

32 -2370

32-2529

32-2584

31-2114

322367

32-2526

32-2581

32-2HI

322364

31-3523

32-2578

^1

32-2090

32-2332

32-2491

322546

^1

3J-20S9

33-2301

32-2460

32-2515

32-W)28

32-2270

32-2429

32-2483

321997

32-2139

32-3397

32-2452

H

d

TABLt IL— CATCHMENT.

It u
rt 2.

It J-
lit 4.

Total qvandties of wtttr letnlting from a giTen cflSxtive ninfall

run off from any nnit of catchment area.
Supply in cabic feet per second throughout the year, resulting

from a given effective rainfall run off from one square statute

mile of catchment area.
Supply m cubic feet per second, resulting from an effective daily

rainfidl for 24 howB over catchment areas.
EqoiTalent Mpply.

^Hl

^^^^^^H

8 CATCHMBKT. [taS

Hve rainfall run off from af^ unit o/eaUAma

R.BW

c«bi.r„,

Cubic r«. |C"bic«d.

lUinf^

Q,bi:B«

lnf«I

•"ci^-ln

J™- '"'"^ Hal^e

liiSe.

mm

1

.0000 |ioooooo| lOOOCO

\r

43560

0-9

9000

9OQOOO

90000

sr

39900

0-8

Sooo

800000

Bo 000

10-

36 3<»

tV7

7000

700000

70000

9"

32670

0-6

6oao

600000

60000

8"

29040

O'b

5000

SOO 000

SO 000

r

95410

04

4000

400000

40000

8"

»t jSo

0-3

300a

300000

30003

S"

18 15a

frZ

aooD

soo 000

aoooo

4"

I4S>o

01

-

10 000

r

.0890
7960
3630

ft09

900

90000

9000

09

3»67

008

Soo

So 000

Sooo

OB

«9a4

0-07

700

70000

7000

07

"541

0-06

6cx>

tioooo

6000

OS

»ij8

oos

500

so 000

sooo

OS

.S.5

O-M

400

40 coo

4000

04

'45«

&03

joo

30000

3000

03

■ 0B9

O02

100

aoooo

itxa

M

7J6

om

100

10000

1 000

M

363

A^.a.-ItqunteilatHtemilc-IHOwTM-JTBTSIOOrt

lsquan:lcigue = 4sq, Londoo mlla-100 untiUMs-lUOj^l

^^^B {tUnricn's). ^H

^^^^H ttqiurcdiua-iooiq. rod«.10O0O«iiiucta^H

CATC/IME.VT.

r a. — Sufpiy in tuhU Jut per iccond Ihroughoul the year,
[ ^uniting from a given iffeelivt annual rainfall run off front
\-mu s^nart statute mile of talchment area.

^F

j|g.iu

riXuL

„tnl'.%.

^If-^

^S^^^

^^^r

™f«t '"

«<™d

*"'

«™d

^P"

■oSSj

2-1

,

8550

4'1

ybzx

^K

-1766

2-2

1

9433

4-2

3-7100

^K

3G50

23

z

0317

4-3

37983

^^b

■3533

I-d

a

IIOO

4.4

3-8866

^^B

■4417

?6

1

1083

4'5

3-97SO

^^V

■S30O

iZ

a

2966

4'e

4-0633

^^r

^iS]

2-7

z

3850

4-7

4-1517

^K!

7066

2-e

3

4733

4-8

4-3403

^B

■J9S0

1-9

a

5617

4'3

4-3383

^K

■M33

3>0

a

6500

6-0

4-4166

^V

■9717

3-1

a

7383

6'5

4-8583

^K

113600

3-2

3-8366

fr

5'3«w

^^L

1148J

3-3

3-9150

6-5

57417

^^H

XZliA

3-4

3-0O33

V

6-1833

^^B

1-3150

3'S

3-0917

7-6

6-6350

^Bv

l-4f33

3-6

3-i8oo

a-

7-0666

^7

1-5017

3-7

3 '3683

e-5

75083

t-B

IS9W

3-a

3-3566

9-

7-9500

' '^

1-6783

3-9

3 -4430

9'5

8-39" 7

J ]

17666

40

3S333

W

8-8333

^.nulafly from I foolofeffecii

e annual raiafell, Oic supply per secood

Frtra I "pare league .

3-t70Q79 a cubic feel pet tccond

„ 1 mitu/y .

00J17098 „ „

r „ impimredBin . .

o-oooii7i „ „

i

^^^^^^^^^^^^^1

^^^^^^^^^^^B^l^^l

10 CATCHHENT. CrAn.in.

Part ^—Supply in enhic fut per siowd, ratilthtg Jrm

efftetkt daiiy rainfaUfor 34 ho»n mer aUchmtmt anas.

POK CATCBUENT ABEAS IH SQDAIE STATtTTB MtLB.

li

FBTi-a tff«llre diHr nLzM U) fnl aiKl d«om>l> oT

0-1 j 009 o-oa 1 0-07 [ 006 1 0-oa 1 OtM 1 0«l [ 0-03 (

Cubic f« pa wow)

3J'J7

19-04

25-8.

12-59

1936

I6-13

ia-91

9-6S

Li-.

64-53

58-07

51 -62

45-16

38-72

3*^6

25-81

19 J6

I( .■

96-80

83-S2

74*4

64-96

55-68

48-4Q

37--»

27-84

1!

ug-i

itd-i

103 »

90-30

76-40

64-50

SI -60

38-70

j; ■

<6i-3

145-1

129-0

ni-9

96-8D

80^

64-50

4«-40

31:.

193*

174-2

154-8

'35-4

116-1

96-78

77-40

5806

iJ:

2JS-9

203-2

180-6

isSo

135-5

111-9

90-3«

6773

258-1

iizi

J06-4

180-6

1 54-8

129-0

103-2

77-40

'Sjjk

»90-«

261 4

231-3

103-3

174-3

US -3

It6'3

87-13

9

3«-7

290-4

158-'

225-9

193-6

161 -3

129-1

96-10

fl

FiiraiieSKUvcdiilrouif'UbiliichsKHliIixd^if ^^H

1-0 1 O-D 1 0-8 1 07 1 0-6 1 0-S 1 0-4 1 0« 1 ^H

Cubic tt« per iccDwl

^H

26-89

24-20

21 SI

18S2

:6i3

1344

to-7«f St9| ^B

5378

48-40

43-a

37-64

3*-»6

26-89

ai-So

•6-U l^P

80-67

54-60

64-53

56-47

4S4C

40'33

33-26

i«-aa i«-Hl %

107-56

96-75

SS-ot

75-25

64-50

53-78

43-00

32-Js)i. -

■34-4

1109

.07-5

94*oS

So-64

67-22

53 -7S

40-J112C--

.61-3

145-'

'35-0

112^

9678

80-67

67-5!

4St^. -: -■

188-3

.69-3

150-5

1J17

III-9

94-11

7S-»5 y

JlJ-l

f93-6

171-1

1505

129-0

107 5

9

242-0

2.7-8

193-6

.69-4

■4S-»

96-S.'j -.

10

268-9

242-0

2151

188-3

I61-3

134-4

107-56 bo-p; ;:■

Similarlr&om i foot of da/i ninfill, tlie sa|>i>1r ii~

From t square Icjguc . . llS7'4or40Colne fiwt w* »aal

„ iccnturj , 115741 „ J^

K liqiUiEcliuo 0-01157 n ^H

■

■

■

■

■

1

^B

H*3l CATC/tAfEtrr. 11

^LMti'meif).~SHffiy in eubkfettptr seamd, resulting

Haw daiiy ratit/aJl for 24 Aouri aver aitehmcnt anas.

■ rOA CATCHUIUT AREAS IN ACHES.

1

H tmm «aKcw UaiJv ninfill m l«I ud decinult of

J

Bott 1 O-OS 1 0-07 1 O'Oa 1 0-06 1 OM 1 0-03 1 003 1 0-01

■ Cubic l«.p«™nd

B*I3

fOI

O'SS

076

063

o-so

0-378

o-JSi

0-116

^M

3'OI

'■77

i-Si

1-36

I'd

0-756

0-S04

0-251

^H

30J

i*S

2-27

1-89

■ S«

'■'34

0756

0-378

^H

H'S4

4-03

353

3«3

a 51

2-OI

'■513

I'ooS

0-504

Kt>8

8-07

7-06

6-os

S'<H

4-03

3-oas

2-017

l-ooS

^E^i

Il'IO

to-59

9^

7-56

6-OS

4-S38

3015

1513

■P'15

16-13

14- 1 J

IIIO

10-08

8-06

6-050

4033

2 -017

K-69

2017

17-6S

IS13

11-61

lO-oS

7 '563

5-041

2-521

B^*^

14-20

Ji(7

UlS

1513

t*-to

907s

6-050

3025

.5 -Si

"■59

I9J6

.613

12-91

9'6Eo

6-453

3117

■ r« M .Ifccu™ dailT ninbll b inch» ^ dcd.ull of

■bV 1 O-B I 07 I 0-e I O'B 1 0-4 1 0-3 1 0-3 1 01

B Cubii: l«l m Kcind

■«'95 i o«»

0-74

0-64

053

0-4I

0-315 JO-2IO

0-105

■t-S9

1-68

147

,»

1-05

0-84

0'630

0-4«>

o-iio

■b-sj

a-Sa

,9.

IS8

1-26

0-94S

0-630

0-315

K-;8

3-36

I '94

"•s«

2' 10

1-68

i-*6o

0-840

0-410

K-s^

67a

S'SS

S"

4-WJ

336

2521

1-681

0-840

W'34

lo-oS

S'Si

r-6»

6-30

5 -04

3 -781

2-5 = 1

1-260

'J-M

1176

10J4

8-40

6-62

504*

3361

1-681

^B'91

i6-Si

■4'7'

1380

1050

8 '40

6-302

4-101

i-ioi

■>-fi9

W17

17-65

.SJ6

li-bo

10-08

7S6J

5-041

2-511

^-»

aiSi

iS'Sj

,6-,3

I3'44

.0-76

i-<Aj

S'378

2-689

Tz 4

B J

E^i^^^^m

0

C^ TCHMENT. [t«1* l^f

Part 4, —E^uivaUnt suppfy. ^|

Cubic

eet per sec

□d, p«i minale. «ad per dar. imo GindHj

second, per miiiute, and pci dnj.

P«

..„d

Per mlnulc

Perd«yof24h<«in

feet"

Giliona

C«t.ic

<i>U«u

Ua

G*lk»

O'OI

006

06

374

8U

; :'

D'OZ

0

ii

1'Z

7-47

1718

li- -

0'03

□

19

1-8

2SK

,r. 1

O-M

0

^5

2-4

"4-9S

343G

31 r

0'D6

0

31

3-

18-69

4370

it,.

O'DB

0

37

3-6

*a-43

StU

j!

0-07

0

44

4'2

16-I7

6048

O'Oe

0

5

4'8

J9-90

6912

4';, .

0'D9

0

56

6-4

33 -64

7 m

4-'--

O'l

06a

&

37-39

8010

S3- ■

016

ItH

10

fa -3 J

14400

89:..

D33

3-ClS

20-

IJ4-64

ZB»0

I79»»J 1

O'S

3ii

3D-

IS6-96

43200

a69n]

066

4'l6

40-

J49-a8

47600

%^'M 1

0'B3

S'M

BO-

311-60

72000

«S7".

6-i3

60-

373-9*

66400

53^--

1-16

7-27

70-

436-14

too 800

133

831

BO-

498-S6

"smo

7'r

1'5

9-3S

80-

StoSB

129600

»«:■

VG6

io'39

100

6J3-W

144000

89;;

MS

7-11

69-4

431-7

100000

633 Jv^

1'93

14 -P

IlS-7

865-4

200000

3'47

a. 63

imz

IJ9S-1

300 000

'31

4'63

=884

l.V-1

1730-8

400000

S'7a

36-os

346-8

ai63-s

sOOOOO

.^^^H

6M

43-26

i16'6

2596-*

600000

'S

S'lO

50'47

4S8'

3018-9

700000

9-n

57-68

65S5

3461-6

BOOOOO

1&41

64-89

624-9

3S94J

900000

'S

JV67

73-10

694-4

43i'7'S

1 million

IS

■. rf

■

BJ

^^H

^ll^l^^^H

^^^B^H

HH^^ CATCHMENT, ■

-per second, pei minute, aiirf per day, into Cubic Feet per |

iccond, per minute, and prr day.

^

Per minute

PerdiyofSlhoutt

CWKfBB

G>U<n»

Cubic Ihi

G^.

Cn«c,«

0-016

B

0-96

8640

■385

0-032

12

I -91

17280

a773

0-048

IS

2SS

2592D

4158

0-064

24

3-84

34S60

S5«

ooSo

30

4-to

43200

6929

0^

3G

S-76

1>I840

831s

t:i

6-7*

60480

9701

0128

18

7-68

69120

noSr

0-I44

M

8-64

77760

12473

0160

GO

9-62

86400 1 13S58

0017

to

160

WOO i 1310

0-053

2D

3"

28800

4619

O'OSO

3D

4-gi

43200

6929

0107

40

64a

67BOO

9^39

0134

50

8-03

72000

11549

o-i6o

ED

9-6*

86400

.3858

0-187

70

11 23

toosoo

16168

o-3r4

eu

"•83

116200

18478

o-Mt

90

I4«

I2SG0O

207B8

0-J67

100

16-04

I44OO0

33097

o-iK

6B'4

Itl-4

100000

16040

0-J7I

11S-7

200000

31079

• Si;

208-3

334 a

300000

48119

07*1

W-1

445-6

400000

64159

0-9JS

34S-B

556 ■<<

soocoo

80199

1-114

4tG'6

667-3

600000

96339

r»99

480-

779-7

700000

113378

14SS

665>6

8911

800000

13831^

i«70

m%

lOM-J

900000

r44J58

Its*

tM-4 \ 1 113?

1 niillion 1 \t<aw^

H

^^^

_^

Tabu IIL— STORAGE AND SUPPLY.

F«Tt I. Capuat]P of icKTToin and supply from otchmcnL
Part X. UtUintioD of > coatinnous tapplj of water.
Paft 3, £qai*>lent of coDlinuous Eupplj.

^H

^1

^^^^^1^^ ' STORAGE A.VD SC/PPir. (tmi^^H

^H Part ^.—CapaHtyofnurvoinandsufplyfromeaiaaiM^

^" A K,« «O.Tm' SUWLV.

C«dOKl

Supply •ffonlaJ

CwubuqC
Uiu«pply

iliip on Ihi avnge

•ilhlii;

Cubic r«i pci

CuUcf™

Squi«f«i

ajM-iHi'

i3 3^8«»o

7776000

o'SjfiTi

2

466S60W

15 551 WO

i-firiij

3

69984000

233JS0OO

j'swii 1,

4

63 3.SOOO

31 104000

3W

5

■ 16640000

3SSk)oHi

4-1I]

G

13.) 563 900

46 656 000

S-OK

7

16J3960™

54 432 000

SS5I

B

18661400a

62 MS 000

6'69

9

209 953 000

69984000

r«

10

233ISOOOO

77 7'»ooo

Sjd

M951

a7S;K40D

9i9lSoo

2'3901

55 7S6 «<»

18 ;85 600

3-68M

8j 635 aoo

37 S78 4<»

4-7802

111 S'3 6<»

37 17IMW

E'S753

139393000

46464000

7- 170*

i6j J70 400

55 756 800

S-3664

19s 148 80a

65049600

9-SG04

Z13 P17 JOO

74342000

tO-76SB

150 90s too

83633300

I1'H06

j;S 7S4 oco

gl 91S 000

« so simple as not to te.julre the aid of Ubio. ^H

^^^^^^^^^^^^MHi^3 ^T^^^H

1 {continued).— Capacity of Ttsaivirs
from eatchuuiil.

■1

and iupply ^^^H

n. .. .»HT MO.T«.' ,..,l,.

^

S-

It..! wppi,

s^B.

Cxdiniint ust

i

P=

Cubic f«t

SqLm«f«l

Squanoiila

20736000

6 9t2noci

■7438

^1

41 472 OQO

13844000

1 -4876

^1

6ia>8c«>

2O7J6 000

22314

82944000

2764SOOO

2.9752

^^^1

103680000

34560000

3-7190

^^^1

124416000

41 472 000

4'4&2S

^^^1

I4SI5'«»

48 384 000

52066

^^^1

165 SES 000

55296000

5-9504

^^^1

IS6 624 000

62208000

6'6y42

^^^1

207360000

69.20000

7'43So

■

1

27 878 400

9392 Soo

,

■

1

SS 7S6 800

18 585 600

2

1

83 63s 200

27 878 400

3

^^^1

'

111513600

37 '7' wo

4

^^^1

I

139 39J 000

46464000

5

^^^1

t

167 27a 400

SS 7S6 800

6,

^^^1

1

)9S 148 800

65 049 60a

7

^^^1

;

223 027 200

74 342 000

8

^^^1

)

250 905 6co

83 635 200

9

^^^1

'

278 784 «»

92 928 000

10

^^1

Uein.

J

^^^1

^H

^1

^^^^klH^^^H

tt STORAGE AND SUPPLY. [taM^^H

Part i iamtmutd).—Capadly ofrtsereein and supply ^^k
cttlchment ■

FOR A SIX MONTHS' SUPPLY. *

Sappir i>9bHtd
■h-fin^lSOd-yl

RKTVDir CO hold

ital^pply

Sni&ciaflhu
K«TToirir34fca

u.l804'i>

CbWc fed |KI

Cubic fm

Squinful

^»—*-

1

IS SSI 000

5184000

osnc

Z

31 l&JOOO

10368000

t-nl

3 -

46 656 000

i5 5S3txx.

.■67J

4

6i3oSooa

20 736 oco

2-33*

6

77 760 000

15920000

2789

6

93 3«*«»

31 104000

3-347

7

IOSS64O0O

36188000

3-90«

B

.24 415 000

4i47i<»»

4-4fi)

3

139968000

46656000

S-OM

10

I5SS20 000

Sr 840400

S-S7<

1'7326

27 878 40a

9393800

3-6652

55 756 800

tS 585 600

&3778

83 63s 200

a? 878 400

7'I7M

111513600

37 171 aoo

B-ssao

139 391 000

46 464 000

107M6

167 270 4«J

55 756 800

!2'H32

195 14S800

65049600

I4'M07

313 0J7 a»

7434*000

t6'1333

350905600

•83635300

9>

17'9?59

378 784 000

9» 9jS 000

10

1

J

^w. rAki

ll STORAGE AND SUPPLY. 19 ■

Ht {^am^au^—Capadty of rtitreoin and
^1 cahhmenL

mppiyfrom H

roft A FOUR months' sopplv.

m tax maothi

Oinlinli of

Suriaci of lh«l
dOT> 00 U^ .veoigf

1.-U: ftei pu

Cubic Fell

Sq»«f«l

Squ«n>U«

1

i0 36Sotw

3456000

03719

ao 736000

691*000

07438

ji 104000

.0 36So<«

IIIS7

41 47a 000

13834000

1-4876

51840000

17 280000

1-8595

63108000

10736000

11314

73576000

14 19* 000

16033

81944000

27 648 000

1-975*

93 31*000

31 104000

3-3471

103680000

34560000

3-7190

en

17 878 400

9193800

1

8777

5S 756800

.8585600

1

era

8363s wo

37 878 400

3

^

111513600
139 393 000

37 171 300
46 464 000

5

2000

167 170 400

55 756 Sdo

6

'SOO

195 "48800

65 049 600

7

^61 tt

3J3017300

74342000

S

h89e

350905600

83 635 200

9

MBS

178 784 000

93 918 ODD

.0

1

.

\

STORAGE AND SUPPLY. fiAtLK li

Part a. — UtUUalion of a eonlinueus mpply pfitiattr.

~^\

Al5 At 7* Alio Alls

AiSO

A. 26

AIM

gUIOD. g^lQH gllt<»u

gilloni

«lll«u

p.rb«d p«h«d ^rh<»d

p^h^ad

puhiHi

^'h!^

£i

djjly d.il, (Uity

'l.i.y

duir

107732

7iSk>

53866

359 .0 1 26933

21546

\m

2.5464

143640

.07732

7.8»

SJ866

43093

w '

313196

2154.0

.6.598

107730

80799

6,63c

i3»5i

430928

3S71S0

a.5464

143^

1077 3J

86. W

7ils»

538660

3S91O0

169330

'79SSO

134^5

.07931

m^

646392

4309*3

3»3>96

aiS46o

.61598

.29278

loTJJ*

754'^

474740

377061

237370

"88531

,50825

"Mi

86.856

5745^^

430918

187280

1.M64

.7'J7'

UJ<*i

96958^

(.V-lio

4S4794

313190 242397

'3391J

i^iM

i__^

LOJJj3ol 718:00

538660

350100 z^-mv^

215464

mvfi

All

AHi

At 2

A.21 At 3

At 4

cub. f«.

fUb. f^^l cul. f Ci

^r iiMd

dj,[y

.Jaiiy

■^iii" '"^t"

iliilj

"'^ ^

Popuiiiian nihplirj

86400 5 J 600

45;oo

34560 2SS00

21600

,V!"

I7ifkx) 115200

86400

69110 57600

43300

}4i«

:S920O T 72800

129600

1 03680 K64OO

64800

SiS*«

' 1

345600 IJO4O0

[72S00

138240 .15300

86400

69i»

1 5

43JOOO , 2^8000

216000

172SOO .44000

loSooo

g6t»'

1 ^

318400

345600

259:00

207360 . .72S00

125600

.C3b*|

7

604800

403200

302400

241920 ' 20.600

.5.200

12C9fc;

1 B

6gi2oo

J45600

276480 ; 230400

.72800

.3S24O

9

777600

5.8400

388S00

31.040 1 259200

194400

tSSS»

"

S64000

576000

4J2000

345600 1 188000

2T6000

,jm.

ciplanalory examples following Tabic IIL

■

I

P

w

J

^H

^|H

H

^^^^^^^^H

F

H

P

m

F

Part a.-

-(continudi).

MOO

Ai76

At 100

A. 150 ■ Aiaoo

A. 350

AlBOO

^*K

™IS^

tiT^

^jz 1 rx^

:^rc'

'^^C,

l««.

ptrwL

l«m.

pcim. pM«c

p.f-c.

^■"■■^

Num^

,rf««,itrig.ted

so

75 "00

IJO-

300

350

300

lOO

tso WW

300

400

500

Mo

ISO

ais 3W

450

600

750

900

JOO

300 1 400

600

Soo

1000

IJOD

J50

375 ' 500

750

1000

1250

1500

ioo

450 600

900

1200

1500

1800

y)0

S'S

700

1050

1400

1750

3I0O

4DO

600

800

1200

1600

3000

2400

4S0

675

900

1350

l830

2250

2700

) ifiO

7SO

■ooo

1500

2000

2500

3000

J A. 800

-^0

A. 400

jueoo

AI800

AilOpO

A.iaoo

1 .*.<.lul-.

>4. dubi.

^, ch^n.

1 p-~>t

SST^

rjT^

z.t.

•cri

Km%'?

TrT^

1 xmnt

■Ecoad

leMd

KCDDd

wor.d

KCUDd

«™nd

NuntercJ «,..«■

.h=i,>.(R«™«l.,>)im

ai«L

soo

300

400

600

8«,

1000

1200

( 400

boo

Soo

IIOO

.600

2O0Q

3400

) boa

900

ISOO

1400

3000

3600

1 Soo

1300

1600

»4O0

3K»

4000

4800

1500

3000

4000

Sooo

6000

1 l»0

1800

1400

3600

4S00

6000

7SO0

MOO

1100

iMoa

4WO

SMO

7000

li4«>

t 1600

3400

3100

4800

6400

Sooo

9600

f ISDO

J700

3600

5400

7300

9000

108a.

It""

3000

4000

f<oaa

800a

ICXX»

IJOOO

L i

t

^^1

1

■

H

■

■

■

E STORAGE AND SUPPLY.

[tasls

.J

Part 3. — Eptwaknl of amfinuffiu

supply.

Contianous snpplj- xa cubic feet per second into
Tieeyenl

lotal qtiaQiiiui nd

^r=r?^

For 9

P«S

l^L ■ IT±

~1,

S2

316 360

■06

■04

■ot -ois

■013

■«

630 720

■u

■08

■a* 1 "030

xa?

XA

9«0B0

■18

11

t* -0*5

■040

■^

1Z6IM0

■24

16

■08 -060

■053

■o*

1576 BOO

■30

20

■10 1 -075

■067

■OS

1832 160

■36

34

■II -090

'oSo

■06

2 2O7S20

■4J

=S , -14 , -105

■093

■07

2 622B80

■4S

32

■16

-120

■(□7

-oS

2 838 240

■54

JG

■18

■'35

■,20

■09

1 million

■1903

1258

■0634

■04T6

■04»3

■ojijw

2 millions

■3S0S

= 537

-I26S

■oSst

■0S45

■OSJIJO

3 ,.

■5 70S

jSoS

■1903 ; -1427

■126S

■095119

4 ,.

■751Q

5074 ' '2537 ''901

'1691

.126S39

6 „

■95 '3
1-1416

6342 1 ■3'7> ■*378
7610 -3805 -2854

■2114

■=537

■isiw

■19M»

7 ..

.■33.S

8S79 -4439 ■i^^<)

-1960

■12.96, 1

8 ,.

I-5Z3I 1

0147 5074 -3405

'33B2

■3536;*

9 .,

1 7123 '

1416 1 -5703 1 -4280

■3S°S

■jSsjSS

10 ,.

i'9oz6 1 1-2684 -ej-jj 1 ■4756

■4228

■3i7«<

■

■

^^^^^J

^H

^^^^^^^^^^^^^^^^^H

^^^^^H

^L. rUT 3] STOKACE AND SUPPLY. 33 ^|

^Part 3 {continutd'y — Equh'aUnt of contimious supply. ^^1

171 that is equivalcDl to ■ certain numbcT of walciin^ in a month.

3IZ

AiSO

Ai IS A. 10

■utringi wale ring!

At 4

petuumh

At a

permonih

All

Cub^f«,

ManihJj tupply is cubic I(<l per Hcood

Kiooa

■IIS7

■ 'OS??

15386

■0154

■0077

■0039

sooo

■1041

■0510

■0347

-0139

-0069

■003s

eooD

■0916

■0463

■0309

•0113

-0062

■0031

7000

'oSio

0405

■0271

■0108

■0054

'O0J7

SOOO

0694

■^347

■0131

■0091

•0046

■0023

5000

■0579

■0289

■0193

■0077

■0039

■0019

tooo

-0463

■0131

■01 S4

-0061

•0031

•oois

3000

■0347

■0173

■0116

■0046

■0013

■0011

2000

•0131

■01 r6

•0077

■0031

■00.5

■0008

^BN

-0116

-oosS

■0039

™,5

xooS

-0004

^P

.,

■050

■03J3

■0133

■0066

-0033

^Bv

■09

^S

■0300

■0120

■0060

•0030

^Hk

•08

■040

tw67

■0107

■0OS4

■0027

^^p

■07

■OJS

■0233

■0093

■0046

■0093

^Hh

•06

•030

■oaoo

■0080

•0040

■OOM

^Hd

■05

■oas

■0.67

■0067

■0032

■0016

^|k

■<H

■030

■0133

■0053

■oorf

■0013

pSn

■03

■ots

■0100

■0040

■oow

■ooio

^ ma

■03

■010

■0067

■00S7

■0014

■OC07

»

VI

■005

■0033

•ootj

■0007

■0003

k..

1

STOXJGC .Asay scffi.r.

of dK jof boa ■ itnia aMA b Bp ke
a«afkUi^Hm&fakaa&Barf3i fat duMC

Ob^faMlfaT^ted* jwmrinlwewifcKafaiam

I

lAsSSSooo sv^

4 m; n> •i4.'S

6z2oSo 'OttJ

82914 -0030

5rS 100 ;;4 i3;6--5

'.iJle rimfall of on£

557 J6S0C0 2S-8S3

250 yo5 600 1Z0999

17 87S -ooa

STORAGE AND SUPPLY.

ymbtneii iirigftUon *Dd watci-wark scheme rields t8'a34 cubic Teet
I <:n<l 1 wlul amount ofluid oiid of population could it supply, at the
tn n/ 150 acre* pel cubic fiiol per second, and or 7^ (^ons per head
»dicm, if ODc-foimh u lobe used (or the water- worki ?

Tie snpplj- ■Tailablc for irrigalion will lie = i8-i34— 4'5S8 — 13'676
- net per second ; and from Table lil.. Part 3, wc obtain Ihe required

FatniUllon.
287 3Sd

^ tnwB has a population of 40000, requiring water supply at 3 cubic
I'M held daily, and has suburbs 10 liie extent of t 400 acres re-
■-•■-i ittipiion ai 150 aeies per cubic fool per second of supply : — what
■■^■■^&\ am will tie necesaiy lo provide [his, if the annual raiafall it
> ho, out of which a half can be utUiMd ?
'.iiunlliig to Table III., Pait 3, the supply necessary will be

a vomi^lati

Total cuIhc red

■('"

U\

Fut I.

Tabu IV.— FLOOD DISCHARGB.

P«

Table of flood discharges in cabic
ment areas in square miles, and
ial in the formula —

doe tocat^-
to a coefficient

Q-ftxlOO(E)t.

Part 2. Flood discharges in cubic feet per second doe to catchmrnt areas,

with values of i 6om 1 to 20

Part 3. Flood waterway for bridge-openings under coefficients 4- 8' 25;

andi-12.

T«LX IV.— FLOOD DISCHARGE.

Ttble of flood duclu^es in cubic teet per seMod, dne toottck-
ment aieaa in square milei, isd cotreipoDdiiig to t coeEEcienl
i — 1 in the lonDuU —

Q-2xl00(E)(.

^PB^^J

■

^

^^^H

^^H

^1

^^^^^H

■

FLOOD DJSCH'iRGE. t^Im^H

Fast. i.-^Mood dis<A<irgtt w cuiic M P*' Ma)^|

Cucb-

^'"iA"

*=a

*-»

1-4

* = 8

O'OS

33

33

44

SS

0-1

3fi

54

7»

90

l>2

eo

90

110

ISO

D-3

63

in

t64

aos

W

100

ISO

aoo

•SO

as

tiS

«7T

336

»95

O'G

'36

*04

«7«

340

07

IS*

138

304

380

0'8

170

«S5

340

435

O-S

184

376

368

460

1-

ioo

3°o

400

Soo

?

336

S04

673

%ifi

3-

476

714

9Sa

live

4-

668

849

1 13a
133*

14»S

i«ro

6'

766

1149

1533

iWS

7-

860

119a

I7M

a ISO

a-

9S*

14*8

1904

.j8o

9-

1040

1S60

30S0

atoo

ID

lis*

1686

3348

3 810

20

iSoa

3838

3 784

4T30

30

3564

3M

J. 38

6410

40

3ito

4770

6360

7 950

50

3760

5640

7530

9400

BO

4310

646S

8630

10 775

70

4840

7160

9680

13 too

80

5350

So^

lO?-*

I J 375

90

5844

8766

116SS

14610

1M

63*4

WS6

1364S

ijSlo

1

1

L

J

■

^V

kBB

^fcr 1] FLOOD DISCHARGE.

n

Hkiu, vUh otktr valua tflht tot^ent Ic

h 1-9

t=a

t^4

i-S

1 6314

9486

■ 1648

I5S10

10636

'5 954

It 17a

16590

M4i6

Ji6»4

18831

36040

.7888

16S33

35776

44 720

3tt43

31 7»3

41196

5*870

34I4A

36369

48 49*

60615

37118

40817

54436

68045

30 084

45 116

60168

75aio

3»864

49*96

65718

Si .60

J5 5«

S3 349

71 13*

B89.S

S9S14

89711

1.9618

149 53S

8107a

lit 60S

163 144

101680

IOOS94

150891

lot iSS

asi 48s

118 gao

.783S0

137840

297300

136346

M4S19

171691

340865

• S3oj8

119587

316116

38^645

.69.80

»S3 n°

338360

4« 95«

184804

177106

369608

4610.0

aooooo

300000

400 DOO

5oocx)0

336358

504537

671 7.6

84089s

4J6 570

714 855

953 140

1 191 415

564710

847 06S

t 119 410

1 4". 775

668 740

1003110

1 337480

1671850

1 J«732

1 ISO 098

' 533 464

1 9>6 830

1 86070*

1 191 056

1 731 408

3 .51760

«'366

I4J7049

1902731

23784.S

t 039130

1558845

1 078 460

3 598 075

t 1146B1

1 687 013

2149364

18.. 70s

^L '*

1

^^^^^^^n

^

■

naoo Dtseauscs. fnn^fl

Pmz x(d

»t:).-Jfaitf AafcBTo ». aiitji^ftr

ClB^

1

S

»-•

*.»

*>a

f=U

i-

IHB

■

na

1^

»7«

•t

M<

ito

»«

3SS

M

9*1

?»

^

4Sa

n

J*

««»

49*

65fi

H

^

ve

60a

Sao

|j

,

«

^B

•»

j«i

9«4

1

H

sn

Si«

toSS

I

*7

6ol

7*>

9" 1 J16

1

[h4

680

8}o

looo 1360

1

W

73«

*»

1 104 1 471

"

,

Soo

ITCO

IIOD 1600

,1

;

'iM

I1S0

10(6 26SS

3.

y

1904

2j3o

2S56 1 jfoS

I

zrf4

2SJ0

3396

4 5^8

5'

5-

1672

33*3

400S

5544

6*

?■

jgot

3830

4596

5S0S

n

juo

41OT

5160

6SS0

g.

*

3S0S

4760

5 7"

T6i5

9:

9-

4lte

Saoo

6x40

S320

10.

10

4496

5620

6 744

8992

11:

20

7 5*S

9460

"3;i

15135

lii

30

I0 2i6

II 820

-5384

10511

IS'

M

12710

.5900

190S0

as 440

3T6

M

15040

iSgoo

MS60

300S0

37*

*i

17240

aiSjo

25S60

54480

«'

73

igjSo

24200

290*0

38720

4S«

M

21400

26750

31 100

4aSoo

S3J

90

33376

29JJ0

3St*4

467s J

sJ*

10Q

25^96

j(6kj

o7 944

5039*

fij*

■

^^H

lULt IV. r

UT 3] FLOOD DISCHARGE. Xt ^^|

• ■ .---/^^

-i^nl anas with other values oj the aeffieUnt k.

1

1=8

4=13

t=ie

4o80

1

■Xi

35296

37 944

so 592

63*40

:v'i

4^544

63S16

85088

106360

."]«

57664

86496

■15328

144160

^H

"5S«

107328

143 104

178 8S0

^^1

-•-.a

84592

126 sss

169 184

211480

^^1

I'-.a

96984

MS 476

•93 968

842460

^^1

7--*}

108872

163308

217 754

272180

^^1

. !»

120336

180504

240672

300 B40

^^1

■-:]0

13US6

197*84

262111

328640

■

■ m

142264

813 396

284528

355 660

■

.in

2J9 256

358884

478512

598140

■

3J4288

486432

648576

810 720

■■..0

401376

603564

8ai7S2

1005940

^^1

H)

475680

71352a

95' 360

I 189200

■

!««

MS3S4

818076

1090768

1363460

■ ■■'■«)

63J 232

918348

1864464

1530580

^^1

l<)

676720

10150S0

1353480

1691800

^H

■rt

739 »>6

110SS24

147843s

1848040

■

■■■jQ

Sooooo

1200000

1600000

2000000

■

■iiC

'34S432

2018148

2690864

3 363 580

o)

19062S0

2859420

3812560

4 76s 700

^^H

■n

2258840

338SJ60

4517680

5647100

^^H

.1)

2674960

4012440

5 349 920

66S7400

^^1

■ Hfl

3066918

4600392

6133856

7667320

^^1

, /uiflO

3441816

5164224

6S85632

8607040

^H

J acfU

3 80s 464

S7oH'96

7610928

9513660

^^1

1 nan

41569W

6235380

8 31 J 840

10392300

^^1

Lr»

4498728

674S092

8977456

11246820

■

1.

J

^H

■

■

»

FLOOD DISCHARGE.

[^SuH

Part 3.

—Flood wattrwayfor briJgt eftningi m^

(O0dau k=8-2ft.

|Bj Colonel Dickdu.)

Cuchn.Pl

Flood

diKhMI.

=;,

Find

NtuOier

Squu* B.ilQ

Cii)^<: fta

ptrioc-

^r

S.^

•0016

6S

"■S

'0O31

a-JS

■0047

15

3-

■0078
■012s

31

1>

■0250

5>

s

IQ-S

■0625

103

6

IS-

•1250

>T3

6

jg.

>!£DQ

19t

6

49-

■6000

2

3
S

7

490

'A

J 55°

6

7
7
7

7

81 ■
137

aoo
170
400

SI

IQ

4640

7

20

7804

8

97S

30

10 577

8

ijai

fiO

15605

9

I 734

too

16094

9

1899

200

43SS4

4388

300

Sy48'

8715

500

87^55

to

1000
2000

146 TJ7
J46;6o

n

14673

M451

;s

3000

J34487

3D40S

M

6000

tx

40886

ao

10 000

68750

30

20 000

1 J8S 74* "J

106745

40

30 000

,«70 96i ij

■43 9»>

45

50 000

I 695 690 14

190 «6
306 tSj

S

100 Don

4 6j9 *74 >S

k

»A>T 3] FLOOD DISCHARGE.

ml.). — fhod waterway for bridge-openings under a
mfficient k=12L
(By the Author.)

diKh«g(

.'^X

Flood

■^:r-

S;ao

Hciihi

.

Cub-fm

P^'i^.

"^^

No.

F«.

F»«

96

5

«S-8

5
5

3
4

J

3

'i

31 -s

5

6

44-9

5

9

3

J5-4

5

'5

4

ISO

6

as

s

a5i

6

4*

s

S

6
6

7

17a

3

6
6

6

a 016

7

aSS

3

8

j«S6

7

408

3

9

,coS

7

ISI

5

9

7

5

';«

7

96+

S

10

"JS

8

1694

S

iS

13

n

8

I9M

S

30

13

s

«S6o

9

a5°8

s

40

'3

S

ess

9

4 2>6

6 -Si

7
9

40
40

;i

00

»S«6

8650

9

SO

10

00

■ «S»8

10

13660

60

20

BB

iS

10

21 340

"5

60

*s

B

J]

31636

17
»3

80

So

25
*s

7IJS.M

S9460

30

I 100 oco

IS

40

aoiSuS

n

IS5 W4

36

ISO

40

n

JS594M

13

219 956

18

40

DO

4 ori 440

186604

29

150

40

BD

6 74«Wi

'S

449874

4S

iSO

40

■' .■ * .••-■■

ij

Tablk v.— sectional DATA.

SXCnOMAL AESAS (A) AND Hydrauuc Radii (R),

Part I. For Rectangular Canal Sections

Put 2. For Trapezoidal Canal Sections having side-slopes of one

to one.
Part 3. Dimensions of Channel Sections of equal discharge.
Part 4. Values of A and R for Cylindrical and Ovoidal Pipes and

Culverts.

FOK USE IK THE GENERAL FO&MULiS,

TVkss TabU mt^ U used with any unit of measunmimi.

^^^^^^IBI

38

SECTIONAL DATA. [tjuu*.I

Part i.—SeeHanal Areas (A) axd HydrmdU J?<J

_■ ._■ —1

d

R 1 ^

R A

X

OS

0333 IS

0-37S

0-4

076

';5

0'4J9

iij

o-S

3

0-54S

!■

0*5

3-

0-6

0-666

m

a-S

o-SSS

375

0'6Si

5

*»769

1-5

0'6«.

4S

0750

0-857

I're

35

0*36

5 -as

o-goS

7

<^33

2-

0666

6-

o«S?

8

MS

4;S

qM*

6-75

09

9

iTf? i

2-6

o'7'4

7*5

0937

tn

5-5

0733

8»S

0-971

I'lU 1

3-

6'

0750

9-

!■*» 1

3-S

T

0777

lo-i

1-050

'4

larj 1

8-

oSoo

1-091

■ 6

;:s :

5'

o»33

'5

I-IS4

20

1

- • 1

R

A

^

^

»

M-

OS75

16

0-88S

iS

V25

I7'5

1061

1-080

i»-S

i»i8

t'S

1*44

^

1Z62

a?

\-iSt,

I-7S

S4'S

1-397

z8

1-434

3' -5

1-468

?

I-5SS

31

I'foO

36

1-636

2>26

3' '5

1701

36

1-757

405

r-8oo

2-6

35'

t-S4i

40

1904

45

'■«3

2-75

38-5

I '97'

44

j-oso

49-5

3-109

3'

42-

45-5

z'Z30

48
5^

2-181
j-jii

iS.

!I

3'5

49'

a-3i3

56

1-346

1.3

4-

1.:=

a '447
a '545

60

tyi

675

il

4-26

S9S

J. 6*4

1774

j6-i

4'S

63 ■

3741

71

1-8S0

Si

]■

4-?5

66'5

1-833

76

1-979

ss-s

JIO,

5'

;o-

1-9I7

So

3-080

90

j2

6'5

6'

77'
84'

3-080
3 130

SS
96

3'S6
3W

,s

/■

9»'

3-5«

ita

3 733

■ t6

ISIJJ

1

t

1

■

|_

■

1

u

^H

^BfA» 1|

SECTIONAL

DATA. 39 H

^Hb»j'K/dr sections of Chantuls, Canals, and Aqueducts. ^^k

^Ktw>UDttf>>

of iValtr IS).

■ *-•

»=.

.=!»

JT

K

^

Jf

R

is;

's

0-800

'';a33

0-857

9

08S7

ia-5

"5

'■035

1-091

IS

1-154

18

1106

U
16

rziS
1333

175

'■S95
1-429

M

'

357
5

i'aS6

ig

1-440

aa-5

'-S53

97

636

1-364

1-538

as-

t-666

30

764

f4i6

l'6lS

27-5

1777

33

SS7

• ■s

14

1-714

30-

I-87S

36

ut;

26

1-794

32-5

1970

39

106

aS

1-866

35-

2-058

42

ao9

^PS

1-666

V

t-938

37-5

ai43

■•^

304

I-7M

i^

40-

48

1-875

40

2 -III

50-

2500

60

2-727

^B *

.»

.=^

t=M *=«

jr

^

R

J,

g

^

g

JTjI

30

0-938

35-

0945

40

0-953

45

■■3f'4

SaS

i-38a

■-398

i7»S

ao

1-764

70-

1-793

80

1818

1-901

67-5

1957

78-75

1994

90

8-023

a 083

7S'

r;s

87-5

ai87

iiSS

Si-s

5*-a5

a-377

a-4aa

90

2-500

105-

a-56a

a-6io

^K^

a-S79

97-S

2-673

113-75

2-741

'3°

*-79S

=734

105

3-835

122-5

a-9'9

140

2 -982

^Ks

aSiU

I J 1-5

3-

I3i-a5

3-071

150

3-099

3-030

3-156

140-

3- 16a

160

3333

j-160

137-5

3*3"

148-75

3-421

IS

3*505

3-308

'35

3-456

'57-5

3-579

3-672

^Ks

3-3J7

Ha' 5

3-6oS

166-25

3737

190

3-838

IS

'SO

3750

'75-

3 944

aoo

165

4-oa6

191 ;5

4177

h

4-oso

iSo

4186

4473

440

•i

195

4'544

ai7-5

4739

4906

140

4 773
S-220

\Z

5-
S49"

280

320

51S0

S7U

^

jl.

I J

■_ ^a;

IS

• ^

:'/'.

; ' .

t

f.

/y

I
't

'•"i

"■-1"

* -- " V

NX
3CC

1

■

■

■

■

■

^H

Ih

■

^^^aTH]

SSCTIOXAL DATA.

■1

^^tlaMgu/er Sitiionf ef Channels, Canals, and Aqtuducts. ^^k

■B

£*f""

^WaUri,^,

s~~

t.l«> b.I«

.=.„ 1

■91

A

*

R

R

90-

0-978

0980

0-984

09S6

fo-

1-915

200

■-9IJ

240

.■936

iSo

1-944

»-I«

"S

;:;i;

270

2-169

315

3-i3o

1-369

150

300

2-400

350

2-414

47 'S

n?;

a7S

a 606

330

1-619

385

2-&^6

TO-

300

1830

3to

a-8S7

410

1-877

JJ-S

J-OJI

3^5

3-053

390

l-^l

455

3-106

•s-

3145

350

3-27 1

420

3-307

490

3-333

S7S

3461

375

3-4S8

450

3-529

S»5

3-560

so-

3-671

400

3-704

480

3-750

560

3-784

fas

3-S83

435

3-917

510

3-969

S9S

4-007

•OS'

4-091

450

4128

540

4-186

630

4-228

M7-5

4»96

475

4-J38

570

4-401

665

4-448

ISO-

4-Soo

500

4'54S

4-615

700

4-667

*7aS

4-701

S'!

4-75'

630

4-8j8

735

4-8S3

495"

4-900

550

4-95S

660

5038

770

S-ioo

17-5

S098

575

5-'S7

790

S-*47

80s

5-3'3

5-192

600

Vlll

710

5-455

840

5-5=7

P'S

5-488

62s

5S5S

750

5-659

87s

5-738

8S

S-679

630

S7S»

780

5-865

910

5-948

07 -S

5-870

67s

5-947

Hio

6-068

945

6-156

630-

6-057

700

6140

840

6-269

980

6-364

65«S

6 ■144

7*5

6 '332

870

6-468

1015

6-569

575-

Xt^.

75»

6-SH

900

6667

105°

6-775

^-s

775

6-7»

930

6863

loBs

6-977

r2o-

6-79J

80b

6897

960

7-059

7-'79

TWS

fi-97*

8^5

7-oSi

990

7-^53

1155

7-380

J6S-

7-150

850

7-265

7-445

1190

7-579

787S

7-325

875

7-445

1050

7-637

1225

7-778

Sio-

7-505

900

7-627

loSo

7-826

t:6o

7-976

832s

7 ■671

9'S

7-805

8-015

1195

8-171

^*'

7«*4

950

7-983

8-101

• 330

8-364

8T7-5

8013

97 S

8- 159

1170

8-387

'365

8-559

900-

B-iSi

8'333

8-571

1400

8 -7 JO

990- 1 S-839

9017

1120

9-»9S

15*0

9SIO

loto- 1 947J

1200

9677

■ 440

■6S0

IO-244

1

L

_

■d

■

■

1

■

■

■

^H

■

^^^^^^1

».>

SECTIONAL

DATA.

1

fK/or Sationt of Chaiwih, Canals, and Aqittduets. 1

^ D<f*ki ^ Wait' UY

t.^

*-^

»-

W)

..,«

g

^

*

_j

R

^

K

1-967

1"

1-969

560

1-971

600

1-974

i«9

a -453

700

2.456

750

2-459

«<»7

780

J-93*

840

2-937

900

2-941

3-164

Hi

3170

910

3176

97S

3-181

3-401

910

3408

980

3-414

1050

3-420

3-636

975

3-64S

lOJQ

36S2

IJZS

3-6S9

3ST1

3-880

3889

^V\

4-10*

iloS

4-irs

1190

4125

'275

4-337

1170

4349

1160

4-360

'350

4569

I3JS

4-583

'330

4*594

14JS

4-8W

IJOO

4-S.S

1400

4-SJ7

1300

4-839

5-030

1365

S-04S

1470

S'o6o

IS7S

S-073

S-»S9

1430

5 '277

'S40

5-291

l6jo

5-305

S-487

1495

S-508

rfiio

5-5"

172s

5-537

S-7M

1500

S73S

rbSo

5-754

1-7^

SW

1625

S9^3

r750

S;9S3

-8?5

6-167

1690

6-19*

iSio

■950

6-230

':5S

G'4l6

1890

b-m

6460

6-s]2

6-643

i960

6-666

6-689

I'dl^

6-869

103,0

6-894

217s

6-916

I9SO

7-090

7-119

2250

7-144

7-a74

»oi5

7-314

1170

7-343

2325

7-370

ry»

ao8o

7-536

JMO

7'S67

2400

7S96

il

7-978

J380

S'013

2550

8«SS

ajio

8-417

2520

S-4S7

2700

8-49*

8470

8-S52

2660

S-89S

2850

8-935

S-ajo

2600

9'2S6

2800

9-333

3000

9-375

9-6S4

m^

9;7I6

2940

9-767

3150

9-807

10-076

2)i60

30S0

10-.98

3300

'SZ

10-494

3990

lo'les

1230

10-627

34 SO

10-909

3120

IO-9S6

3360

1 1 '052

3600

11-331

ss

11-404

3500

M-475

3750

"•538

II-7J8

i:-8i8

3640

n-S9S

3900

.1-96.

12546

!S4»

11-639

39!0

11-727

4200

'2-793

!j:fS

3900

13-44S

4300

13-549

4500

13-635

4160

I4-S47

44»o

14-3S9

4800

14-458

"7-«43

!">

■7 333

5600

17 -SCO

6000

17-641,

I

^^

^

I

■

■

^^^H

■

■

^1

^^^^^^^^^^^H

MMXS y, FAST 3} SECTIONAL DATA.

A

mi^*

L> (f ) OMf ^;»/l. =/ WV« (^.

<

-^

K

rv

6=-

nr

0

T

0793

9'

0-831

0-858

13-

0-877

»

9-06

0-950

1.-56

14-06

1039

16-56

1066

»

llli

1-098

'4 IS

1-164

'7 -25

S3

.-246

l»

l-»38

.7;o6

13'8

20-56

37S

1-420

16-

1373

1-464

24-

53.1

28-

r-586

w

i8S6

I-50J

13^

r6oti

27-56

684

32-06

1746

6

a IIS

f62i,

d,i

VU2

31-^5

831

36»S

1-901

76

J4-06

•747

2956

35-06

971

40-56

a 051

'7;

1864

33-

39-

MO

45-

2-197

?S

1-979

3556

1^

4jo6

49-56

2-339

33'5

2091

40^ZS

2-249

47-25

375

54-15

J-4?7

36'56

4406

2-368

5 '-56

502

59-06

J-6I2

40-

2-311

48-

2-486

56-

628

64-

3 745

SJ-

S73'

6s-

3936

75-

3-107

85-

3-252

1

..«

*=«

^

*

^

K

^

ft

_f

X

0

16-

0-934

31-

0-944

36-

0-952

41-

0-957

39-75

'■3S9

47-15

1-380

54 75

1-395

6225

1-407

M-

1-761

64-

1-795

74-

.-S20

84-

1840

6, J.

'■954

72-56

1-995

83-8.

2-026

95-06

2-050

fcS-7;

a-i44

81-25

2J7!

91-75

2-iia

106-25

lis.

76-3.

jjjS

9006

3-384

.03-8.

3 ■4:6

"7-56

n*

1-509

99-

I 573

129-

2 '661

«

91 -Sf

»-6&4

1^8-06

2758

.24-31

2-8.5

140-56

2-838

K

9975

*-8sS

117*5

s-939

134-75

3-001

i5a-J5

3051

-TS

107-81

3-018

.26-56

3-141

145-3"

3-197

164-06

3242

F .

116-

3-193
3-358

136-

ri9i

.56-

3368

176-

343'

ds

lM-3t

145-56

3-464

l66'Sl

3-547

18S-06

3-6' 5

!^

>3«7S

l-5'9

"SS'S

3-633

177-75

37J4

3 -798

141 $1

3«rr

i6s^

3800

.88-81

JS98

J1256

3-977

;s:»

3-831

'75-

396s

4070

225-

415s

4136

'95 J5

4»»6

2227s

4406

350-25

t«

■S6-

4-43a

216-

4599

246-

4-733

376-

"HTS

47»

ij7»S

4903

J69-7S

5 -053

303-2S

5-'77

S-ooo

159-

S-Ktl

204-

IS

339-

Sjoi

^

*64-

5S4I

304-

S-776

344-

3S4-

6-i3»

^H

^

■m

I

■

■

■

■

■

■

■

SECTIONAL DATA.

[TABUI V. M«T J

^V Part i {eoni.-).~ Sectional Artas (A) and ffydraalu SaJii {^)Jfr

Camif^HikKf A>

ykritmStd

'_

*=10 *=M »=

r.

'- '1

^

^

^

j(

4

ji

,

I'O

si-

■964

61-

0971

If

0-975

Sr

i,i:s

2-0

laj-

I-S6S

1*4-

I-8B9

•'<»3

164-

IH!

2-K

11756

1-0S6

140-06

16256

11Z9

185-06

IHJ

2-5

'3''*S

i-joo

156-25

2-330

ia.-»5

2-3S2

206-15

ti»

2-75

us-t*

1-5 II

I7J-56

1-546

200-06

1 571

127 vi

3-

'S9'

1719

1S9

1-760

219-

1790

3-2S

■ 7306

1-927

»5 56

1-971

lj8^

J-006

3-5

187-33

3rj6

3-iSo

157-15

3 -no

3-7S

201-50

i-3'6

239-06

3-3S6

176-56

3-43'

t-

Il5-

3-S»3

as6-

3-590

196-

3WO

4-2G

13056

3-717

173-06

379'

315-56

3-&*7

'\ J

4'S

145 35

3910

290-15

3-991

J3S-*5

4 05»

3k,';;

'■' : 1

I7i

100(16

307-56

4-188

SSS-oa

4156

.jj 1

%■

»75;

4-287

335- ^

4-384

"S"

4-457

;:;; 1

S'ZS

4-473

W3-56

4 577

395^

4656

S-S

505-25

4-656

3'«-»S

4-768

415-15

4»SJ

57S

320-Sb

4-838

378-06

4-957

435 56

S<M9

fr

336-

5017

3')6-

5-145

456-

5143

B'2S

151 sfi

5<95

4 14 06

5-330

476-56

5455

6-S

367 -'S

5-371

432-25

5 51 5

49725

5 -626

6-75

383-06

5-544

450-56

5 ■'•97

51S-06

58.5

7-

J99-

i-7l6

469

5-877

539-

6Tmi

PIS

415-06

S-88J

487-59

6t.s6

;6o'0()

6-18K

7>S

431 'IS

6-056

506-25

6-234

58- -IS

6-373

77S

447-50

6'«3

535-06

6-4oy

601-56

655s

8'

464-

(.■3S9

544-

6-584

614-

673^

8-26

480-56

6-553

Sf'3-"6

6-757

64556

6^1 J

B'S

497-^5

58215

6-OlS

6672s

71^5

J 75

SI4-Q(>

6-8rr

(W[ 56

7098

689-06

7171

9'

53'-

7 ■037

611-

7-a67

7tr

-■44»

3!5

548-06

ri^*

64"- 5&

7-434

733 «^

7*13

9'S

S^S'SS

7'JS3

660-15

7600

755 2S

!S

9- 75

*K;S6

7-509

6So-o6

7 765

777 St-

IP-

600-

7-W.S

700-

7-929

800-

»'V

(.;(-

S173

7Sr

8-571

891

8 Si a

tool-

«■

744-

SH6j

864-

9197

984-

9467

1104-

»

A

^

fc^

_i=

■

^^

■

■

■

^^^^1

^H

^^^^^^^^H

^^^^^^^1

^B.T. rAtTi] SECTIONAL DATA. 47 H

" 1

TraptsMial Sutions of Canals with Side Slopes of One So One. ^H

wUl

u (*1 BiJDtpihs if Waltr {J).

,^^

R A

«

in

A R

91-

0-980

0-982

0-^5

141-

0-987

1

lS4-

1-913

204-

'■93'

244-

'■942

284-

1-950

S

»7'5&

1-154

130-06

2->6j

27S-06

j-177

32006

2->87

a3<-*5

1-3S3

ali-jb

2393

306-25

J -410

3S6»5

1%

SS5-06

2-609

337*56

2-642

392-56

^ig

>79-

>S33

309-

2-848

369-

2-872

429-

S

joj-o*

3055

33S-S6

3-073

40056

3-10I

465-56

3-121

s

317 ^S

yv('

36i-2S
389-06

3296

432-25

3-328

502-25

3-35'

35" 56

3-«94

35 "7

464-06

3-553

539-06

3579

3-711

4.6-

3737

496-

3777

576-

3-B07

3916

44306

3-955

528-06

4-

613-06

4 ■033

*I39

470-15

4171

560:15

650-25

4-25K

^■4SO-o6

4-35'

497-56

4-3S6

592-56

4-441

667-56

4-481

4 56*

625-

4-659

735-

4703

K soPTjfi

4-769

580-25

4-8. i

657-56

4 876

762-56

4-924

5 _ws-»5

49?6

5-021

690-25

5092

800-25 5 ''44

^5 sso'56

S-181

608-06

S-S30

72306

S3o6

838-06

5-363

L 576-

5 397

636-

5-437

756-

5 '519

876-

5581

^ 1 60.-0

5-58?

664-06

5 -"43

7S9-06

573'

914-06

5*797

fc^

57SS

69!-»S

5-848

822-15

S-942

95225

6-013

S-9S6

7»-s6

6-050

855 '56

6-151

990-56

6-226

■ «9'

6-184

749-

6-25!

889-

6-359

1029-

6-439

Hjos^

6-380

777-56
606-25

6-4S»

9!a-56

6'5u6

1067-56

6-651

^■»i-as

6-SJS

6-652

956-25

6-772

1106-25

6 '86(2

■e:

6-769

B3S'06

6-849

990-06

6-976

"45-06

7-072

6-961

864-

7-046

1024-

7-179

1.84-

7280

7-153 I 893-06

7-»4'

1058-06

7-382

1223-06

7-4SS

^ ' SpiS

7-34^

922-25

7-43S

1092-25

7-583

1262-25

7-695

K 864^

7 '530

95156

7-618

1116-56

7783

1301-56

7*900

Sfl.

7-717

9S.-

7-819

1161-

7-983
S-iSo

13^^56

8-105

iS 9l8'n6

SS

<o.o-s6

8-0IO

119556

8-3S9

L wi-^s

1040-35

8-<99

1230-25

8-376

142025 B-sil

■ 9T3-S6

8-271 ' 1070-06

8-3S7

1265-06

8-57*

1460-06 8-713

^b<M-

8-454 1 ' 'oo-

8-575

1300-

8 767

1500- K-OT!

9-173 1 laii-

nii

'44J-

?-5.i6

1661- |o>7or

^^»4-

9-876 1344'

IK-OJ

1584-

li.-29

1824- j .04.,

L J

^^^^^^^^^1

«a

SECTIONAL DATA. [TABUt T. H

Part 2 {conl.).—Sictwml Areas (\)attd BydraulU/iadiif^^

1

- '-" - 1

^

^

f:

^ K

f'O

i6'[>

o-9Sy

181-

o-y90

0991

2'0

3J4-

1-956

364-

1-961

404-

1-964

226

365-06

I- 194

41006

455-06

a-jos

!-S

406 'IS

1-433

456-as

2-439

50625

2-445

275

44756

J-66S

5W-56

1-676

557-56

3^3

3-

489-

2-901

549-

J-913

609-

I-9II

i-ii

530-56

3- '36

595;S6

3-148

660-56

3-" 58

3'5
37S

57a-a5

3-36S
3-S99
3 519

689-06

3-38*
3-6IS

76^-^

l^

*■

656-

735-

3-847

816-

3862

4-25

698 ■06

4-058

783-06

4-078

868-06

4^

4-6

740-25

4-286

83025

4308

920-25

4-3»6

476

782-56

4-512

877-56

fWs

972-56

4-55?

h-

S)5-

4-738

925-

1025-

4-78J

&25

867-56

4-962

97* -56

4-991

1077-56

S-ois

B'S

9>o-a5

5 -185

IOM-25

5-"7

113025

5*43

57S

953 '06

5-407

to6ii-o6

5 ■44s

nSjoe

5 -470

6'

996-

S-6*fe

5*666

'X^

S-69T

ea

1039 -OS

5-848

1164-06

5-889

5-9*1

6'6

io8i-as

6-067

I11I-25

6-Ml

1342-25

6-I46

67S

U1556

6-285

1260-56

6-33*

139556

6-370

7-

1169-

6-498

1309-

6-552

1449-

2S

725

iJii-56

6-717

1357-56

6-770

1502-56

7'5

i»5635

6-iW7

t406-as

6-973

\its.

7*JS

775

130006

7-146

«4S5'°6

7-ao6

7-»5S

B'

1344-

7-3S9

1504-

7-422

1664'

7-474

•

9'

1432-25

1521-

7-781

1602-25

1701-

7-KS3
8-279

177^-25
I8HI-

7-910
S-J41

9'&

.6.0-.S

8 -6??

1800-35

8-702

l'f90-25

8773

in-

1700-

9-029

190a-

9-122

o-iy>

IV

1881-

i^i

2101-

2^

2J21-

lu^ll

12-

1064-

10-64

ayy-

•077

2544-

10-S7

13-

1149 ■

ii;43

'm-

11-59

J7&9-

11*9

W'

1436-

2716-

12-37

*99«.-

12 -S"

Ifi'

26/5-

r2 97

2925-

1J15

3225-

13 -JO

!&

jSi6-

13-7*

3136-

'3-9*

3456-

14-09

5

■

d

1

■

■

■

■

^^H

^H

^^I^^^^^H

^Bt. FArT>j SECTIONAL DATA. 49 fl

X^tuiJal Sectisnj of Canah with Side Siopn of One lo One. H

»iMlki (bt aKlJ€/lJt^ o/naUr [i).

1

1 i=%ta b^no b=na »=)(«

\ A

jf

^

f

^

^

^

K

■ r484

1-970

514-

1-973

564-

1-974

604-

1976

^

fe6»S

i45«

656-25

J-457

706-35

3-460

756-35

2-463

7^9-

»*934

789-

1-939

849-

3-943

909-

3-947

s

790-S6

3'J3

855-56

3178

9»-s6

3183

985-56

3-188

i

8S»*S

3-411

9*2 -IS

3-4 '7

993-35

3-4»3

1062-15

3-428

rs

9Ut>6

3-647

989-06

3-65S

1064-06

3-663

1139-06

3-667

976-

J -884

to;6'

3-891

M36-

3900

1116'

3-906

!*

.ojSt-l

4-"9

113306

4-139

1308-06

4-136

1393-06

4-144

[

uoois

■»-3|3

1190-25

4364

(380-35

4;J73

1370-35

4-383

rs

..6»-s6

4-810

"57-56

4-599

135356

1447-56

4-619

IMS-

131S-

4-833

1435-

3-4s

1525-

4-855

a

.M(7-S6

S-053

139156

5-067

1497-56

5-079

1602-56

S-ogo

s

'550»S

Sa83

1460-35

5-399

1570-35

5-313

1680-35

5335

ra

mi-Ob

5-5'4

1518-06

5*531

1643-06

5 546

5'559

1476-

S-744

■596-

5-763

■ 716-

5778

■836-

5-793

a

;is??

S-97)

.664-06

5-993

1789-06

1914-06

6-035

B

6101

;^:i^

6-333

186335

6-341

i99a-3S

6257

n

.66SS''

6-419

6-453

■935 -56

6-470

2070-56

6-4S9

ijig-

tW.

1869-

6-680

2009-

6-701

1149-

6-720

S

I«J56

1937-56

6-908

3082-56

6-930

3337-56

6-950

s

i85fi-3S

7-106

1006-35

7-134

3i56;3S

7-159

3306-25

7180

?i

7-331

1075-06

7-361

7-386

3385-06

7-392

I^.**

7-SS4

1144-

7-586

3304-

7-613

3464-

7-637

s

31 12 as

8-000

3381-35

8-03S

2453-35

8-066

2632-25

8-091

»24r

8-443

1411-

8-«8i

2601-

8-5 "S

2781-

8-545

i

ii7o»5

8-S8J

356015

8-925

2750-35

8-962

2940-35

8-995

JSoo-

9-319

3700-

9366

2900-

9407

3100-

9-443

5

363025
M6f

m

3840-35
398.-

9801

IO-34

3050-25

3301-

9-849

IO-29

3360-25

3431-

1033

Ibss^*^

3133-35

10-67

3352-35

10-73

3582-25

10-77

111H

3»64-

3504-

11-16

37*4*

lilt

^^^^>s

11-46

3406-15

n-53

3656-35

11-59

3906-35

;::a

11-88

3549-

M-96

3809-

4069-

ia-7a

3836-

i3-8o

4116-

ii'SS

4-)6-

11-94

'3 -54

4115-

1364

4435-

13-73

4725-

1380

M-36

4416-

14-47

4736;

14-56

5056-

■ 46*

||no'

«7-53

5600 ■

17-69

17-8J

6400-

17-9S

^^^^H

k

1

■

■

■

■

■

■

■

1

so SECTIONAL DATA. [T^w* T. f^l

Ru>i;crioM MuLTiFLiEis fok R. ^|

SedJcm, from ihoK of R ^ven for RcctnneuUr Seciiunt in Part in

i ii the relio of (he bed-wiilth lo the depth of water. ■

^

IUliHorSd.SIap.1. fl

0-5

K«lr. Atol. Itol. itol. lt»l. lloL liwl. ll.»l. »g

t-o

1179

1142

1-82S

2-o5j 2-154

;«

2*435

D?5

fios

(■i6o

1-SJ6

1692 y-inl

\>*U, >'\

i-oS:

fii9

1-391

1-500 , 156:

l«o6

1-62S

VZS

iiAt

1-095

1-305

i-jSf.! 1434

1460

1473

1-S

I -054

1-078

1-249

1-313

■-34S

-364

1-371

V

!■

I -040

I -OSS

riSo

1 222

1M3

1-249

1-149

«

!'S

fOJl

1-046

1140

1-170

l-lfl3

1 184

1-179

3'0

1-026

i-03»

1-136

1-135

3-5

1-023

'■°J3

I-^

I 113

■ 1.7

1106

4>0

1-029

i-oSj

t-og6

1-099

IC93

i-oSj

4'5

I -016

1-025

1-072

1085

1-OSI4

1078

.■069

$■

1016

1-023

I 064

••<'73

1-073

106;

I-OS7

H

G'

:;oi3

1-OI8

1052

I -059

I-OS7

1-051

i-oti

fl

7'

(-016

1044
1-038

t-049
[-043

[■04;
1-039

1039
1-032

f03i
fo»3

9

9-

1-D09

'■03 J

■ -036

■ 033

roj;

roti

10-

1 ooS

l-oii

i-ojo

1031

i«9

1-023

1-014

0-1-

12-

1006

1009

1024

f026

1-023

1-017

1^)09

H'

roo5

l-DOS

I-OI9

t-006

16-

locn

1-007

I'oiS

1-016

tvat

18-

I-004

1-006

1016

1016

I-OI4

rooj

a-

I-0O4

1-005

1-014

1-014

l-OII

t-007

l-OM

9

30-

1003

1-003

1-009

I-009

1007

rix.4

J

40-

1-002

1-003

1-007

1-007

roo5

1-000

60-

1-001

1-005

loos

1004

0-999

BO-

1-002

i-o?5

1-005

1-004

oT>99

ra-

1-004

1-004

1-003

D-999

BO-

l-OOl

'-003

1-003

0-W9

90-

1-003

1-003

i-ooi 0999

100-

i-o

l-OOI

1-001

1003

1-003

I-D02

l-OQl O-^^

9

To obuin values of A ihe aecti. nal area for uiy Mwiodal a^l

Irvine / to 1 u the ratio al the side slopes, adJ A/- ta (he nJiH M

given lax nelugulu sections in Pan i. jH

1

■

■

■

■

■

^1

I^^I^^H^

H-. MRTi] SBCTfO.VAf. DATA. Bl ■

H RCDUCTIOK MlILTIPLIBRS FOK R. ^|

Kaklog Vdaa (rf ff, il.« Hydiuulic Radius, for any T«pezoiHd H
SfCtion. from ihOK of B given for Trapezoidal Seclions haviog Side H

SLvoofOneWOneinraita. ^

4 ia the nlio of the bed-widlh to the dcplh of wMer.

H Ri.io. of Side Slope.

1

owi. A»i- *wi. it«i. iu,i. iMi, U'oi. Hi»i. »toi.

P

■*437

°-533

o-ssi

o-Sii

0-9S4

10

1-03S

!-o8o

i-:i6

75

■5577

a'6t6

0-647

0-8S7

0-944

^■m

1-056

1-077

6381

06^

0714

o-SSS

0-957

1-039

1-050

ra

*974

074a

0-764

0-910

0-967

;-oi7

i-ojo

s

7418

0782

o-goo

0-927

0-974

1-oia

1-D17

1015

&H5

0837

o-Ssi

0-949

0-983

roos

1-005

0-994

s

8*53

0-871

0-8S4

0-964

0-989

0-997

o-gSi

1

8741

0'897

0-907

0-974

0-993

0-^

0-992

0-975

ta|«9S3

0916

0-919

0-979

0-996

0-997

0-989

K9099

o-9a8

0-933

0-983

0-997

0-994

0-986

0-966

■^15

0937

0-944

0-988

1-000

0-994

0-985

0-965

•""

0-947

0-9S3

0-991

1-000

0-994

0-984

0-964

r -wfi.

o«S

0-963

0-99S

1-001

0-994

0-984

0-963

«S'

0'9&6

0-970

0-997

I -001

0-993

o-9»4

0-963

•9635

o-97a

0-976

0-999

1003

0-993

0-9S4

0-964

0.977

0-980

1-003

0-994

0-985

0-966

^ wa

o-9ijo

0-983

I-OOI

lOOJ

0-994

0-985

0-967

^■^^75

0-983

o-9»6

fool

1-003

0-994

0-986

0-970

0-986

0-989

1-003

0-994

0-9I7

o-97a

0988

0-99I

0-99S

0-988

0-974

0-990

0-991

0-99S

0-989

0976

^B^i

0-991

0993

I-OD2

I-O03

0-995

0-990

0978

11*9930

0-996

0-996

looa

1-O03

0-997

o'993

0-983

•WSO

0-997

0-998

I 002

1-002

0997

0-995

0-987

■9960

0-997

OT©8

I-OOI

0-99S

0-995

0-9S8

^y6o

0-997

0-998

I-OOI

0997

0-995

0-990

-9970

0-99S

0998

I-OOI

0-998

0-996

0-991

•9980

0-999

0-999

I'OOt

I-OOI

0-999

0-997

0-993

-9980

0-999

0-999

0-999

0997

0-993

■99»0

0-999

0-999

I 001

l-COl

1-0

0-999

0-997

0-994

m-ilol M ihe ntio of Ihe »idc slope*, .dd rf* ('-l).o Ihe values erf __^m

^^^I^^H

SECTIONAL DATA. fr*ni T. rmj 1

Pa*t 3.

-Dimtnsions ef tgwU-£idm^^L

M

JIN Widths

MEA.t Wiin-iis ^H

100

BO

SO

70 60

60

30 ^^1

dcpi!^

I-074

1-16,

1-376 1-408

>'3l4 I-61S ^H

1'6

I-6I1

I7*a

1-919 ■-'35

1-5

■-704 1-998 3-466 ^H

J-ISI

a-33J

»-S64 a-86»

3-*;5 >-674 3'3*o ^H

Z-5

1-689

a9*i

3-1II 3S9I

2-6

1-850 3-3S9 4'>t6 ^H

3»30

3S11

3B64 4-3>7

3-41S 4-050 s«<s l^H

3-5

37TI

4-IOJ

4Sn S-o«

JS

4-0OJ 4744 SW *^H

*3"

4*95

S179 S'8«4

4-581 S-44S fr»" "**■

4-&

4 '854

5 189

5-838 6-567

4'&

s-t6i 6-IS4 iMt 'i-y 1

6

S-39'

5H84

6-503 7-3M

5-746 6-868 8795 ij'Oi 1

6-6

SMS

6-4S1

7169 8-087

6'S

6-331 7-585 97Ji M*» 1

6-483

7-079

7 '840 8-354

6-917 8-306 to-7J Ifr'l 1

6-6

7 -016

7-678

8-si» 9-614

6-G

7-504 9-034 1171 17a" ■

7-S70

8-178

g-184 10-40

8-091 97«6 Ii7» >f-

7'S

S-..5

S'6&l

S'S8o
9-486

9-861 ii->8
lOM «i97

7-5

8-681 10-50 1373 11;
9174 "14 "47S «~

9754

10-69

11 -91 U56

e-5

9S66 1.-98 .578 "'

10

lo-Ss

11-91

ij-19 is-16

10-46 li-7j} 16-Sl riv

11

11-94

'313

1467 16-78

8-6

11-06 ll-4» 1787 *'■

12

13-04

M-3S

16-07 '8-4>

11-66 U-»4 iS-fl] P^

k

^

^^^^

1

■

1

1

H

■

m

■

^^^^^

■I

^^^^1

^^^1

■ ■ t T. r«T 3]

SECTIONAL DATA.

1

mefFUmin

Canali

and Chanmh.

MtAN Wr

.r.<s

Me

AN Widths

18 le

14

13

13 10

8

e 4

dcpii»

dcpfiu

1-079 '"'n

i-30<

1-465

1 I Kg

1-374

1-759 ?'6io

M

i-«»3 1-776

1-97 J

J '137

I-2& I-44Z

1734

»-244 3-399

j-170 *-3«a

»<S7

3031

1-6 ■■737

»-|0O

2-7SI 4-230

M

aT«8 a-993

33M

3847

1-7S 1-033

1-473

3-266 s-'o6

3-ajo i-611

♦■061

4-683

I 2-331

2-849

3-787 6-000

J-8M 4*3a

4-777

5S36

V& 2-630

3-23=>

4-325 6-931

4-377 4S60

S-501

6-404

2'5 3-931

3-6'S

4-875 7-SS8

*^S

4-flJ3 S-491

6-137

7-a86

zrs 3-233

4-004

S-43' 8-KS7

5-«o 6-ia6

6-979

8-179

3 3-S37

4-397

6-000 9869

i-S

6-051 6763

77»4

9-064

3-6 4-147

S-tga

7-158 "-93

«*« 7-404

8-47S

to-

* 4-761

6-000

8-345 14-05

H

7173 8*«T

9-234

10-93

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6-817

9550 16-22

7T» 8*9S

9998

11-86

S 6-O0O

7-644

10-78 18-44

M

8-301 9'54S

"077

12-80

5-& 6-634

8-478

12-03 20-69

8»7 9-9W

"■54

'37S

6 7-350

9-3'8

13-19 22-98

«

9-433 10-65

ii-p

14-70

6-5 7-878

1017

1456 25-29

9-999 1131

1310

iS<S7

7 8-508

II oa

iS-SS 27-64

M

105? "■9T

.3*8

16-64

7'6 9-«39

11-87

17-14 29-95

..-.3 .J-63

1470

.7-61

8 9-773

12-74

18-44 32-37

k

1

I

1

^

54

SECTJOXAL DATA. (i

P*ET 3

(««/:V

—Dimouunu ^t^mai-iii^--

DoTHS or

WatM

Dw-THs or

W*m

1 1-S

**

a-9

3

3 S-S «

4-S i

W 55^

3685

»7-i3

»i-55

« 80-J7 66-77

56-90 i

» 49«

33 30

14.59

19-58

90 7«-*4 6o-»i

s<-«i .-

K) 44*44

»975

MtH

17-61

» 64-48 537»

459J '

79 3S-W

^-10

i9-4»

■S-63

TO S6j» 47-19

«0-44 Ji,

tt J3-54

M-65

1$^

>3-63

GO 48-56 «o-6s

34V y*

» aS-oS

19-80

14«

11-63

SO 40-Go )4'io

•9-J* '5*

« >2-6i

»5-4r

"73

9-S8

40 33 ■6a a7-S»

.3-86 =i

30 17-14

.1-8?

9-10

J-So

30 24-63 »o-9i

18-30 :-

M 1.-64

8-it

6-41

5-35

Z\ 16-63 14-14

iJ-5* n .

DdTHS OF

WATXft

Depths uf

WATtI

1 1-9S

i-B

17»

a

2 s-ss a-5
20 17-19 is-oi

»75 1
13-44 "1'

a 1475

ti-6«

9-6i

8-21

S 13-31

K.-S3

8-73

?-48

IB I5-S» «3S6

ij-17 .

IS 11-87

9-4a

r*i

673

16 13-81 la-ti

.0-89 -

U tD'43

8-3>

6-93

5-98

M 11-13 10-66

9*> S

0 S-98

7-19

6-01

S»

13 10-41 9 -JO

8-3t :

10 7-S3

6-07

S-ii

4-45

ID 8-73 773

7-00 r

8 6-dS

4'9]

4-iS

3<6

8 7-<" »»4

5« :■

6 4<ia

379

3-M

»8S

6 S«9 4-74

4^4 4«

4 3-'3

3-61

J-J6

'■

4 3 57 3^

..■

^

ri

■

L

J

■

M

^

. f«T 3l SECTIONAL DATA.

1

.J Flow in Canals and Channels.

LiLrnis oi- Water

DtPTHS OF

Water

^w« 7 7-6 S

S 8 10

U

13

BA-wUlh,

^Kff «3-57 5S-«> 53-67

100 85-59 7478

66-41

S9'8a

^Hv S7-47 .S3'6S 4S-e3

90 77->8 67-56

6o'ii

54-ai

^fts S>-3<'

80 68-75 6C.'28

53-74

48-56

^BfB 45->J

70 60*31 S3 '00

47 '36

4* '90

^K|i 39-^ 35 '99 33 '39

60 51-87 M'7i

4096

37 -ao

^■•3 32-90 30-37 2E-Z3

W 43-38 3840

34-53

31-45

^^■91 >6'M 1467 33'oa

40 34-87 3' '01

28 '04

2S-59

^K^7 ao-37

30 i6-34 33-57

SI -49

19 '66

^^fc 13-95

20 .7-73 1600

14-63

"3-5'

^^KriHS ov Water

DCKTHS Of

Watkk

^^K

S 6

0 6 7

7-0

S

^^■■WiBdioc BHa-

^thi

lO^Vidlhl

^^B> U-34 13

Sa 11-31

20 i6'36 i3'95

13-03

I115

H^ US9 tl

36 1019

ia 14-78 IJ'SS

.1-83

ir-13

^Ks7 K'53 ">

19 916

16 13-19 1133

to '61

taoa

^^■3 to'<7 9

M 813

14 11-59 lo-oo

9*38

8 '86

^Hl S-79 7

8s 7 '07

12 999 8 6s

8'.3

7-68

^Bs

61 6-00

ID 8 '39 7 -29

6-B7

6-50

^B^J 5-99

37 4-89

8 678 5-90

557

5 'as

■$■17 4 57 4

12 377

6 s-ii 4-50

4'a6

4'04

< J48 3-M »

82 2-59

4 3 '44 3'»5

iM

a '76

-

^

■

■

■

^H

^^^^^^^I^IH

1

SKCTIONAL DATA. ^S^|

k

Part ^—SecHonai Anas (A) m wJ

■

CVM«D«CAL C.;LV£«TS A.D r.PHS. ■

Di™™

Full. T*o-Uurd>fuiL 0»^|

•*^|

3 inches

O-0491

00615

0-0347

' >.

O'o872

00833

0-0618

6 ..

0-1963

0:15

0-1390

B ..

03490

0'i666

0-3472

3 ..

0-4418

0-.87S

0-3128

10 ..

0-5454

o-iogj

0-3807

0-243

O-IjJ

F«t

1>

0-7854

0-S5

0-5562

1-26

i-i2ja

0-3115

0-8565

0-364

IB

I -7671

0-375

I -2514

0436

o-ji

1-76

2-4053

0'437S

vf>m

0-sa»

2-

3141a

OS

2-2248

0-5S,

0-9I

2-2S

3W60

0-5615

2-8.57

0-6S5

o7ii

^i

4-9087

0-6JS

3-4262

J7B

5-9395

0-6875

4-2062

0-800

3'

7^86

075

S-C058

0-873

3'2S

S-195?

0-8125

5-8747

0-9Q6

3'E

9-61 .1

0-875

65635

i«i9

3' 75

1 1 045

o;937S

7-8215
4-8992

3-92

*

I2-5W

■ ■I&4

i-S

15-W

1-125

11-263

I-3I0

*Ml

5-

■9*3S

I -25

13 90s

'■■155

6'6

W75S
»8-374

1-375

■ 6-8J5

i-6oi

6-

'■5

20-023

»-74T

,s

G-E

3|''?3

<-&.s

13499

1-99J

?■

38 ^ss

'75

37-254

71

7'6

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^.875

31-2S6

fr

SO'i^S

35'S27
40-185

2-3*9

8-5

56745

a 125

»47S

.6-56

9-

63-6(7

a-15

45 -OS^

2-620

18-S6

9'5

70-SS3

a-37S

50-197

2 -765

30«8

10-

78-540

2-5

55-620

2-91 1

a>-9ai

Thf vsluet

of ^ for f yl'mdrioil culreris luiir (idl an the d^|

for fill! cylindri

al culvtdt of llie sanie diunctcr. ^^B

■

b

^^M

H^^l

^^^^^1

^Kr. UU4I SECTIOmL DATA.

J

^Bh/^ Radii (R) in Ftef, for Culverts and Pipes.

J

HAWKSUn'

^^H

ruiL

T<n>-lhitd< hW.

'J^<^■thi^

„„,,

' A

jf

^

fl

,

j^

o^SS

0-3766

0-6714

0310

02569

0-198

1-3550

0-3117

0-9138

0-362

03496

0-231

^Kr

17697

0'3688

■■'936

0413

0-4566

0-264

^■r

11414

04149

1-8650

0465

0-5780

0297

^■ir

17653

0-4610

0-517

0-7136

0-330

3 -5457

05071

2-2506

0-568

0-8627

0363

^^v

3-98»

oSSJ>

2-6856

06^

1-0276

0-396

^■r

4 ■67*8

o-5'>93

3*' 434

0-672

I -2050

0-419

^■'C

5-4199

0-6454

3;6SS4

0-723

IS

0-462

^Hv

6 Mi?

0-6915

0-775

0-495

H£

7-0790

0-7J76

477*4

0-826

0-5/8

7-89S

0-7837

5-3754

0-878

a-o6o6

o-;6.

^■(r

8969s

0829a

6-0426

0-930

2-3I2t

0-504

99SM

0-8759

?'IIS

0-981

2-J760

0-627

iroei

0-9210

'■033

*-SS44

o-6tc

^Vr

W-I9S

0-9681

1-0S5

3-1464

0-693

I4'638

r-oi4S

90024

1136

3 '4508

0-726

1-0603

98657

i-.sa

37749

0759

IS'9'8

1-1064

10-742

I240

4-1104

0792

.7 -281

1-1515

11656

i-igi

4-4600

0-825

^H**

iS'fk)!

.-19S6

12-574

'343

4-82O0

0-858

lo-tSa

1-2447

'3*595

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52020

o-8gi

11 '68a

r»9oS

.4-622

■■446

5*3942

0-924

»3-*S3

1-3369

15-683

1-498

60006

0-957

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^1:0*

t«'»S7

1JB30

16785

'■550

64225

0-990

^^^^H

J6-567

1-4391

17-91H

l'6ol

68560

1-023

^B''

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1-4752

19-098

■■653

7306a

1-056

3oiir

I-SZI3

20-255

1-705

7-7643

11)89

3«-563

"■5674

21-502

'15^

82414

33871

1-6135

M-S44

i-EoS

8-7407

'■'55

^■r

35-838

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24170

■859

9-24S4

■ ■lis

H

^Btncitii

Dielcio 1-3929 Kirn

a»erse diimeter in

lawkiley'i

avoid.

i

' r

=im

>«ol iS&.;

15*5, "*^

f r

r ^vi; M-ir'>

W546

1-73*1 ^--KP

^Hk v. fakt 41

SECTIONAL DATA.

1

^^mifjJrau!uJ?aiiu{R) in fttt, for Culverti

1

JACKSON'S P

<0N.

■

Dwww

Fun

T«..iiH

full

One-thJd full

■

■\

^

f.

,

J,

^

■

i*r«Tr

1-038S

0-I68

0-6458

0-280

0-3433

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.■4.36

03"

0-8790

o-3»6

0-3296

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1-8463

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I-M81

0-373

0-4305

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'»?»•

»-3367

14531

0-420

0-S448

0-2^6 H

•^rr

J -8848

0-447

1-79*9

0-466

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■

•x2-9-

3 '4906

0-49I

21151

»-S'3

0-8134

■

•«»o-

41542

0-S36

2-5834

0-S60

0-9686

■

•-yr

4-8?35

o-SSo

a-oj'T

o-6o6

' 1355

1 ^1

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5 '6542

0-624

3-5'62

0-653

■ ■3.86

'xjr

64909

0-669

4-0340

o&w

'■5'34

0-^76

■.*'r

7385.

0-714

45928

0-746

o-SoS

r«rr

8 3J7'

0-759

S'S43

0793

1-9425

"■539

t-rsT

93469

0803

S-8ia6

64776

0-839

»i79*

0-571

•-rr

10-414

0-848

0-886

2-426S

0-603

•■STO"

MS39

0-893

7-I716

0-933

3-6016

0-634

'.ST

IZ72Z

"■•IJJ

7-9115

0-979

2-9668

'.rr

t3'963

0-982

8-4608

1-026

32336

0698

'-s-r

15-261

I -037

94932

1-073

3-SSS8

0-730

ir«r(r

16-617

1-07"

10-334

1119

3-8744

076.

•xffr

iB-ojo

riiS

11-21S

1-165

4'jai 1

0793

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l9-5<"

1160

12127
13-078

4-5420

0825

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21-030

1-205

1-259

4-UOJ2

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226,7

1-249

14-065

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0-888

rxra*

I4-S61

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15-091

1-3S*

56529

0-920

'y^rv

25964

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16-136

1-399

6-0538

0-952

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277=3

i-3S4

17-244

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6-4595

0-983

'.ffO-

29-540

1-4^8

■8 371

1-492

68440

1-015

31-416

I-47J

19 537

1-539

7-3206

1-047

rxf r

J3348

l-5'r

l°W~

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77700

• ■078

=. ij-«rr

35 339

1-562

1-632

8-2340

Lr.ffO-

37 3»S

1-607

X3-2$0

r-679

87175

■ ■14a

k

J

1

tabl« VI.— hydraulic slopes and gradients.

Part I. Reduction of hydraulic slopes uid inclination<i.
Pirt X Reduclion of angular declivities and gradients.
put 5. LinJting Inclinations, Maximum Gradients, Angles of Repose,

BV!>RAULtC SLOPES {too.* n. tm r

Part i. — Kt^ietitM ^ ^JrauHe ilefti.

dis-

<>.>

'tr

S^

OHb

_'S."_

Ml

.««»

o^rf

>

1000

i"

HS

so 000

o-.ose

MS

Son

i«)

•a

jj JU

C(s8*

^s

666

IV

HI

J5<«

B^III

i-re

571

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?

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1.51

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o-iiM

2«

444

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M

400

,!•»

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N5

36*

I4-P

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11 ti.

0-4-53

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333

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1 176

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50

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^

AND GRADIENTS.

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P.VRT 1 {conHnmS).

m

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f Ml per

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900

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0-0115

O'o66o

800

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700

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0-0880

600

1-666

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o-U«,

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300

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0-3640

200

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26-40

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0-5180

130

5 -163

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0-5SS7

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5*555

19*33

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170

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0-61 1 1

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6-250

33-

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0-1150

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160

6667

3S-30

^^^1

0-1333

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140

7143

3771

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4060

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^

HYDRAaUC SLOPES iTASLi vi. «t t

Part i.—Rtductim e/gtadients.

*^l^:

Kstia

RKiuol.,1,

AhiIe in

B>I><>

.^t^

1°

57-29

■ 0OO2

21"

261

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38-.9

100 tlj

22

J-48

107 ■85

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100 1>6

23

a -36

108 «4

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argo

lOQIO

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315

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1908

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PAST 1]

A,VD GRADIE.VrS.

Part 2 (tunriHucif).

RbI»

Reduoion of

Katio

R d cri of

Ancle

IW f«l

Anek

""•"'

horimul

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100

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100-01

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101-38

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6-25

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11 19

I01-99

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■7 6

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►06-41

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3 49

100-31

2-5

31 48

107-70

U

4 S

loo-JS

2-2S

*3 58

109-43

■ . "

4 »4

10030

*

26 34

ill-So

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4 46

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176

*9 45

11518

■ "

5 "

ioo'4i

1'S

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12017

■^

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loo-so

1>25

3i 40
45 0

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141-4

1 . ^

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1

HVDRAUUC slopes, [tablk vi. ruffjj

p

Part 3.— Various Sopa and Gradients. ^^H

OKDINARV UNITS OF tNCUNATION IN ClUNNaU. ^^^|

I in 500 ooD Least canal slope lo produce motion. ^^^
'I'in 'e^JLi™" of tidal naviEalion for laigecanab. *!

n

n

\ Fall of most caniJs.

\ ^1 *'''" °^ *'"*"" "^*^ chtinneli.

a

^ ^1 Fallot most tiveis. ^^^^^^J

n

3^ 1 FoU of totnwb. ^^^^^H

25 Ilou
iOD"l

J

rs generally.

in 50 Ordinary railways.

in 30 Turnjiike loail.

in 10 Public load.

in 16 Private load.

in S For wheeled vehicles.

in 4 Beasts of burden.

io 1\ Hill.walking.

,hii^k.
(I.

I Grjvd,
\ dry :^

fVciiclable ta<±.

N.B. — Welled soil requires a less slope IhaD dry soil generally.

Minimum for slated and lileil roofs.

Maximum for back slopes of rammei! earthen dams.

Maximum for breast slopes of rammed earthen dams.

.M

87

Table VIL— CANALS AND CHANNELS.

ifpnximaU velocities of discharge for cancUSj channels, and
straight regular reaches of rivers, for various hydraulic mean
radii (R) and slopes (S) according to the formula —

r«<>x 100 (ii.iS)* when e^\.

Put I. When the hydraulic slope is represented by a ratio in the
<t form of a fall of unity in a certain length.

Fart 2. When the hydraulic slope is represented by iS^ the sine of the
^pe ; and S per looo is the fall in locx) fset.

Part 3. Conditions and dimensions of equal-discharging channels of
^pezoidal section, with side slopes of I to one, under a coefhcient of
*gosityii-« 0-025.

N,B.—Tai the use of co-efficienU (e) and (a), see Table XIL

CANAIS AND ClIANA'ELS. [Till* 1

Part i.— IWwm eflkt txpresam loo ^ES.

36[3P7o|ri

I

■

1

1

I

!

!.

1

1

^H

RVni. TAtT I] ca.vals a.vd channels. G9 ^I

Part 1 {(ontinued).

looojaooolaooofiooojsoooleooo (7000 Isooolgoof |io 000

IS

^■937

3'3i5

.7a»

*-490

2-273

2-105

1-968

:-8s6

1-761

4"

3 -160

1 818

iS30

2-309

i-r38

1-

1-886

789

S74S

4^1

3 '3' 7

;.sr.

1-569

1-345

!-f71

2-031

i-915

817

SAll

4 -US

3-367

>s

2 -608

2-382

2-204

2061

1-944

814

r'

4183

3-41 S

2-646

2-415

J-236

2092

|-9;2

8-1

*a43

3-464

3-

1-683

2-449

2-267

i-ii.

897

6-083

4-301

J-5'»

3'04i

J-7K.

J-483

j-199

1150

924

6-. (,4

4-3S9

3-SS9

3'oSi

s-757

J-SI6

1-330

2-179

i-oilS

9-19

fi^5

4-416

j-6o6

J-122

iSi

2-548

2-360

2'2oS

y7S

6i«s

4-47»

JOSI

J16J

2-581

2-390

2 -236

!-iq8

■. i-, 4-538

1-696

3-««

.«,

2-613

1-421

1-264

2-134

3-025

1 :■%(>%

3-741

J -240

2898

J -64s

\%

1-191

z-l6o

2-049

! ''11

3-786

J-»78

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2 -680

2-318

2-186

1074

1 '^

38J9

3-316

2-707

1-507

1-345

l-oyS

t 743

3-873

3-354

Y

2-738

1535

1-371

1-236

. -■,479*'

3-910

3-391

3-033

J-769

1-564

1-398

J-26t

;a

..Si6 4'S4S

3-958

3-428

3066

1-798

1-591

1-424

2-285

6-91S

4-«M

*-

3-464

309S

I'SiS

1-619

2-449

2-309

191

7*

4-950

(■041

3-S

3-'30

JIS

7-646

1-475

2-333

7-071

5-

3-S3S

3-162

2-6J2

2-5

1-357

236

frt

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rs

3-194

1-914

1-699

2-J3S

2-380

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ft!

7aii

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4-164

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1'944

2-725

2-549

2-404

Ir3

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5-148

1-104

3-640

2-972

2-75'

1-574

2-427

301

M

73*8

S196

t-J43

3674

2-999

2-777

1-598

1-449

H

7-416

5-244

4281

3-703

3317

3-027

2-803

i'6ii

2-472

345

M

7«8J

5-192

4-3M

3-743

3-347

r^

2-828

2-646

2-494

366

&7

7550

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4-359

^a

3-376

2-854

2669

2-517

387

s-s

7-616

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(-397

3406

3-109

1878

1-692

1-539

408

H

7-68r

5-43>

1-434

3-840

3 -435

3 -135

1-903

271s

2560

429

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7746

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3873

3464

3-162

2-928

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2582

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6t

7810

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3-905

3-493

3->87

i-95»

1761

1-603

470

M

7-874

n^

l'S4t'

3'937

3-SJl

3114

J -977

2-784

1-625

490

■'1

7-937

♦■583
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3-968

3550

3-240

3-

2-806

1-O46

510

%■

i-6S7

+ ■

3-578

3-264

3-024

2828

2 066

530

!-o6i <-7or

*-6S4

4031

3-606

3190

3-048

16S7

55°

S114R74S
I-.8S s 788

1-690

4 -063

!'633

3-3>6

3-071

2872

.-708

570

*-7*5

1-093

3-661

3-340

3-093

1-894

2-718

S88

"3

8^4* S 831

1-761

4-123

3-688

3-366

3-117

2-915

i-6o8

6-3P7 S-S74

4-796

V&

3-71S

3-39'

3-138

1-937

1769

2-627

l-j*7 s-916

4 -830

3*742

3-4*5

3161

1957

l-78fl

2-646

J

CANALS AND CHAKNEtS. [usu til
Part ■ {fontinuedy

Foi ti>ili«in£ ilnpv oTiBC n

, aooo ; 3000 \ 4000 1 5000 [ aooo j 7000 pooolw

1 li-l

,-.>i;

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1.

■

■

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1

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IH

CAIJALS AND CltANNEtS.

7

1

~Valttei of th< Exfmswn lo

dVRS.

■

P««laBofSp«tb™i.-,ndof

I

4fi 1 4'0 3'S 1 30

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6-335

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4-47*

i:|,6

7-071

6'6t4

6.IJ

S-59"

5-

7746

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6-7oH

6-123

5 -477

s-«r4

8-367

7-8*6

7-146

6-r>i4

5-9.6

9*87

s-m

8-J67

7-746

7-071

6-325

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9-487

8-874

8-1L6

7-S

67o«

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9-3S4

8-660

7-906

7-071

1-124

K.-4S8

9-8.0

9083

8-191

7-4'6

1-619

10^54

10147

9-487

8 -660

7-746

(■093

11-401

10-665

9-874

9-014

S'o6l

1-550

"■832

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10-147

9354

8-367

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u-^S

11456

9-082

S-660

J-4«6

I a 650

if83»

10-9S4

8-944

S-8J9

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1.-191

.0-308

9-320

»'»yi

13416

li-SSo

io-&^

9-487

f6»

i3-7«4

i2-»94

«'yj7

.0-897

9-747

14-141

13-3*9

.1-247

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14-493

'JSSS

is-sso

.1-456

10-246

i:SI

14-831

13874

.1-845

11-716

.0-488

,5-.66

14-1 »6

13134

.1-989

10734

^^^H

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15-491

14-491

13-4.6

11-147

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15-083

13964

11747

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15-652

14-49'

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,3-697

13-147

■974

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16-733

15-492

14141

13-649

n-sss

18-440

.7-348

15-469

14 577

.3 '038

yiiS

i9-y74

'7-74«

16-433

15-

13-416

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JO-

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14.41

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»o'976

19-611

18166

16-583

14833

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10-494

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17 jii

15491

2iSo4

I' -33'

.9-748

18-oig

16. Id

S-ioo

»3-«4

21136

20,194

18708

16714

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32-9.3

1I-J13

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33-664

31-909

17-888

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16-458

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F « {amt V— Ki/«a ^^r £

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r

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3] CASALS AND CHANNELS.

n

^ SMtaife te Canals and Channth.

F« nJuu Df 5 ptt ih

»«dof

o-io

086 1 0-aO 1 &65

050 1 0H6

0 40

Afqiniimalr wJciaiM of diMjiirjr in ttrl pel t*tpr>d

^H »*a6

J 550

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1-336

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a-»50

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3-

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3-708

3536

3-354

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33'7

4583

4'4I6

4»43

4-063

3-873

3-674

3-464

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4596

4-4.6

4-03'

3-824

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4769

4-5K3

4-387

4-183

r9'-9

3743

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4'9J7

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4-S4I

4-3 J3

4-108

3873

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l-ai,t,

4-6()0

4 '47'

4243

4-

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5156

5050

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4-610

4-373

4-114

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S'40B

5-'96

4 975

4743

4'S

4-^43

766

5-SS7

5-339

5-m

4 -873

4-633

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■^

S7o>

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S-^44

s-

4-743

4-473

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S-374

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4-861

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5-744

5-500

S-344

4-975

4-690

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5-6=4

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6-481

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6-134

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fi'9i8

6633

6335

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5-657

7-; 14

7-4J3

7-141

6837

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7-937

7*649

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7-036

6-70S

6-364

«-367

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aii**. .pply ihc Mi.«t V.I11

ofo. SwT.ble

XII.

1

CA.VJIS AXD CHAif.VELS. {tjUU TO.
Part 2 {a>*timitedy — PUWc of the Exffrssipn

J

0-3ft O-W I

h'oi true vclociiits. ipfly 'hi

■

1

1

1

1

1

■

1

I

■

1

1

■

I

CAMALS 4,V1>

CHANNELS.

^

■•tiens vf equal Jts

hargine channels

with l07v n

lean i

eloeities ^H

'th, fffr Trafvsoidal Actions having

tide-slopes

fmu

/. ■

■•'^i-K

ia tartk. a

vi in good average

order, with a co

tffid^nt H

J ltd trrtgularily.

i=o-<:

25-

.i.-iiiyiliuhnTEM): r.thcm

fon velocilv in

reel perMCondi^pei 1000 ^H

i.iUni

MM : A Is Ibc l«d-wiiiih ;

islbe

ileplh

ofwat

> in ^g

\-<3

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1

IB CAt/ALS AND CHANNELS. [li

Part 3 {eontinued).

B°l piittw qunnlUy ditchaiged ; 1", tbeniran TclodtyinffetpoKcmlid
Sil U the fkll io t OOO i t ii ibe bed- width ; il is the depth uf wMr t>

J' 3' 4-

o-s* o-it 0-34 o-is 013 o-io 1-87 0-I7 l«
1-40 078 I 117 0-86 I 1-00 0-7S I j-oo 0-83 1 1^

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6-

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156 0-93

125 0-

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CAA'A/,S A.Vr> CHANNELS.

77

'aht 3 {contiHutd).

^(; nuamity dischnrged ; V, Ihc mean velodij- in feci pe
the (>inn 1 000 i » U the bnl-width ; d U the <lepi!

second ;Sp« 1000
of wale, in feci.

aa:

156

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l8s

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1-35 isa 104

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but (at accurac7 ia a

EXPLANATORY EXAMPLES TO TABLE TO.

Example L

d CsmI has B hrdnulic

Hi of y2 feet, a hydinittic Elope ul
a iquare ImI, tequired ihe discharge,
• eo-<fRcient of rtigosil]' of "OJ.

rl I of Table VIL the unnuxlilied mean velocil]' of disckurge ^
a fel s«e<iid, and by Table XIL Ibe value of c the co-eflii;icnl
B to this [adnu ajul dope a ^66. hrnee the tfue dj&charge =
|F— ■66- loooi J »5-iix8cubic feet pcriccend.

Example II.

e Ihe canal mentioaed in Ihe last nample to have s hydraulic
[ '0015, the reniaining data being as before, required the discharge.
« the fall pel rooo is 1 5, amJ by inlerpolating I'ml 1 of
til, to the hydraulic radius, yz feel, an unmjdified mean velodly
e 8'Sj feel per second is obtained. Taking the suitable co-

■ «-fn>tn Table XII., the liue discharge^c > J > r^-65>loooi
^74^ cubic r«1 p«r second.

Example III.

ineanh b of irapcz'iidal section nith side slopes of I to one,
h U 40 (ret, its dq>th of water 5 feet ; it is to discharge
et pa sn.'ond', when in moderate average order, with a Co-

■ of rugosil)- n — o-oi$. What hydraulic slope must il have?

n 3, Table VII., the hydraulic slope isooooio, uto*2g perl 000,

Example IV.
will be the discharge and the mean velocity in the canal
d In the Uil cumpic, when it has deicrioralcil lo a condition

BCEli-na! (tain. Part 3, Table V., page 4;, ^'315, and /f-^4'i;;:
*za pet 1000. Also from Pan I. Table VII., we inictpolaln
Mt> 100 v*/**'^ 2-88! ftom Table XII. we obiain, when »i = 0-030 for
rtlaei of It and S, 1-0-63; hence K« 0^63 ■ s 88 ^ I 81 4 feel [let
1. anJ ^>|-Si4i>. 125-408 cubic feet per second.

irioiu values ol

81

Table VIII.— PIPES AND CULVERTS, JUST FULL.

Part I. Approximate velocities in feet per second, when €==1, formula —

Parts. Approximate discharges in cubic feet per second, when c»i,
formula —

Part 3. Approximate diameters in feet, when <?= I, formula —

rf--L.o-23(|!)i

Part 4. Approximate heads in feet for a length of i 000 feel, when r= i,
formula —

A --7.0-648

V'

Part 5. Conditions of equal-discharging culverts and drain-pipes, running
just full, under a co-efhcient of rugosity nxsO'013.

Note. — For correct results, apply values of c from Table XII. in
Parts I, 2, 3, and 4.

For the use of co-efficients (c) and (u) see Table XII.

V

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X. R. - For conett velocity. !

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FIFES AS'D CUI.yE.KTS.

iWll. PART ll

n

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pXH.

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■

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I-ART I] PIFBS AXD CUU'ESTS.

1

nfittptrittond.

1

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1-8

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J

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ge

PIPES Alio CULVEETS. [tabu vim. w

Parf 1 {conlmu^.-Att'c^

or, Vaiius of the £jifm

JlTihwond

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066

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■47

SO

■55

■60

•49

•6

47

■51

S4

■59

■65

•n

■7

SO

■S4

58

'62

-66

■69

79

■8

S3

•S7

61

'66

70

•73

■u

'9

56

■60

64

■69

73

77

■88

!■

58

■63

66

•71

76

■80

■9*

f1

6a

■6s

69

75

79

■S3

■95

12

6s

■67

71

77

■8a

-86

-99

V3

64

■70

74

'?s

■89

tta

1-4

66

■72

76

■82

■87

•91

13

1-S

6H

■74

78

■ss

■90

■9*

1-B
1-7

7Q

•76
■77

Bo
82

:g

■91
■94

■96
-99

;:;i

1-8

73

■79

84

■91

■96

1-9

7S

'81

86

■«

-99

1-0 J

I'lS

2'0

76

■83

SS

■95

t-oi

1-05

(■21

!■!

78

■84

S9

■97

'■03

1-07

l-lj

2-2

79

'S6

91

■99

1-04

1-09

1 s6

2'3

-87

■93

]<ci6

1J8

^i

S2

■S9

■94

fit

108

flj

rjo

^S

Hj

■90

■96

1-04

riS

131

t%

!s

■9;

■97

■ ■OS

1*17

>■><

27

S6

■93

■w

■ ■07

'■13

1-19

'■J6

28

87

■95

109

•■IS

1 J8

M

SS

'■>!

1-40

3-0

■"1

■97

■ ■03

Ml

t'i8

.^4

|-4«

Mndily Ihe diwihargc by > CQ-efScienl (^) btforc •pplrine It to

ine -J

lo find the cwiecl danicwr. See T»ble XIL - - - -

I

■

■

■

■

M

■

^H

^HHars] PIPES AND CULVERTS. fiS ^|

^ 1

tmaU dUtharp and high inclination. ^H

TiboLir

m

r«>k>p"°'<»<ia

Mo: lob.

r J 1 1 1 I

QOO tOOO l&OO 2000 3S00 3000 4000 oiIir tlopn

1

■So

'92

■99

1-05

l-io

I 14

lai

■a3

t

1-05

i'3i

'■39

'■45

151

1-59

•30348

3

1-24

1-41

I 54

1-63

171

177

.■is

.35692

♦

I-jV

ISq

173

I ■83

191

199

■40045

6

I-5I

1-89

2-09

a-17

I JO

■43780

B

1*3

1-S7

215

a -25

3 '34

j-47

■47096

7

111

1-99

a't6

a 29

2 '48

a '63

-5C091

8

aaS

a-53

2-^

278

■5284-

9

1-93

a 39

'■S3

275

2'9I

■55389

a

a-oo

a -JO

a -49

2 '64

276

2 '87

3'04

■57773

11

2-08

j-39

"■59

2 74

a '87

a -08

3"5

■eoots

12

a 15

a'47

a-68

2-84

a -97

3-o8

3 '37

'62144

13

ass

176

a '93

yai

3-<S

337

'64166

,■19

a63

a '85

3-oa

3-.6

3-»8

3-47

•66006

15

1-36

a7i

2-93

3"

3-*5

3 37

3-57

■67946

IB

3 '41

278

J'Ol

319

3-3»

3 '46

a '66

•6972J

17

»'4S

a 84

joK

3 ''7

3-4?

,1'54

375

71414

1»

a 53

2 '91

3-16

3 '34

3-50

3'fi3

3'84

730I6

IS

J -59

J. 9;

3-12

3 ■41

3-57

370

39a

746S4

30

3*03

3-39

3 '49

3-65

378

4'oo

■76231

30

311

3;S7

3-87

4'lo

*'f

4-45

47"

■89655

U

3«

4-34

4-99

1 -ooso

u

38:

tss

475

5-".i

5 at

S-45

57S

IO.J98

«

410

47'

S-ll

S-41

s-e"

S87

621

.'1830

rii

■(■36

5 -01

5'43

575

6'02

6-24

6-61

t'25S3

80

4-60

5-38

573

6'07

6 '35

O'SS

6-97

1 ■3173

9U

4-8^

5*54

6-O0

6 '36

6 '65

6-90

7'3'

1-3913

"to

S-03

578

6j6

664

6-<M

7 '20

7ta

^m

664

7 ■6a

8-27

876

Q'l6

9 'SO

■

;ii

'■"■

8-97

97a

lOJO

M-B3

aiSao

1 ■

^ludifif UiF dwhaigc by a cD-effidem (r) l«toreapL.lvinc it lo the tabic

■

^Ebe contct diimclcr. be..- Tabic XU- ^H

L .A

I^^^^^^^H

96

/IWfiJ ^AB CULVERTS, [tablx 1«

Part i^~P!pes. Appn

Fotd-mm. («(

For 6h-

B

cuhit'fc.^l

■083

■lea

■25

■33S

'4ia

W

OT

(2")

(3'1

(M

(M

0-01

l6l

0504

O-066

O'OIS

0-005

O'OZ

64-5

A-QXh

0-06J

O'DS

MS'

4S3S

o^S97

0-142

O.H6

0-04

25M^

8-o6>

1-06 J

o-*S3

0-08J

0-05

403-1

12-597

1-6^9

0-394

o-iig

C'C5

5>io'i

tS-o=;6

J-jS-i

o-zS^

D'O;

790-0

34-6^

3-^5'

0-353

O'Oa

io;i-S

32-248

4-247

i-ooS

0-330

0-03

■1

40-8 rs
50-4

5'375
6-64

i-i?5
'■57

0-418
0-516

■2

t,4.w

a6-54

6-30

2 -1*4

■a

145 13'

45J'S

5972

i4'i?

4-644

Sou-z

io6'l7

'5 '^5

8-356

■5

1J59-7

165 'Sg

39 '37

■E

1805 -6

=3S-SS

56'(»)

'«-57!l '

I40<)-Q

3^5*14

77-16

n--H\ '

3JJ4-8

424-b7

ino78

ii-oij .

■9

4tjSi-s

537-48

1-27-54

■v'-rot <

I'O

S'-iS-g

663-iS 1 MTA(>

si-y2 <

M
V2

8oi-qo
955 5'
1111-40

SIf

62-433 '

1 i'fl

3«<-&3

101 -131

(■a

1492 -gg

354-25

ui.-<^i

17

169S-U9
I.)l7-fi7

403-11
455 '"7

1.12-oyo

149-118

1'3

2l4q'9i

SO.'>-44

i6:-ir7l

!■!!

_

3054 '21

ti:<j-i6

"■■■"•

1

^^^H

h

c

^1

^I^H^^^^^I

^m

^kny^aT 4] PirES AND

CULVERTS.

1

.' ''^:r a hngth of i 000 feet.

Tabulir

OS

0-BS3

oeee

0-75

0839

dmdwl'Ly

len

(7*)

(BT

(9-)

ao-1

A„r«„.L™«iW„.-

.«inf«.

■■:\

O-207

0-096

O-049

0

017

0-016

0-00648

0-S19

OJ&I

0-197

107

0064

0-02591

1-866

0S63

0-443

J46

OHS

0-05831

JJ18

'■SJ5

0-7S7

437

0258

0-10368

5-.84

ij9S

l-JJO

6S3

0-403

0-161

7-*'>S

3 454

1771

9S9

0-580

O-2332B

m

10-163

470'

»4ii

119,

0790

0-3175*

08

'3«7'

6140

3-'49

748

1032

0-41471

fr9

16796

7753

3-99S

211

.-306

0-52488

n

»7J6

9-594

4021

'73'

1-612

0-648

n

aj-noi

ii<6oS

5-954

3-3<M

>-9Si

0-78408

n

J9-860

•3-8.5

7-0S6

3-932

13»2

093312

n

3S"Oi4

16.».J

8-316

4-6'S

2-725

1 09511

II

40-643

.8-804

9-645

5-352

3-160

1 17008

■5

46*56

».-S86

11072

6-144

3-6rf

1-458

ii-°^

14-560

T»'597

6-991

4-118

1 '63S88

39*9»7

37716

14-MI

7-893

4-660

I -87271

67-185

3" -084

1 5 ■94,1

8-847

5224

1-09951

74-857

34-633

17-764

9-858

5-8»l

1 -339^8

?o

81944

iS-375

t9'683

:o-6j4

6-450

1S9*

fi

91 -446

4»-3»9

ii-7or

ia-043

7-tii

2-85768

2-2

100-J63

45-377

»3-8i6

I3-I.6

7 -804

3-'363a

2-3

109-693

50751

»6-t>3i

14-445

8-5 10

3-41791

2-*

1 '9-439

5S:'6o

*8-343

15729

9-i«8

3-73248

2-5

l»9-6oo

55-961

30755

17-067

10-078

4-050

2-6

140-175

64854

33-»64

18-459

10900

4-38o4«

t1

151165

6y939

35-873

.9-906

11-755

47139a

■J

i(.a'S70

75-J15

38579

11-408

iz'641

S-o8o3a

174M90

S0-6SJ

4« 383

"■965

13-561

5-44068

1H&-614

86-344

44-JS7

34 -576

14-5"

5-832

Mn-lify the diichirEe by a co-efficient

c) before

pplying il.

to find ih

^MHCjhcAd.

^

1

■^^ h

1 1^

m^^^^^^^^^^^^^^v

/ ^^.W

/ ■' Jw

/ 5*J*

/ 'OS6S

1 16^ /

/ *3J»S I

1 ^'71* /

/ <• 47* /

f 52*88 / ,

^^^^^^^H

I 1 '

1 '^■^ I K

^^^^^^^^^M

1 9J J" / la

^^^^^^^H «
^^^^^^^^^v

1 •"'"i" / u
1 "7WS 1 ,2,

^^^^H ^

^^^^H ^

1 3'tl

^^^^^B

1 *'Jo

^^^H

/ « "4

^^^^^H

/ 4915;

^^^^^H ^
^^^

//;aj

p

H

H

^^^1

^H

^^^1

ABUT

n. l*ET4l ^^^SS AND CVLVILRTS.

•J

^nximafi Head far a length of i <x^feet.

1

Fur diamcUn Tn rt«

Tibulu

I

' ■-!

divided by

"'

3 1 . 1 . 1 e 1 ,

1

1

OOOJ

0-0006

O-OOM

0-00008

0-00004

0-6

2

ooooS

0-00033

0-00015

3

0D*4

O-00S7

□-OOIS

0-00035

5-8

0*043

0-0033

0 -001 33

b

0-067

0-01 58

0-0051

G

0096

0-02 zS

0-0074

0-00300

0-00139

23-3

;

0131

0-00408

0-00189

3' 8

■

8

0167

00405

00133

0-00533

0-00147

41-5

■

9

0116

0-0513

0'OI68

0-00675

0-00312

S^'5

»

0267

0-O63J

0-0207

oto333

0-003S6

64-i

■

IS

o-fioo

0-T434

0-^,66

0-0.875

O'ooSGE

I45'8

■

ID

1-067

o-iSJi

o-oSl9

0-03333

0-0.54'

259'2

2S

1-667

o'J'JSS

01296

o-oSioS

0-014.0

405-0

90

1-400

o'S69S

0-1S66

007500

0-03470

5S3-a

V.

3167

0-775*

OiSW

O-ID208

0-04733

793 '8

i\)

4-J67

1-0133

o33'8

0-I3333

0-06169

1036-8

5-10O

1-2815

0-4199

0-.6S7S

0-07875

6-667

IS823

0-5.84

f?ii

0-09659

8'067

1-9143

0-6273

0-11603

1960-2

Dlj

9-600

a378i

0-7465

o-ljSSo

2JJ38

£S

11-167

2-6736

0-B761

0-35208

0-.62S9

*737-8

m

13-067

3'joo8

1-0161

040K33

0-1889=

3'75-*

rs

15000

35596

1-1664

C.-46S7S

0-21687

3645-0

80

It. '678

4-0500

i'3i7i

0-53333
o-CwjoS

0-24675

41 -7-3

te

19JI.7

4S7SI

l-4gSi

0-57856

4681-8

90

2><6oo

S-iasS

16796

0-67500

0'3I23O

51488

%

no67

5-7112

i-B7.4

075208

0-34796

5848-3

■

100

63*81

a -0736

0-R3333

0-38S5S

6480-

■

ax

2S-31JO

18-3944

3 33533

i-S42aa

35930-

300

56-9530

iS-6624

7-50000

J -46998

SS3W

■

1

the dbchnrge by a co-effieieot \e) XxXoa applying

t, 10 find ttu

J

J

^■«7 2

■36

per

58

o-8i o

8j

i-f'7 2

55

>.;r [

ooo

'4-3 4-

S

"SS 0-9^

5f>9 316

9 'J?
489

3-43

0-9S .
J-39 :

per

oai

",'

6-ff i

tr.

°-!l5 0
4S» 3

. . "^ '■-' 3-3!

■

1

m

mi^^i

■

■

M

Wi«T SJ -^//"^^ ''A'^ CfU-EKTJ. ffl

1

f,- ^ tamg tkt Irannvrse diameter in fitt, S/iv i ooo Hie /all

■

<tr ueonJ.

■

IIawksl

v's Ovoid Cvlvest. wiih a, co-c(HtiBnt of mgosiij', »=<}-oi3.

■

I'D* I'l" i'4" r6"

111

S|S Ul . . . 3'6- 4'o" 4 4'

-1

■ 1 ooa

j'W 3-16 i-6o 077
ofi8 091 0-94 0-97

'h, J.Vi>criOQo r87 o'9o o*c

0'4t ^H

"^ jfl ... |-i6 i-ig i^

4t.s a'95 a-ifi 1-78

I r . .

4-9' 377 3'»'

:77 V

10" I'a" i'4" i'6-

|rf . .

4'0" 44" 4'«"

S'o- ■

rp« 1

ooc

I7'(7 7-31 .V5I ■■86
o-*S 0-9: 0-94 o'97

" lr;'.°"

1-34 081 o-SS

o*

6-03 4'43 3'J9 3-6«

4-39 37S 3-*3

2'Sl

I'a" i'4" I'fi' i'»'

(rf ! !

4' 4" 4' 8" S'o"

5' 4- ^

CKX

ij-oo 6-a* 3'39 1B6

80 l^l'"'™^

I -OS 071 0-50

°'3«M

o'9l 0'94 0-97 0 y9 i

110 l'23 I -13

''Z'H

5-90 4-S* 3-57 ='S9

( I' .' .'

4-»8 3'69 3'zi

I'lH

I'V rS' I 8- r'lo'

I'd . .

4-8" s'o" 5-4-

5'rH

ow

9-7S S" '-89 176
(.•94 007 0-99 i-oi

90 j.^i»..occ

0-90 0-53 0-45

1-23 123 1-24

;:^.|

5-65 4-46 3-61 2'99

t r : .'

41S 3*J 3'8

.«;■

i'8" r 10" I'd" I'i'

Irf . .

S'O" 5' 4' S'S"

S'S'V

>P« 1

ooc

6-48 386 I4J l'6o

,00 I .-' l«r I o«

077 o'ss 0-46

04. T

0-99 i-oi I-03 i-ni

'"" ].• . .

123 i;4 1-24

r.S

5-43 4-48 376 yii

\v . .

4-03 3-53 3'3a

3'7

I'lo- I'o" a' 4" I'S"

d . .

S'4' 5' 6" 5' 8"

6'o"

9^1

OOI

» 6S6 4'i8 1-87 0'9o

120 . ■■* pel"™

079 066 o'S9

rji

l-oi 103 I'D? I'O

114 125 «»S

S'97 5« 3'«9 1 83

V '. '.

4-24 3-99 380

33S

I'O" 34" a' 8" 3'o"

d . .

5' 4" 5' 6" S'S"

&o"

*P«»i

oos

s 6'67 a'90 1-41 075

,40 .fP^'°«

106 0-90 0-80

o-SS

1-03 107 110 III

las 115 ia6

1-27

6-a» 461 353 J78

r .' .'

4-94 4*5 4'4+

s-g'

J' 4" »'8" 3-0" 3' 4"

Id . .

S'6" s'o- 6'o"

'■" 1"^' '

oai

> 4-i6 a-oi 1-07 0-6I
I-07 110 113 fi4

'M \'r'^

1-17 i«3 075
I -25 fJ6 i-a?

5-J4 4-a4 3-3-1 2-71

ir . .

S'3i 3-<H 4-46

3- 8" 3'°" 3' 4" 3' 8"

(d . .

S'8" fi-rf-

" '

ot*

» 358 '■90 109 06s
110 113 Tis 1-16

180 \f^.'?°'

1 -28 o-gl

I 26 127

■

565 4-46 3-6» '99

iv . .

370 if!

S'tf- 3' 4' 3' 8" 4'o'

d . .

fo"

'■ '

OCX

B 3t« 169 i-OT 0-64
I-I3 IIS 117 118

200 fP*:'."*

I IS

127

■

" -

5-S7 4-5J 374 314

V . .

5-s8

■

r udiiDCDt. Fdi long ilmmtlcT and seclional ilala, nee Tabic V. Fori 4. ^^|

^^^^^^^^1

m

PIPSS AND CULVERTS. [table vt^|

Part $ {(out.)

t^!m

Metropo

ITAN OvoiD CwLiiKT, mth*tt>-efiidentorntgcau7r^|

ill...

Ijl -i

I'o fi" l'4" 1-6"

sli it . . . a- :,■■

« J Spetiooo s-31 a-3° i'» "■«

1* ... 1-17 ;

o-8g ogi 0-95 09S

r ."

3 48 a 56 '-96 IH

\v . . .^i, .

<f . .

10" I'a" i'4' I 6"

i . . . f<r :

g Spcriwx

n-92 S" a« "IJ
0S9 092 0-9S 0-98

n «["■•<» o« -

r ! I

S-aa 3S4 a-94 a-ja

r .' ■ .' 3-8? i

^ . .

I'J". 1'4' I'e" I'S"

d . . .,V .:

g S per I 00.

910 4-39 »-3» 1-33

gj flp«I0«.O7S •

091 0'95 0'9S I'oa

r ! '.

5-II 3-9a 310 a-S'

V ; ; ; 3?.' ]

,dIsp^''"«

,■4- j'6' I'S' ,',(,■

1 . . . ,-8- J

6-85 3'6i JOJ 1-23

ng S pet t 000 0'6l4 ;

o>9S 0-9S roo 1-03

K i .

490 3-87 3'3 a-S9

1- ... 340 3

il . .

rS" I'lo" id- a'j"

J . . . s-.y i

,5 Sptr.oo.

456 371 173 '■"

im .-<P"ioooois ,

i-oo I-03 105 I-06

" . . . I-J4 1

r '. '.

470 389 3-i7 J-7N

'' • ■ . 3 » i

frf . .

t'lo'-a'cT a'4" a'S"

{' ■ . . S'4- =,

20 l5pCTI0«

4-8j 300 1-34 064

00 «P"iooo<,0

^" ](! . .

1-03 i-os toS i-io

^• . . . 135 . .

Ir . .

S-18 4-35 3w »«

1 r ... 3*; .:

d . .

ao' a' 4" a' 8' s'o"

' . . . !-4- <

26 fP«'i«x

470 aoj 099 0-53
I-os "OS '-'1 113

y. 5 per t 000 oT« u

r \ '

5'44 399 306 a-«

>■ ■ . . <->9 .

>f . .

a4" a-8" j'o" 3-4"

' ■ . . r«' s

30 .Speriooc

a90 1'43 °76 0-43

tea 1^^ P« < wo oi)9 ^

F .' !

4-«o 3-67 J-iW a-35

r . . . 4«o .;

d . .

a-S" 3'tf' 3'4'' tr

d ...!■«-,

40 fiperiooc

a-S3 IJS 076 0-46
110 114 116 117

« f-'.~;2;

Ik .' !

4-90 3'87 3''3 ^-f^

1- . . . SIS .

rf . .

3'o- 34" 3'8" 4'o"

d . . . fs- ,.

M f^.'T

a-09 1-40 073 0-4S

^,«F.I«».-„ .

114 1-I6 I-I7 1-19

^ t ... 1^7 l;^

V '. '.

4S4 3-93 3-24 27>

■^•■'54' 4^

r

or ItHij diunctn ami Mclional data vx T>blo V. hrl 4^H

^^^^^^^^1

t 1

tuu viii. tAKt 51 f/^ES A!fD CULfERTS. 103 ^M

f full; A being Iht iransiierse diameler in fat, ^ per looo f/ie fti!!^^

t ptr steond. ^H

- I'lD {Pec-top Section) CuLve

RT, with ico«;fficient of rugosity. n-ODiJ. ^H

. . . Ttf* I'J- i'4" f6"

■

s^S rf ... 3'6- 4'o" 4' 4" 4')rM

[« 1 ooo 7-33 3'5 »S5 073

. . o«7 o-i» o-oj 0-96

'ao ,''l»"«»'78 088 058 o39^|

«" . . . .-IS .-.8 119 I20^B

3-85 fSi i-n 177

V . .

471 3'^! 308 i'65^H

iV I'l- I' 4' l"6"

' 4 . .

4'tf' 4' 4" 4' 8" S'C^^^H

r coo

16-50 7-06 3-41 l-8i
oSt o'90 0-93 096
578 414 3*5 2-57

^0 Spa I ox

1-17 07S 053 a37^H

V '. '.

4-21 3-59 30] Z'TO^^H

i-j- 1-4- I' 6' i'8-

d . .

4' 4' 4' 8" 5'o' i'A'^M

: 1 00c

n-56 6-04 3n4 iSo

gj . ^pcTi ooe

113 069 046 o-34^|

a'jo 0-93 096 099

fit, IM t'23'^l

S-66 4-33 J-4» 277

V '. '.

4'io 3-54 3-08 271 ^H

,■4- 16" I'r rio-

Id . .

4 8" S'o" 5' 4" s'S"^!

I 00c

943 493 »7lt "-68

go ,Svri^

087 O'6o 0-4J 0-31VH

09J 096 099 101

in 1-23 i-2«^H

5 41 4*8 347 a86

V '. '.

3-98 3-47 305 i?»^M

t'S" I'ltf' 3'o" a'2"

d . .

5'o" 5' 4" 56" 5'"''^|

6*3 370 2-33 1-54

,00 .Sper 1 00c

074 OS3 045 o-39^H

099 101 103 I OS

iM I-2J 114 i-Hf^M

S-M 4-30 3-6' 3-08

V '. '.

385 3-39 3-i8 S-oa^H

I'itf' i'o" 3-4" a'8"

d . .

5' 4' $'<•" 3' 8" b't/.^H

: 1 on

» 6-S6 41 1 i-8i 0S7

,20 «I«" «x

076 004 0-55 (i-4t^H

i-oi i-oj I'oe I-09

I-I4 l-M l-aS I'S

¥ '. .

573 4-8l 3-54 J7I

V '. '.

406 381 360 3 31

9 . .

a-tf- a- 4' isr 3'o'

d . .

5' 4" S'6" 5' 8" 6o-

f-pBt toot

6-43 179 1-36 07J

Jg . .fper I OOC

loz 087 075 o-ss

I-oj 106 109 111

r34 i-*4 *H 1-26

eiM 4-4» 336 >*7

r . .

474 446 4«> 375

3-4" a'8" 3'o- 3'4"

d . .

5' 6" J'S" e'o"

r 1 00

> 4-0O 1-94 103 059

,60 . ^^V^' ' -^

113 0-97 07J

I-06 109 iia 1-13

125 lis 1*6 ■

5-31 406 J-21 160

V '. '.

S'09 4-80 4'i8 ^m

a- 8- 3'd' 3' 4" 3' 8'

d . .

M

- 1 001

> 3-4S ii4 ro4 063

m ^^"^

i-io 0-91 ^H

I-09 III 114 116

^M

5-4J 4-a8 3-47 a-S6

V '. '.

^m

3-0- 3' 4" isr 4'<»"

d . .

^M

I oo(

3Ki 1-01 097 0'6i

jjQ Spetl OOC

.11 H

1-13 114 116 1-17

1-J6 ^H

S-3S 4-33 358 3-01

F .' '.

H

.^fiidof V in »ewci» jhoulci eiiceed 1-5 feel pci second lo pievem Jeposii. ^H

^^^1

explanatory examples to table viil
Example L

Whu is the ilisch*i^ et a new gluccl 3-incb pipe haTteg > ti]^i'^'<
ftlnpr of I in 400 ; and wbat would Le tis tcast ^ill ditcharp alioi '
iirnpcctivdf of leciialuU obstiuCtioD f

lijr Tihle VIII., Paii i, the appro ximiiedisch urge U -06 oiHt fcc ;
»«ond 1 and by the Table of Co^ffideais (Table XIL, P«i J), fm *
smixilh sarfacet, including smooth plaster, and cuametlnl or gluvl f . ^
(lie co-eflicienl e for a pipe baring this slope and a hydnolic nii
■rhich fui cjlindiical pipes tunning full is one-rounh of the dianuii:.
■84: hence the diKharge when ocwia = -34 1 -06 — -os cubic f«i pet «-■

If prcferteii in any other unit, refer to TaHe [I., P»rt * p. 1;, ■
inspeeliii)' which we find this to be 18 gallons per minute.

When the [upe ii nihet old iu surface will be as loash u thi'
otdinary metal, and taking the eo-ellicient for melal with ihis tinf -
railiut In be '6t, the discharge is then~ -61 ■ t]6= '037 cabic feet pa ><i
tir 14 ^llons pet minale.

Note.— In ihii example, the oo-efGcient adopted for MUgflioot!"
gljred surlnces is O'oio, and thai for unglaied mi-lal nurfices ii oi'i
the coTcaponding co-cfhcienli of velocity will be found under tlic^' -
Tible Xlt.

Example II.

A cylindncal miHinry cnlvErl [uu a dluneler of 43 inches. uhI j :
of 5 in t ooc^ Hhal Is its diwhaige when just ranniog Full ?

By Put 3, Table V'lIL, Ihe ■pproximsle diKhnrge is 63*63 Cubi^ '■
prr iecond. Had (he co-elhdenl For this slope and a hydraulic n\U-
'S7;feet will according 10 Table XII. Iv rto ; hence the ictnalcUich 1.
will be i'ioii63'03 = 7oeubie feci pet second.

Note. — The co-effideni oF roughness (h) for new ashlar maifmti
0013, Uie requited velodly co-cfficienis {a) will be found uniltt 1^ i
Table XII.

Example III.

What must be the diamelei of a cylindrical rftsl-iron pipe lo dicthaij
20 cubic fec( per second with a slope of one in 500?

By Part 3, Table VIIL, the appioxitnale diameier will be 3-&| J
and hence (he hydiaulic radius ia 0'66 feel ; from the tible of co
(Table XII., I'oR 3), take ^=t'03: and assuming a modifial I
chatp; 2- 19-4, refer ogitQ to Pari 3, Table VIII., and uhuln sd
diameiM-a-fiafeet.

PIPES AND CULVERTS.

■^riet of gkied pip« has n toWl licad of 30 feet, and contisls of
i< :t of 8-inch [»pc, X TOO feel of 6-incli, and 60a feet of 5-inch ; re-

'le diuhnr^ and head necessary for each p'pe.
-ainc any discharge as
It laboUi heaila due 10

.. the same proportion.

V93I «S-6-l7;9
20-Tnti ' 3-1 - (3-56
61-61)8. 0fi = S0-9S

Total -3SW

-30 + »9= B-TTfeel
I30 + D3-HIS „
••.tO-^93 = IOOS „

Tolal-Wfeet.

e by Ihe squares of ihe suitable co>cf[icients, obtain actual
S a llisi Bpproiimaiian, and reduce them by ptopotiioo.

j|74-I'a5)'- e-11 6'll»30-i..tS-2a=. ^WfeetinSdOO

IB4.('8'1'-1(''!)3 lH'62>30H-3'.l:J2-U-a't „ in U IW

|8+(»1)'-H-|9 li-l!Jx3O-f-39-e2=I0-86 „ in 600

Total = 39-2S Total = SO- feel.

\ '- Ij'" cO-5T cubic feel per seconJ : and this by Table IL .

Example 3.

inline tA joo gallons per minute is required Itirough a series of
% Ir n pipes eoinp<<scd of Soo yards of 7'inch, 300 yards of 6-inch,
~o ynids of s-ineh ; what is ihe head rcnuired for each pipe?
. TflbloofEquivalcnUlPart 4, TablcII.). yw gallons per minute-
I .ic feel per second. Taking Ihe corresponding tabular beads in
I, Table Vni., ■> first appro timali 0119, and modifying these by the
litable eo-emcitnli given in TaMe XII., we gel the ime

illdll»'2TI'<0-D>lll)l
> huh 83-01(3 > 0-3- H'91

flfl BU feet
— Th* squares and the re
■^ ihrou^ tlic Table of I

MJ + (.flG). = .W5*jrtel

ii-S4-^(-iia)-'-3a-So „

9-91^(MI)'aaB78 „

Total BO-13 f.

iprocals leijuired with co-efficit

iwers and Roots in the Miscei

tC8 PIPES AND CULVERTS, [mu

ExAHPix 6.

Rtquirtd th« dinauions and conditions of > brickvoik sciti.
•relioo Meln>|Kiliian Ovoid, tn dischaige SO cubic (eel per second; 'i'
liyiliaulic slope, (II (dl per I ooo of t '40 licet, when running jun full.

By inspetting page 107, Part 5, T«hle Vni. ; the mem reli)d()r »il
3 91 feel per second, and tlie Iransverse dtamelet wil] tit 3 feci 4 inrr
lefening 10 TaUe V., Hurt 4, pa^e 58, Us long diameur is J feel, tn-L :
sectional uea 11*76 squsre feet.

EXAltPLE 7.

What will b* the mean velicrly in the setter last tncoliaiiei). vtur
supply U re<Iua!i] w that il nini one-third fnll, tlut is, the depth of I1 :
is one-third ibe (Leplh ol llie wer?

By Table V., Pan 4. page 58. the section of Bow will be j'ijSk" '
feel, ajid the bydnolic radius 0689 feel, and the faM per I 000 is ttvlh :
feeL By ioletpoUting Pan ■ of Table VIIl. «! page 8;, ihe Bj^nmij.:
velocity is 3'I>9S feet per second ; onrl ablalning frem Table KlI
co-efBdent suitable to these values of Jl and S, which is i -oS ; we I'l '
the irae Tclocity — S-Oiis x I -OS^II-HB feel pet second; oko p«JI-
3 16 > 3-36' lO'Sa cubic feci per :,i'cond.

EXAMPLX S.

What will be the dischnigv in the same tew«r when it h raoninr 1 •■
IhiHs Bill, or Blled 10 two-tliiids it> depth? the rcnuining Gonditioia :-'-

ByTableV., part 4. pa^e 5S, Ihe section of flow will be Sh--
feet and the hydraulic radios 1 -052 Teet ; Ihelillper lOoijiiilill l'j->!
% Table XII. ll>eco-efficienlorvelaciiy under Beooij will lirl'll ■
inlnpololinE Part I, Table VHI., page Ss, ihe sppmximate tcIk-
3811: hence ^- J. e. 100,''^-8-l ■ llS x 3-S3^-3T-8Bciib>:fe<:i :

NciTK.~MBiiy of theM calculations may be ahbrrnatrj by 11
nccenied four-liguie logarithms. For tables of reloeity and iltKhare^
culverts and pipes of various sections under dilTcroit nine* ol ■• xi
•Canal and Culvert Tables' (London: Allen, 1S7S).

107

Table IX.— BENDS AND OBSTRUCTIONS.

Fut I. Giving loss of head in feet due to bends of 90° in pipes cor*
vcspoodtn^ to certain discharges. — (Weisbach formula.)

h'^i:-.

; li a radius of bend.

2(/ tli

Pirt 2. Giving loss of head due to bends in channels corresponding
to certain velocities. — (Mississippi formula.)

A'«JV.F»x 0001865.

Part 3. Giving approximate ri«e of water in feet due to obstructions,
bridges, weirs, &c. : — (the whole section of water beings 1), and corre-
ipooding to certain velocities. — (Dubuat formula.)

V = --HLy:^-lY when(?«0-96.

Note. — ThU table does not allow for variable co-efficients, and hence
!• merely generally correct for ordinary purposes.

■

■

».

HEADS AXD

OBSTKUCTlO^rS. [tab

Pari

I.— r«^/f ^n-wv lost of head itu to one timi

LMofh™ior-««;«rrTi

Oaac

,ur

bod

0-01 0-oe 01 D-a

f«,

Fv«

C=^.pWi., «> diKh.r(« In cbic (« »--

(11

■083

■5

■oi

■04

■OS

tA

(5-1

'166

■6

■07

■T5

■33

S,

IT)

■26

1-

■'5

■34

■49

(4'1

■33

(■

'36

59

■S4

vxi

IS")

■41fi

I'S

'43

■96

'■33

>^J

(H"l

■i

I'S

•61

'3S

\-9»

a-7i

(D

-683

1-5

■81

i<i

a-56

3*-

V

■7&

V5

V5

I-06

294

3 '34

SSq

(ii!-.

■83

vs

1-57

j;5^

4 'OS

7114

CI")

■9IE

1'5

5.9.-,

112" 1

Ml
1'25

1'75
2'

3'4

5 -OS
77

7'.S
10 '9

IS'^t '

V6

2-5

5*0

>i-3

15-9

1-75
3'

3'

4'

6-g
9"-i

■5-3

V,l

jo-y ■ J
4r-9 ; 5

2'35

a-5

II ■«

i6-s

38-5

yyo 1 *

2'5

S'O

irfi

JI7

46-.

bU ' *

2-lb
3-

6-

177

31-6

56-0
6&-6

79'J 1 a

3-35
3-5

B-5
7-

!s'J

55-3 ' rs-2
64-1 907

110-6 13

.a.1-1 1 I!

3'75

7'5

j:-.)

7VS ,oi-i
Sj-9 IJS7

147-= '*■
.67^9 !«=

4'5
5-

9'

,i7'4 , lO-^-o i4g-9

2617 , V>

SS

!?■

7.- KS- 221-
S-i- iSS- 2(i6-

^- \i

(r5

S:

..tj- -■Ji- 313-
"5 1 ,136' 3',3-

441' 5*
5"J' 1 bi

^Sk il BE/fDS A.VD OSSTXUCTIONS.

\drual fifies v»tk Jifirenl discharges.

I oe

adi,cl».ge

in tublc Ice

p..«™nd

or

■11

■"3

■14

■15

■16

■17

-33

■48

■53

■57

■6:

■64

■68

■96

i-oS

I-I9

r28

1 17

146

"■53

at;

1-87

2'05

*'36

25'

1-64

3-74

3-05

3-34

3-6.

3-S6

4-00

4-3"

6-09

4-»9

4*9

5-07

s-**

5-75

6'o6

8-S5 1

S7J
7S»

8-,4

678

S-90

7-25

7-69

8-10

10-64

11-46 .
1505

9-SI

1178

T2-49

1317

.8-58

<I13

11'8

14-09

I4'94

is;s

22-27

ira

I4'6l

IS78

16 '87

1789

rl<S6

26-67

i7to

19-01

20-31

2155

2271

3»-ij

144

a67

28-9

30-9

327

34-S

481

Ji*'

jyi

4S'l

47*9

504

71 '4

4i-9

S3S

578

61 -8

65 6

69-1

97-7

66 -a

715

78-3

83-7

8»^S

93-6

i3*-4

83-8

91-8

992

1060

112-4

1.8-5

.6? 6

■ 03-4

I1V3

■ 3S-8

1463

206-9

1=5-1

137 1

l^t

IS&-3

.67 9

177-0

250-3

M«-9

1631

^■}b■i

l^H•^

199-9

2107

297 -9

1748

'9i'5

lofi'lj

j2ir

234-6

247-2

3497

2af»

ij-*'?

156-4

272-0

aS67

405-5

-'M-s

iS5'o

JTS'4

194-j

311-1

.W9-*

465-5

>6S4

J908

3M«

JJSS

356-1

375-4

5309

.M5»

307-1

396-!.

424-0

449-7

4?4 0

6704

413-8

45" -3

489-6

5^3-4

C5S2

fr

827 '0

SOI-

548-

502-

033-

6;2-

S')6-

653-

754-

Soo-

843-

II92-

f-W

766.

8.7-

885-

9tS'

9S9-

'399-

Sil-

888-

cjto-

1026

loSS'

1.47-

162a-

ipctai oTiiipe, sQd obiaia the lou ol biiui-bv lnir>po1aliu

I

BEyHS A.VD oaSTXUCTmKZ. IrtmxtLi

-Loa ef Memd dm if SaUi ff QaamJi.

^^

%-tV«i., m

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u.

"•

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t-

•0006

■0009

XOI9

-0037

^^

■

1«

■0009

■oois

10029

«*J

W

-««1

-0043

«u»l

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■0019

■0019

■0057

■0>I3

■0171 1

%

>

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■oow

■0075

■0149

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0047

■0071

■0141

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;

■0,56

■0084

■0168

■0336

■oSa*

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■001,0

■0197

■o3»t

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f^5T

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■0W17

■0131

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0786

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■0298

0597

^;

-0164

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■0674

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■07S5

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■0140

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■0155

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■"^33

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ri

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■oj8i

■05B4

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^336

■0671

■343

h

■0263

■07-a

-.576

•23"4

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■"457

•o9>4

mSjS

-1:4*

■0550

T.5;5

■1049

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■2387

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■0*11

■Clt74

■13*7

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V

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■3730

559;

^b tx. PART J] I/SyDS AND OBSTRUCTIONS.

Itt 1

^" Part ^— Rise from Obslrtidiom in Channtls.

W

©■i aa 03 0-4 o-B

0-6

RiK ID rect

ve,

oooo

D-OQI

o-ooi

0002

0003

0-000

OQ04

0-ooS

ootj

o-ora

0-oos

0-017

0-028

0-050

O'O04

o-oog

O'OiS

0031

0-051

O-0S9

01006

o^iS

o-o'S

0-047

0079

o-rj6

0-009

0-068

0-II4

0-199

0-ou

00*9

OOS4

0091

o'SS

0-272

o-ots

0^38

o'o7a

□-130

0-203

"■355

0'04S

0-OJ9

0151

0257

0-499

0060

o-tS8

O'JI?

O'SSS

0'oJ9

007s

o-ijj

o'aa7

o-3h3

0-671

o-oJS

O0S6

o-iSM

0371

0 4S6

0-798

004.

019J

0-318

OS36

0-9J7

oai8

0117

o-nj

0-JO9

0'6JI

ltW7

0-OS5

0.34

0-247

04*3

0713

ii48

o^z

DISJ

018:

0-4S1

0-81 1

1-410

0070

o-'TS

0'3iS

OS43

09i(i

1-6.3

0-079

0-194

0-J56

0-60M

i-027

'797

OfA%

0394

0&79

1-144

O-097

0-2jq

0-4.W

0-751

I-J68

a-i.8

o-iI»

oiSy

OS,;*

' S'-*

2-6S4

0-140

0-344

0-61J

1-083

1-SlS

3-i*'4

0-164

0404

0-76S

i-:7i

2-|4»

3748

0-191

0-468

0861

' 474

i-484

4' 547

o»l9

OSJB

0989

169^

28SI

4 9' I

0-149

UJS

19=5

3*45

5-t-r8

oaSi

0691

1-370

i-'73

36^3

0-315

0-774

1424

i-Mh

4107

7-lKO

s^i;

o-i03

■ 587

2715

4'S76

%-^q

0956

1758

3-008 S-C.70

^^■^

BEADS AUD OBSnVCTIOKS.

EXPLANATORT EXAMPLES TO TABU: IX.
Example i.

A lotB A pipei hiTC to £schai^ ; s^Don* {<«( »(«») ,
beaidt la tbe pntion Ibt onuisu of J-iacfa ppe, 4 te Unl o(
■ad 8 in thn «f 7-wch ppc : wlun a ibe tool low of had a
time bend* ?

Fmo Tabic ILPBft 4, pee 13, S e^Uofu paieeotd-fft
per MGOod. Takiog the bekib stpantcly bom Tibk IX. Fu I,

T badi IN S-mch eive T ■ UitlB-U^lS fc

s .. ..r „ ., Hx»«)o»o«N .,

Toal tns at tc«l-0-SU fa

Tbe head on tbe pip(» must tbeiefiuc bM oolr be saSt
cuknc feet per .second throagti the pipes nada caiSnwj
must (Iso be incceased b; 0515 ieo. on iccoonl of Iiiwli

A chuDcl liu one bend of 15°, two of 30*. and oiwo(9(^,
:atal loss nf head npendod m ovEicomioe ihac tenda, lAes'

1 bend of IS^EinsI . OOSSS = (KWa fed.

S ,, ,. SO" „ 3-0'MRa>-(K)»W „

I .. ..90* ., 1 .0139'J = irlS«i „

lota] htad expended >U tSSt fad.

EM.VHPLR 3.

A chinnd hiiiDg a hjdiaulic iJope Ici thin (root hM il
nincitd by the piers ainl abulncnis of a biiitgc 10 ihc olaU
th<^ nnrma] tElocily being 3*5 pet second, what la the me da
bridge?

By Patt J. Table IX.. the rite win be o 117 feet.

XoTE.— Foi chamncli baring stcepei hydfanlle ikif»
more than I fcil In t 000, apply a i;oiiMlion according M tl
ui the l«K^ page iu6.

Tabu X.— orifices and overfalls.

■in of disclurge in fed pet second for sluiceii, and onBces, due

II h«*da (or cenain co-efiicienls, also Iheorclical velodlics to

eSdeat may be applied ; beinc an application of Ihe

y=<ix8-0!Bv'ir,

that tot oririoet fl'— deplh of cenire of molion of oHItce.

Dw mnf lable alio applies to overfalli, weiis, aod notches, but in this
Wc naig tbe nine general (ormula. If i& the depth from still walei lo
iU-te*cl ; ttui the velocity given in the table must be reduced by ooe-
' ■<! obtain tclociiy of diichaigc for any ovetblt, u by tbimula
r-§ . Ok 8-026 v'/r.
r nhieiof ((•) the co-eRicient, sec Parts 5 and 6, Table XII.
:-, table can also be used for the convene purpoK.
ahtaitt Ihe dUchargc <^) in cilher cue
Q~AK
wBBc J a (be bydnulic leciion, kc leit, page 115.

ORIFICES AlfO OVERPAtlS.

Table X. — Orifiat and OverfaBf.

''J^

2-53S
3-589
4'395
5 -"75

S-&75

6714
7-178

7 -6.3

7aa

■641

■SW

1-351

1-445

■908

r2S4

■7W

■973
i-i:;3

I-6IS

1*435

■ ■256

1769

'■573

1-370

I -91'

I-fioS

i-4S(i

2043

rSifi

1-589

i'i67

■ ■92S

i'6M

2 '284

2-OJO

1-777

3-230

2-87,

2 -51 J

3-956

3-516

3-078

4-568

4-060

3-553

5-ioS

4-540

3-973

5 -594

4-973

4-351

6-043

5-37'

4'7oo

6460

5-741

5-025

6-S5J

6-0^

S-3«9

—For ovetMls, reduce Ihe labulai velocity by ooe-ilii'd-

■

■

■

H

^H

H ORIFICES A.VD OVERFALLS. IB
^B Table \.—cmtinutJ.

1

■88

-64

•787

■eae

For orilicD
-62

■BB

770
.•0S9
i-JM
1-541
17M
I ■887

j-179
*-3'"

i«6
3-44S

4 87 J
S448
i-968
644s

7-704

•674
■9S3
If68
1-348

i-yn

1651
1783

1907

2 '023

aija
3-014
3'69*
4-J64

4768

5-640

G-03D
6-39S

6-741

V.lodinr. 0
-584
■81S

(■on
1-167
1-304
1-439
'■543

1-751

1-845
j-609
3-'95
3-689
4-.»6
4-5 '9
4S81
5-2.8
S53S
5-834

■535

■756

■926
1-069
■ -.85
1-309
1-414
1-512
1-604

1-690
1-390

a 937
3-380
3-780
4M40
4-471
4-781
5-070

5 345

-498
-704
■862

■995

I a 19
1-316

1-407
1-493

1-574
j-jaS

3725
3-'47
3-S'9
3-8S4
4-163
4-450
47»

4976

-441
■624
-76s
-883
■987
■ oSt
1169
1349
1-324

1396
i'973

3-793
3121
3-4>9
3'f87
3-948
4-187

4-414

K-B.— Fm oTirrWU. reduce Ihe tabular velociiy by one-third.

J

B^^^I^^BI

TIS OR! f ICES AND OVERFALLS.

1

[mil'

Table X. — tonlinucd.

Si-

^"S^'It"'

«S,jf

r.^^.

^"^31^

r«'"--

1

9

8

"^

■6

■'

v,i™-*^-.frfi^.«.

1.

Sojso

7 "J

6-410

5-61S

4-815

4-.'!,

1'25

S-97"

8-C75

7 178

6-181

IS

4-lSl.

I'S

gSzg6

8846

7863

6-8S0

4''Ji'.

17S

196161

9554

8943

743'

xs>

S.i-'

2'

11-3491

toniA

9-079

ST.

i-^;.

!'75

H-OJ7S

.o-aj4

9630

7 "J

2-6

12-6S86

II •4W

10151

SSii

Tin

*ji-

2-?S

ij'jojg

11-977

10-646

9-316

7'9»i

6-M!

3'
32S

■38997
14-4673

11-510

13'0M

11 574

97JO

10-117

\-&

6-

3-5

15 ■"■34

I3S«

10-509

91X3

7 f-'

375

' 55403

13-9S6

11-431

10-878

gjM

!2;

4'

160500

14-445

11840

11 1.(5

9 6 JO

4'!b

■ 6 '5439

14-890

I3-*3S

11581

9 9j6

%.-..

i'h

17-013 J

15-321

13619

11 916

loau

i-n

17-4901

IS 741

13991

l»-243

IO-494

5'

17-9444

16150

'4-3SS

I1-S6I

.0767

5>2S

18-3876

16549

14-710

tl'871

llfljj

S-5

.8S20J

18-938

15^56

13'74

ii-»9a

S7S

"OSAJJ

'7 3'9

■5-395

13.170

1.-546

&

19 -6578

.7691

<5-7»6

13-760

11-794

K

M062S

18057

16-050

li-ojS

■5

ao-4S98

18-414

16-36S

Mi'i

xt-^

■7E.

30-8496

18-765

i6-68o

■4-.1S

u-jw

;i-232a

19109

|6'9S6

148U,
i5isiS

"739

■25

2r6«79

19447

17S86

IJS

H

21 '9774

16*779

17581

'SiS*

776

si-3406

»-t07

■7 '873

:i«

iJ-<<H

8'

23-69S.

10-41S

18-.S8

1J619

r 1.T "1*-1

ORIFICES AND OVERFALLS.

Table X. — continued.

c<.».

Cl„„

^5.

•luk-u

Fotipedal

V« -tin

^^^X

FormccUl

•98

84

-727

688

-ea

-ss

vtiotiiiti 0

fd..S.-a=

7704

6-741

5-836

5 '345

4-975

4-413

8614

7iJ7

6-5*5

5-976

5-562

4-934

9-436

8-is6

7-147

6-546

6109

5-420

10192

S-918

7-710

7 -071

6581

5839

>o89S

9533

8-J53

7-5S8

6-936

6-2JI

;i:y?

8-754

S-017

7-461

W-6S9

9'iM7

8-45'

7-867

6-978

ia776

11-179

9-678

S-863

8-251

7 -3 '9

\'^t.

11-675

io-io8

9-357

B-618

7-645

i*'53

10-521

9635

SS

7-957 *

U-4IJ

13-612

10-918

9-999

%-ty,

14'9'y

'3'°S4

M 301

:i:s;

9-635

8547

'S-4*>8

13 -482

ll-67»

9-95'

8-827

rs-SSs

13-897

12-027

ll-otS

10-257

9^9

;s«

14-300

12-3S0

"MJS

ES

9363

14-695

11718

.1-65,

9-622

I7M7

IS ■074

13049

n-932

9»6S

17*51

15-446

I3*37»

I2-J47

11-400

10-113

18-068

IS-8o<)

136S6

"'534

11669

10-351

18-4:4

J6165

'jm

12-8.7

11-931

10-584

18-871

16-Sl*

14-295

13'o9»

12-188

10-812

19 »6o

|6-Ki3

14-590

13362

12-439

11 034

1 9-642

17-187

14-879

I3'''i7

12-685

11-253

W016

'7-5'4

iSiOi

I3'S86

12-927

I ' -467

ao38j

I7-«3S

15-440

14 141

IJ164

11-688

K>r44

iSiSi

l5-7'4

14-39'

13-402

1 1 889

aix)99

18481

<5-98l

14-637

13626

12-082

ai'44r

jS't*.?

16246

14-875

'J851

12-287

«79«

19-067

16-506

15117

14-073

124*4

Foi DviirrBtls, reduce the tabular vclocily by oDclhiril.

ia^a

■

■

■

118

0/fIFICES A.VD OVSXFALLS.

J

Table X.^continued.

1

1

Co-»PICI»T> ^M

r-x niiuml

For n..rn»

For«l«i.v

f«wp^

tmmUti

1«^H

ft.i"

Ydociix

lKid|(t
opininp

0°.'^.^

"i^H

!■

'9

-B

■T

6

__s

Vtl«ii,«ofdL«hj.et

""^1

82S

23-051

JO-746

18-441

16-135

T38.U

ii^H

S'&n

^JMt?

II 057

iS-717

16-377

14052

8-?5

23 7.1')

2.-365

18-992

16-617

'4-24J

9'

S4-o;6

1I-66S

19-261

.6-853

I4 44S

9>2S

24-40S

2t-9')S

19526

17-085

M-<a5

9-SO

24735

.97S8

17-316

I4«i>

9-?S

2 059

22-s;3

JO 047

1754I

'i'fjs

lO

25'37S

22-845

20-302

17764

li-117

"'■'

10-S

26-005

23-40<

20804

18-103

ufcj

now

ir

16-617

239SS

21-193

18631

iS-«^>

11-5

27-115

»4-493

21-773

19-050

12-

irSoS

15-010

22-240

19-46<i

12-5

^8-373

ai-535

11-698

19861

13'

iS-935

wj-04r

i3'4S

ioiSi

17-3'"

i3'B

2^-486

»fi-S4S

i3-55t>

20-646

17-697

14'

30-027

27-024

24-021

2I-DI9

IS -orb

is«:

m

JO-5S5

27-503

24-447

21 -391

ligl

i5;>

IS'

ll-oSl

*7-9?3

14 '864

21756

15 M"

15-

S'-S-M

2S-43*

2S'*TS

2»lt5

tSov.

lG-5

31 101

2S'&lt

25681

I9;m

16'S

32-598

irn^

J6-078

t2'8i8

Krv--

'?■

33-089

29-780

26471

13-16Z

ig-.ss.

I7'5

33-sr»

30-214

26-857

iJSoo

\%-

34-048

30-643

27-238

23 3}3

aoj:

m

34-518

31-066

27-6(4

24161

\3-

34-98>

31-483

27-985

24-486

m

ii:sg

31-894

28-3SO

24-806

»

liy»

29-711

35-12*

«m

l::^

1

N

B.-For 0

■

vcrWls, tcduM ihc ubnlM vdoa

■

I

1

I

^H

■

n

H

I

^^^^H

«»LX X.] OJtIFlCES AND OVERFALLS.

1

Table X. — (oniinued.

Co- or

c,.««

Mfeclirt

Foioide

Fniklck

""^r^

For win

'T^-'

n

^

96

64

737

■606

-es

-ee

1

T

V.locid^

fdiKharEC

^h ft26

ill 19

1936a

16-763

n-v,^

14-292

.2-677

W-46.

19*54

17-014

.5-582

.4-506

11-867

ai789

19 ■941

17 -163

iS-8io

■4-718

13-056

i.1-ii;i

20M3

.7-308

16-034

14 -9*7

13**4*

»3'43i

«>-5oa

177-19

i62s6

15-133

13-424

13746

W778

17-987

16-473

15336

13-604

24-056

28049

i8-z;i

16-I189

IS'SJ6

IJ7S^

^K^

a4*j63

ai 3"7

"8-4SS

16-902

'5*734

13-958

^^p

J4-964

*I844

18-910

17112

16123

14-302

*S'S3*

"■358

19-3SS

17-7^7

16-502

14 -039

l«'ll6

23-S6t)

19791

18.25

16-873

14-968

26-6S8

*3 3S*

IO'2l6

iH-SiS

.7-236

15-290

37 IJ*

»3 834

so-613

t8-»97

17S9>

15*605

87 778

24306

21-042

19-271

17-940

15-914

13'5

jS'Jo;

J* 769

21-442

19-637

.8-2S7

14'

28 '£26

25223

21-836

19-998

18-617

.6-514

+ s

'9W7

2S-6;o

20-352

18946

16-807

1.T

jgSjS

aii'ioS

22-603

20-700

19-270

17094

!.iS

3033'

36 540

"■976

21-041

.9-588

'7-377

JO-H.7

16-965

33344

21379

19-903

'7-655

ihS

JiJW

27-383

23-706

21-71.

20-207

17-9^9

\v

3<76S

27 7W

34062

82-037

20-515

.8198

i;-&

32»a9

28200

^4-4 '3

21 -.158

20-815

18-465

»

32686

28600

24760

12-676

18-726

ie-6

33'J7

1899s

iS-roi

H9H8

21-391

18-985

19-

33 -SS*

29-38*

25438

23-298

21-688

I9-2J9

19-5

3^-02 1

29 768

25771

23-«>2

21-991

19-49'

20-

34*454

30- '47

26-091

23901

22-25.

19739

1

N

\

B.— For ovetfalls, i©

ucc the U

ular tdtwitj by one-i

hitd.

,

ORIFICES AND OVERFALLS.

(tuu^^

Table ^—continueii.

Co-«.

..„™

For

Fooumw

Fm

F«

For

F-i™;-;

Kt^d'iT

ta",)^

viloniy of

.p«J

f«i

optningt

1

•9

■8

-7

■e

I !

Velocitlao

diKhir?.

20-S

36-336

31-701

19-068

1S43S

21-801

l8-l68 ■

2V

36776

33-<'98

29-420

>5-743

32-066

.8-38S

2I'5

37 -an

33-49<'

29-768

16-047

12-327

I8-66S ,

22.

37-641

33-877

30-112

16-348

11-585

i8-8;u

H>5

j8-oft7

34-i6Q

30-453

16-646

21-840

ig'Sji

23'

38-487

34-647

30-797

l6-y48

33-098

l9-*>t

23'5

38'9C3

3So'i

31 -1"

27-»3»

»3-J4l

l9-4>'

24'

39-315

35-383

J' 45*

27-520

13-S»9

I?-*;:

2d.5

397S3

35 ■750

31-778

17-806

13-83*

■9*" ,

2&-

40'126

36-113

31-100

sS'oSS

14-075

W-06J 1

!55

40-525

36-472

32-420

iS-367

•4-31S

'^'hI

!6-

40-911

36-379

3* -737

28-644

•£W,

2&S

4l-3'»

37-lSo

33.049

28'9ifi

71-

41700

37 -Si"

33-36C

»9-'90

2S-M0

7H

42-084

iSti

3J-667

19-458

25-250

28'

:=€

33-972

19-715

35-479

28-5

§:i2

34-175

29-990

15-706

31-^^H

29'

432.6

345^9

30-M8

2S-9JT

x-^^l

29-5

43-588

39 ■M9

34870

JOS"

16-153

"il^H

3D'

43 ■■•S6

39-5fto

35-164

3077s

26-374

iil^H

30'S

41-320

39-888

35-456

31-024

rfS9>

»-i^H

3\-

44 -68a

40-213

35 -7 45

Ji-177

i6-»o9

ji-^^H

m

45-041

40-537

36-031

31518

i^^S

Si-

45-397

40-657

36317

31-778

n^^H

ns

4S-75'

41-176

36-601

32-015

VM

.-Q'

46-101

41 -491

36-880

31-270

ai-s

46-449

41 -804

37-159

31 -5 "4

1VS6,

■3'^H

M-

46-794

43-114

37-4JS

3»-7S5

28076

*3'^H

W5

47-'37

4S-4i3

37 -709

33-996

aSiSa

■sJ^H

3S-

47-478

41730

37-981

33-134

1S-4SJ

_^^^|

N

B.— Foi ovdliiJlt, icducc tbe U

ulit volod

J

■

itiriT^H

■

■

^H

U

■

B

^^^^^1

r

n

OK/fi/C£S A.VD OVESFALLS.

1

1

Table X. — continued.

'.

For ~\Jt

Forip«,al

general ly

for oris™

e<Gudjf

':'h2^'

-Sfi

-84

■727

■eee

■62

-S5

Vclwili.^* 0

fdiBchuBt

IMt

.(4-SS2

JO-SM

26-423

24-199

33-528

19-98;

iS*3<JS

JO 892

26-737

24-493

22701

20227

3i7»3

J' 257

27-060

24783

22 97"

20-465

]6<36

31 619

27-373

25-009

23 337

30- 702

J6S44

31-976

27-681

25-353

3J-60.

20-936

y-w*

32-329

27-998

25-633

23-868

21 228

J7-347

32679

28-291

25-910

24-110

21-396

J7 743

33 'MS

ff:ffi

J6-Ig4

24-638

srfiij

3f-i34

33367

26455

31-847

jSui

33-706

39-180

36-734

34-878

33-069

3«-904

34-041

29-470

36-990

25-125

22-286

snH

34 373

J9-757

27-253

25-37'

2J-5«.

39-660

3470J

30-042

27-514

25-613

II -722

40031

3SOJS

30-324

37-761

as85»

33-935

40401

3535'

39604

28-028

36-092

23-146

40767

35-671

30881

28-282

23-355

41-139

3S'9S8

31-155

28-533

36563

23563

41 488

36-302

31-427

28-783

36-891

23766

4r«M

36-<,i4

31-697

39-019

27X)24

23-97!

43197

36-923

3' -956

29-374

27-253

34176

42 548

37-3'9

32-330

29-517

37-478

24-376

4*'8q5

37-533

32493

39-758

27-703

34 '574

43 "'40

37 8iS

32-754

29-997

27-935

34771

43 SS"

38-' M

33-013

30-234

28146

34-968

43-9«>

38-150

33*70

30-470

28-365

35 (63

44 -^S?

38-725

3352s

30-703

38-5»2

25-355

44 591

39-017

33-778

3093s

38-798

25-546

44913

39-307

34-o;9

3'-'65

39-013

25-737

45*S»

39-595

34378

3>'393

29-225

15-925

4SS78

39'a8i

34 '526

31 '610

29-436

26:13

^Bn^Foio

wtfalli. reduce ihr IB

iilni wiodly by ooe-l

hirJ.

1

OftJFICES AND OVEJUfALLS.

explanatory examples to table x.
Example i.

An orifice 6 Inchn in diameter, hiu iu centre under > bou) of G (h
water ; requited its dischttrge.

For a citcuiar orifice osina '63 for a co-e(Ecicat. the YeJodty ef J
charge ii 11 ■121 feet p^ second, and the lectional area, ti
7, Table XIL, being -luaSjlhe dischatEC- -ISSax II-131-1-18M (j
fuel per second.

Example t.

A rectangular orifice it 8 inches broad and ( inches Att^ lad U ri
an cfTective head of 4 feet 3 inches i required its dUcbarKe.

Since the breadth is greater than the depth, ft special c
required. (Stc Co-efficienli la Table XII.)

Here -^ «■ — ^ = 7 auproiiniitely, md -r= -r "O'S.

These require a eo-rfficiml ■6\1, which must hence be a[^Ii«d H
tabular diieharge for natural velocity due to the co-cfficieut IW.'J
discharge- 16-511 X fix ■6\i — ii31 cubic feel per second.

The fall of water throngh a bridge, having a sectional acei
tquaie feet, is 0-06 feet ; required the discharge.

Take -96 as a co-etlicieDt for a wide openiug, and ve {;et the <
- 1-768 x600"879 cubic k-eL per second.

Example 4.

The difference of level Iwtween the upper and loww pnnJl nf *
i<^ A feet, and the communicaling sluice is H feet sqiure in

Usiiig the co-elhcienl '81 and height R, (<ir ■ cuntiint bead of f H
■he discharge is IS-CIS x 1 -^66 D48 cubic (eel per second.

I'he effective head graduatljr deciea^ing, the mean dlKhaige dm
Jii'igiit is %S -IKK cubic feet per second.

if the lock i* 60 long and XO broad, it will hold 7 £00 cubic

OJf/F/C£S AND OX-EKFAU^. 12

I ihc ahow rale will be filled in 218 secondi, or oboul ihrei

, Ihe ditmeter of a vctiiral pipe lu diseharE= ! eubie feet pet

;n-oif under a head of 30 feet.
e co-efficient -84, we olitain from ibe Tabic 36-983 as velocity

o will then

h will require a i

--' 006417 sqnare feet - 642 square
jneter of 3 tithes, or 4 inches, for the pipe.

Example 6.
le tenglb of a weir lo discharge fi SS6 cubic feet per second,
r be^ froin still water to sill of 4 feel,
lo-eflicienl '686, the tabular vEJocity of discharge is 10'6S9,
nc-lhitd has to be deducted to obtain the mean velocity of

'-10'689 -3-663- 7-136 feel per second,
Son - ^^ - neuly 800 feet ;

Example 7.

lies ovei a drowned weir ■ Ihe upper level of water ii 8 feel
:r Ic"el, and is 4 feel above the lUi of Ihc weir, which ii 100
quired the discharge.

r pmtiOD may be consfdered as a utnple overfall with a bead
(Ih ■ co-ellicient 'GOB ; the lower portion as an orilice, with the
Ut a co-eHideiil '61.

X to the Table ihe Telocity of dischai^ fir the one is
t-e-171 f*et l>er second i and that for the olhct is 8-018 fcM
Hence the discha>i;r :

-60 (6-171 »;i + S-fil8.1)-60KS--131
•• 1SG8 cnbic fn-i per second.

Example &
to nice Ihe uppct portion of a river 1 -S feel by means of
tcnail. The nver has a dischotge of BIS cu1>ie feel per

t«

ORJF/CES AND OVERFALLS.

{exAims J

second, and a width of TO (cet ; vhat mmt be the height of the dam-l^ 1
neglecting vclocily of approach ; lod, taking it at K'S feet pet seoondl
1st. Let rf^cicplh of sill of dam below ihe lower water.
Then f'= velocity of upper portion, ot tiue Dvafal! ;

• 3 velocity for head I'S to > co^flicienl -66ti ;
.4-364 feet pet second (from Table] ;
and F' avc'odty of lower portion of orifice ;

= velocity for ahead 1'6 to a co-efficicQl '62;
- G-IOM feet per second (from Table).
Then the total diu:baree 613, ii a& in Ihe Iiut Example
-T0|. ■1-6+ K'x(i|-70(8-516 + <f.6109)
hence i -51221=0-887 feel.

ind. Taking into conaidcratiaa Ihe vtlodty of afpnacfa and nois-
ing the co-eRicients \vidi Table XIL) Rccordingly.

The head due lo velocity of approach 2-5 feet per second, for i Co-
tfficicm e, is from Table IX. about -Ifi feet.

Htnce ihc niwlificii co-cfBcient for overfall will be

•[{-^}~{^}}-™{{-^]-K}}

= -6e6-]'(l-)'-Cl)i| --745

ami the modihed co-elhcient for orihcc will be

•■'('*ra)— "■'■■«"'""-"»■

Making use of these two co-efhcients i<islead of
iirst portion of the i:iample, we obtain other values

■GC6 anJ -62

r=4-894; and P = 6-38fi;

hence ?Ir = 11-6 - 1-5 F+ rfr'-7-341 -ni » B-38B

A

12S

Table XL

Metn fdodties of discharge in feet per second,
in small channels of rectangular section
to observed maximum velocities ( Vx) and to co*efficients

{o), of mean velocity ;
calculated according to the Barin formula —

0. F.

F«.

0 + O'2635'

Also a table of Limiting Velocities for Culverts and Canals.

FF

L^^^^^B

OS MEAM VELOCITIES.

1

Mean Vthdtiu of Dheharge

terra feediMiO

MuinuiiiVelodtio

r

l»&

0-6 1- 15 3- s-5 a-

SC i

o-»4S

0-497

0-74S

0-994

1-241

1-490

1733

IMO

o-»7t

0-S4I

08.3

■ ■OS4

I 355

idi6

|-8«7

»3S

C1-J90

%^.

0870

I'i6a

1-450

r^40

1-030

MO

O-306

0-9 iS

l-»24

i-SJo

1-^36

1-141

a«

o-j«>

0-640

D-9S9

1-J79

I-S99

1-919

1-139

IHO

OJJl

0*64

o-«5

•■3*7

1-65^

I -991

1*313

frtt

0-J41

0-685

I -017

«-370

1711

1-054

1-396

MO

ojSi

0703

I -OSS

r-758

1 log

1-461

»«&

0-J60

o^rg

1-079

I-4J9

iiSS

1-518

»n)

0(67

o-rw

i-io»

1469

1-103

i-S^J

o-re

o-jr4

0747

I -495

l-6t6

I-g". .

<M0

0-J&.

o-7i9

rij9

1-519

1-899

1-^

1-658

»»

0^^

0770

..j6

1541

1-916

i-Jii

1-696

MO

0390

0780

1-171

IS6I

1-911

1J4I

1-731

<H6

o»S

0789

i-r84

1*579

1974

1-368

1-76J

'■'■'

HID

o-JW

079S

;s

^'>^

1-995

1393

H»

O40i

0806

X'Oi4

1-416

MO

«-4<36

08.J

.■119

1-636

l-Oj)

1-458

I-IS

0410

0-819

I-M9

.-6J9

J -049

a«9

t«

o-4"3

0-S26

|->J8

.-651

1-064 1-477

MS

0-416

o<3i

l-ii7

■ ■6<.J

1-079 a*49S

MO

0418

o-J>37

"•>ss

.-674

1-09I

1-5IO

»»

0-411

o-S^

l-»6j

1-6S4

i-ios

1516

I-W

04*}

0-8^7

i-tyo

1-694

iii7

1540

1-4S

0-416

oSjt

1-J7?

i-Tu*

»-ii8

*-554

ISO

o4a8

o-sfs

i-iSj

1-139

1-567

^S6

0-430

O'i>6o

r>89

1-719

1U9

i-s:9

1-60

o-43»

086I

l»9S

i-7«

itjS

1-590

1-K

0433

0-867

1-joo

•734

1-107

1-600

1-n]

•>43J

o-Sjio

IJ06

1-741

MS

vft

0*37

0873

rjio

1747

1-611

i«

043S

;Si

I3'S

"7S4

1191

1-6 p

M6

0-440

1-3 '9

17S9

* 199

1-639

ra]

0-441

o'SJi

1-3S4

1765

*-ao6

164J

i«

0-44*

oSSs

1-317

1770

nil

1-654

J*-

MO

0-444

o-SSS

ijjt

177S

J-IIO

t-663

.■■' ■

WO

0-446

0-8W

1-339

I-78S

1^3"

3-677

?M

o-*|S

n-S97

"-34S

I'.94

1343

1-690

i-Kp'-

^

■

■

1

1

1

1

t

a

■

^1

■

■

m

>l/£-*A' VELOCtTlSS.

^

^ ^^n-ai Maximum Velocities and Co-e£iaa> Is {<:)

Uuimum V.lnriiit

0-25

4-5

6'

6-S

6- 0 5

7-

7-0

8

i-2iS

2;483

2-733

2-<jSc.

3-228

3476

3-724

J 972

D-30

I'-ni

I-9H2

3-3«

35^4

3794

4-066

4-336

ii'35

jgoo

3-190

3-480

3 '770

4-350

4-640

.iG

= 75J

1-060

3-3«

3-672

3978

4-284

4-S90

4-896

jSjS

J>9S

3518

3-838

4-158

4-478

4-798

S->>8

ZitJifi

3'3'8

3-650

3-982

4 3 '4

4646

4-978

5-308

JoSi

3-4i3

3-706

4-loS

4450

4-792

5-134

5-47S

J-im

35'5

3-S66

4-218

4-570

4-922

5-272

5-624

3**'7

3 597

3'9S7

4-316

4-676

5*36

5-396

57S6

j*3"*

167«

4038

4-40<.

4-772

5-140

5-506

S874

■ ■■/s

jj63

3737

4-484

4-858

S-232

5 -606

5 -980

■ J(iO

3-41?

3797

MJe

4-556

4-936

5-3-6

s-^

G-o?6

a-?h

J ■400

3'8S'

4-'36

4-622

5006

5-392

5 776

6 163

0-90

J-5"

3-90I

4!9I

4-681

S07il

5-462

5-852

6-na

t OSS

J SSI

3 947

4-34»

4736

5-131

5 -5 '6

S-9-0

63'6

i'fn

3S0O

3-989

4388

4786

5-186

5584

5-984

6-384

3624

4-0*7

4-430

4832

la?

5638

6-040

6 '44 4

■1')

3 -ess

4 '064

4-470

4-876

5-690

6-096

6-502

J '688

40.,7

4-508

4-918

5 '127

5-737

6-147

6-557

37' S

4-ilS

4S4'

4 '954

s-366

5-779

6-192

6-605

374*

*-(S7

4S74

4-990

5-405

5821

6-237

6-65.1

371*

4-184

4601

S02t

5 439

5-858

6-276

6-694

3789

463 r

5-52

5-473

5-894

6-315

6-736

.■j(j

3-811

4-*34

4-657
4-^J

S-oSi

5-504

5-928

6-35'

6774

3-Sjo

A-nf>

S-T07

5 533

S-9S9

6-384

6S10

.-j)

3*8 !0

4'i77

4-706

5-134

5-561

6-407

6-845

3*>8

4'*97

4-72S

S-'58

5-587

6-017

6-447

6-877

3-S84

4-3 '6

4-748

5-179

S-6M

6-042

6-474

6-906

j'Xi4

■1-334

4767

Sioi

5 -634

6-06S

6-501

6934

1 vfo

30>7

■4'35'

4-7«7

5-MJ

5-658

6-093

6518

6963

1-7S

3^31

4-367

4-805

-5-242

5-678

6-J15

6-552

6-9S9

VWJ

39.H

4383

\-^ia

■258

5-697

6-ns

6-573

7-01 1

1 va',

i'>-^

4 '397

4-838

S-27S

5717

6-157

6-597

7«37

' '-^

3 97'

4 '41 2

4853

S"'94

5736

6-177

6618

7-059

J -98*

4'4S5

4-H66

5-309

575'

6194

6-636

7-078

.■MO

3 ■994

4-438

4-SBj

5 '32^

5769

6213

6657

7-101

V 1(1

«'oi6

V*b2

4-9o'<

5'3M

5-80I

6-247

6-&,j

7'J9

1 2-20

4 ■036

4-484

4 93»

53*'

5-829

6-278

67*6

7 -'74

1.

•"■»

J

1

Ig

ri

■

1

■

■

■

■

■

lit

ME AX VELOCITIES.

[tm. ^

^iTfM Vdodtits ef DistAargr i

vrmpmdh:, .

S-6

9-

e-S 10- 10-5 u-

U-5 M

0'25

4212

4-470

4-7 rS

4-965

5-32

S-46

S"

0-3Q

4-6oS

4-S78

s-iso

S-4»J

5-70

5-97

6-M

frSS

4 9JO

yiio

5 5'o

S-S«,

6^

6-J8

6-07

frW

yioi

5'5o»

■&.4

6-43

"■73

""04

0*5

S'4J6

5-756

6-076

6-395

67;

704

7-36

O'SO

5 '640

5'97i

&-304

6 '6 16

697

7-3"

7*4

O'BS

S'Mio

G'i63

6-504

6845

;:;i

7-53

7-98

O60

5-976

6-32S

6 '678

7-OJO

T-73

S-09

0-fjS

6-114

6 -608

6-8.14

7-194

7-56

7-97

S-iS

070

6'i40

6-976

7 '34*

7'7i

808

8-4S

075

6-JS2

6726

7474

?ll

8-23

g-60

O'BO

6-4;4

6-834

7-214

7-5''4

8-30

8-74

D'85

6-S4&

6-931

7-3ra

7-7°3

8-09

8-47

886

DM

6-6 j»

7-021

7-4.2

7-Soj

S-19

8'sS

8-97

0'95

67I0

7104

7-498

7-S94

8-.5

8-69

9^

'>j-

1'Da

678!

7-t8o

7-S80

7-978

8-38

878

9-15

V05

6 '846

7-248

7-652

8-055

B-46

8-86

9-«.

110

6'9o8

7-316

-,^^i^

8-128

»-SJ

8-94

9-ji

m

6-967

7 ■376

7-;»6

8-194

8-61

9-04

I'M

7'olS

7-430

7-843

8-256

S-67

9 -OS

1-25

7'o(.9

7-484

7-900

8314

a -74

9-lS

1-30

Tlli

7-SJi

7-950

8-36.S

8-79

9-14

1-35

T'S7

7-578

7-t,.j9

8-4'9

S85

927

HQ

7.19s

7.6zi

8-o,is

8-467

US,

9-3»

m

7-a.tS

7-661

80S6

8-512

«-94

93<'

l'60

7-173

7-700

8-. 28

8-554

B-»

9-4J

I'M

7-307

7-736

8-166

8-59S

9-03

9-46

1'60

7-337

7-7<-)

S-joo

8-61J

9-06

9-50

I'ES

7-368

7-801

8-S3S

S-6(M

9-1 1

954

170

7-39S

7-834

8-3(«)

8702

914

957

175

7 ■426

;-MC.2

8 sop

8-734

9-17

9(.i

^80

7-449

7-881

8-3:6

8-7fS

\^

1'BS

7-477

7-916

S-.iS6

S-79S

9-*4

m

7 ■5.0

7-94*

8-J83

8-821

9*7

97"

1'95

7-511

7-963

8-406

8149

,.39

9-73

"'■"'

!'00

7-S45

7-988

8-43*

8 -87s

9-S»

9-T7

lo-ai

|u

2'10

7-5S5

8.032

S-47S

8-923

9-37

9-«»

IO-J7

2m

■j-<-li

St7r

8-5M

%-m

'1-M

9-87

lo-u 1 1

fl

MEAN VELOCITIES.

oburvtd Maximum Velodlits and Co-effleients (c).

1

Muin>uin V.ltaliK

13'

14

15-

1«-

17-

18-

IS- 20-

~

6 4'.

6-95

7 '45

7 ■04

8-43

8-94

9-43

9 93

70s

7 59

S-T3

S67

911

976

10-30

S4

7 "54

811

870

9-28

9 '86

60

7-.i6

857

9-18

9 79

10-40

11-63

14

D45

83<

8-95

9-59

10-33

1087

ri-si

12-15

79

1 rw

8-(,3

9-ig

9'9S

11-38

11-94

11-61

a;

[■5S

8-90

9-SS

■ 027

to9S

11*3

I3-.12

13-01

13-69

'rm

9'4

_9;84

'0-55

It -25

■ 1-95

12-65

'J-36

14-06

' i^bS

9-JS

1079

11-51

li-JJ

11-95

1367

14-39

ll:(l

9 '54

I0-2K

1 1 73

ia-4K

Ij-ll

I3;95

14-68

lt-76

9-65

10-40

11-88

13-37

'4^5

U-80

9-87

10-63

II .19

li-JJ

12-91

1367

14-43

(►BS

10-79

1156

1^-33

13-10

■3-87

14-64

0«)

1014

IO-9J

12-48

■ 3 -16

14-04

1482

O'K

1026

11-05

ir84

1163

13-41

■ S-oo

i.V]

IO-44

lt-i4

11-97

la-RS

13 -65

I4-4S

10.17

II -oK

1189

13-69

14-50

1057

U-38

1119

.3-OI

.3 82

'4-63

10*5

11-47

uay

1311

13-93

14-75

12)

IO-7J

U-S6

US'*

1321

'4-03

14-86

t'2S

lOSi

.1-44

11-47

13-30

14-13

14-97

t'3a

If>«S

11-71

iiji

13 39

14-13

t'SS

10-9S

1179

iib3

13 47

14-31

1H>

1 .5

11-06

IfI7

;;i

II 47

It SI

ti M

II 8S
ii-gr
11-98
iz-01

1I-C9
11-14

WIS
1**3
ia-27
ii-ji
ii-y,

U-J9

"■43
la-ji

'1-55

11-70

iil

ii-'jS

:rs

.3-10
■315
r3-i9
'3a4
■ 3*8

'3-31
1340
■348

1J69
'3-75
1 Si
I3'S7
13-92
13-9*
14 -ol
M-07
MIJ
14-16

I4-JO
14-30

14-34

14-39
14-47
■4-54
14-61
14-68
14-74
14-79
14-S5
14-90
14-95
ISoo

imiTING VELOCITIES.

Various limiting velocities.
t Opbn Canals.

For the worst or most sandj n^

Foi sandy soil EenersJIy ,

For ordinary loam .

Fat ftim gravel uid hard soil .

For tiiickviork, ashlar at rulible in

?'iir hard sound sUatified rock

For very hud homogeneous rock

Minima for Drainac.s i
Small dmin-pipeg under R" ir
Dmin-pipes, 6" id 18" in diai

Larger cylindrical culverts

Limits usual for canals .
Limits for rivers and canals ju
Limits for irrigalin;; channels
Limits for sewers and briefc c(
Limits fur self'Cleansir.g sewt:

181

Table XII.— HYDRAULIC CO-EFFICIENTS.

1. Co-efficients of flood-discharge {k) from catchment areas.

2. Formulae connecting the co-efficients of velocity (o) with those of

rugosity (»).

3. General values of co-efficients (n) of roughness in channels and

culverts.
Local values of n for various canals and rivers.

4. Velocity co-efficients (0) for channels, culverts, and pipes.
Under grouped values of (n) for two fixed extreme values of 5.
Under separate values of ft, in separate tables.

$. Co-efficients of discharge (o) for orifices and outlets.

5. Co-efficients of discharge {0) for overfalls.

HYDRAULIC CO-EFFICIENTS, [tabu xn. PAiri

Pakt i.^-GtMiral and Local CiheffUicnts of fiood-dischar^

from caidiwunt areas,

Fcff :be ibcBiBlA in TjbSe r\'.. Put i, also giycn in the text.

^ = ix 100 (X)«

The lalae of tiixs co-cficiect (ib) can be detemined and made use of
wirV.Tn kcal ixBu:5 objt. as it depends on the average maximiim local
Qov£TK«zr. the eTi4»ca:ian, the qnalitj, inclination, and disposition of the
ssiiKe ?f the are^ ssdcr ooosideraiicm ; it has hitherto been determined
fee rerv few iacnct-v x:>d nx sumciently satisfiwrtoiy for some of those.
In sxne cas«s« iirfvxr^naielv, doubtful flood-marks have been usetl to
cbta:= 'J-rf 3cK'*i jrraiient. an-i the velocities calculated according to very
rsed fc^rBTsLe : in ocbers.. the ob5;rjc:ions caused by bridges and embant
z:> hive vi:ii:ed all the bases of calculation of discharge.

Values of*

Fv^r v*ry large Indian rivers near their months . . 0-3 to 2

Fm catchnr-est areas ia Oudh generally . . . 1 lo 2

The Madras Prw.:iesc>-, :he whole Kaveri 1 ^^^ <,.
The Gvxiavery. Kistna. Tumbaddra, Pennair, \'igay J *

The Chi:ta-.ir, Palaar. Manjilanthi, Varhazanthi below 5*
For the Kanhan Rix-er. Central Provinces, according to

the highest £ood yet known, less than . . 5*
For Bengal and Bahar. rain£ill 2 to 4 feet — Col.

Pickens gives a co-efficient of . . . . 8*25

}1 9 1 (i

For some rivers in Berar and the Central Provinces,

according to calcubted velocities only . . . 16* to 24*

Some further data for Indian rivers will be found in the * Hydraulic Siatistia'
of the Author.

^MT »] HYDRAULIC CO-EFFICIENTS.

\ X. — J^ermu/a amnecting the Co'tffidents of Vtloctty (o)

viith those of Rugosity (n).

. 1-811 , 0-00281
— ^ + *l-6 + - ^, ■ -

C=^ — 7 o-uoaau n M-'SS

.(.,...f-»)^

e ^ b the mean discharge in cubic feel pcM lecond,
is the MctioQ&l area of waler-way in sqaaru (eel,

Jit ll the hydraulic radiua of the scClion in feet,
S is ihe siae of the hydtaulle slope of the witct sorfice,
the co-efficient of rougliocss.

ii may be reduced into the more convenient Ibim,
te « it a Tuiable dependent on H and n atone.

Bnaj b« (iirthct modified into the form,
Jic co-efEcieal of mean veludt^,

mott lioiple fonn, Q^AV,
B Vis the mean velocity of discharge In feel per second,
I F>*c.IO0v'^i ff being a variable quantity.

Note.

^ Tatuei of S, the sine of ihe hydraulic slope, are more gnerBlly et-
far coDcisencu in ihc (onn of S per thousand in the Tables. Ibui,
innd'O-liiutcadof 5-0'0004; sod 5 per thousand ^ 30, in-
'S»0OS.

^^^^^^^^^

m

i

1

HYDRAULIC CO-EFFICIENTS. £tabl« xil ?ut J

Part z— General or Avtrt^t Values of Co-egidnti M

as^pptUiby&i

Aquedvcts, C*ii*u.

O'OIO Puce cement in England >nd Europe generallj : im
Glued DialeriaU of eveiy sort; glaied, co.ttd. oi

(hDIS Brickwoik and uhlai, in squcrducli, ciDils, ind culvcTO 1
Ordiniry asl and wrought iron. Urglaicd iloMTrtie /
Materiils menlioned uadei O'OlO when in bid orde Bid

IHH7 Rabble in cement, in good order. Alio, earth in hi^
Materials mentioned under 0-013 when in bad onttt ui

0-02(1 CoaiK nibble, let diy. Rubble in cemenl in bul cODJh

0-0225 Dry coarse rubblf in bad order. Kubl.lc in wmnil,

Canals in Naitral

0-020 Class I,— Very firm, regular gravel, carefully LrimmcJ aiid
0-0225 Class ll.-liarth. Cmali and channels. (Da.^cJ un
0-0250 Class IIL-Earlh. Canals and channels. (Ba:rf;d ua
0-0275 Class IV,— Earth. Canals and channels. (Based on
0-030 Class V. -Earth. Canals in bad order, rather damajcvi.

Central values of n for Temftnty
0-009 Well-planed limber, in perfect order and alit;nmenl, ami
0'0l2 UnplancJ timber, when perfectly continuous on the inside.

o-oisC"

l Kcclangular ivouden troughs, with battens o
0020 Reclatigolar wooden troughs, with battens o

,-alues of n, suitable to rivers

and natural chini

illy determined for other rive

IS, or may be dedu

itb other data and condition:

i. They vary beta

r 3l nVDRAUUC CO-EFFICIENTS. 135

whiMS, for various Materials, and CiinJilions cf Surface ;
ri*th! Tables.

'ORKU> MATEKIAL.

:iial \a itefcctiic places. Trimmed e&rth in peifecl crdei.
-us data by Ihe Aulhor) ; above Ihe BvciBEe.
'US data by lli« Aiilhoi) ; in good avernge order,
...in data by ihe Auiliut) i below the average.
.;!:il]f overgrown witb weeda, or obstructed by detritus.

"itrmliimi, ddtnnuud by Kulttr.
I'.vlly ilraight ; olherwiie perhaps O'OID would be suilable.

lally. may be obtained by compariion with those already e»-
1 coiuideratioD of Ihe observed muimuni velocilies in con-
.juiU of D-020 .uul O'OSS. See Kutler's local values, p. I jG.

136

HYDRAUUC CO-EFFICIENTS, [tabu xil pj

Part 3 {ami,). — Local Values of the Co-efficient n of Roi^k
and Irregularity^ according to Kutter,

Natural Channels.

0*0200 Bayoa Lafoarche.

0*0210 Ohio, Point Pleasant

0*0220 LechJ

0*0227 Rhine at Germershetm.'

0-0228 Tiber at Rome.

0*0232 Weser.

0*0237 Hiibengraben.

0-0243 Hockenbach.

0-0243 Rhine in Holland.

- Generally free firomobitiiid

00250 Seine at Paris.

0-0252 Ncwka.

0-0260 Speyerbach.

0*0260 Seine at Poissy.

0-0260 Haine.

0-0260 Rhine at Speyer. »

0-0262 Ncwa.

0-0270 Mississippi.

0-0270 Saalach.»

0-0270 Plessur.'

00280 Saone at Raconnaj.

00280 Salzach.i

0-0285 Elbe.

0*0294 Ba>ou Plaqucmine.

0-0300 Rhine at Basle. >

0-0305 Isaar.*

0-0310 Meuse at Misoz.*

0-0310 Rhine at Rheinwald.*

0*0345 Simme at Lenk.>

0*0350 Rhine at Domleschgerthal.>

Obstructed by detritus.

1 Obstructed by detritus.

t XU. »*1T il HVDXAOUC CO-£FFiCl£XTS. W

t 3 {(»itt,) — LcaU Va/uei of Iht Co-f^amt n of Renffknett
i frrtgtUarHy, ftUfltJ from BaaM a*4 KutUr.
AminciAi. CuANSEts.
/h Ceatml.

S«riei Na, 14 of D'Arcjr and Bidn, wmidrcolu.

Scriei No. t of D'Arcy and B^iin. (KUn^lai.

Series No. 15, D. & B., wilh onp-Uiird und. KniidiaiUi.

/■ Aihlar anJ Bruiwfiri.
Seriei No. 3, D'Atey ■nfl B»zin, bricLnoik, reclangulv.
Scrlci No. J9, U'Aicy and Baiin. luhUi, icctanguUt.
Series N09. 1 & 2, D'Arcy ind Boiin, ashlu', rccUngulu.

GonlcnbachKbite. Dew, diy, semicitcuUr.

Series No. 31, D'Arcy and Buin, ralhtt damaged, recwnguUr.

Stfries No. 33, D'Arcy and Bailo, rallici damaged, KCtinguUr.

Gninnb>cb«cba]e, ijamiged. dry, Minicinnikf.

Gctbcbocbschale, damaged, dcj, laaicticatu,

Seiiis No. I -4, D'Arcy ind Bazin, roujh.

Series No. t'3, D'Arcy and Baiin, rough.

Senei No. i'6i D'Arcy and Baim, rough.

Seiie* No. I ■$, D'Aroy and liazin, rough.
1 Serie* No. 44, D'Arcy and Baiin, wirh dtposils, rccUngulai.

Serirt No. 4.(1, D'Arey and Baiin, wilh depotit), rectangulii.
I Serici No. 3;, D'Arcy and Baiin, damaged, tiapeioiUd.
I Alptnchschale, much damaged, semicircutai.
/h Sammitl Gravtl.

Seric* No. 17, D'Aicy anil Uoxin, j-inch thick, semicircular.

Sedc* No. 4. D'Arcy and Hsiln, ^-inch thick, tcclongular.

Setiei No. ;, D'Aicy and Baiin, ij-inch thick, rectangular

/r Earl/t.

A Canal in England.

Lfntb Canal, trapeioidal.

Mlneillcs Canal, rounded.
"VU rannridcn Ciuul, IlulUnd.
• •-SA Jtr,! Canal.
v\JM Ijiuter Canal. Nenberg.

Encher Canal (detiitiu).

ManneU Canal.

U)e*ipcake-Ohio Canal, rounded.

^^^^^^^IB

1 .

IiyDKAUUC

CO-EFFICIENTS, [table, vx.

Part

4— Cfl-

fficients of w

tan vtlocity suited to n

riotunuUnil

calailalid/prafixeJ value of S=(}()(il.

_ K

«<.f-

in feci

010

■013

-017

■030

-0225 -0850

-0275

■osw

(1)

C

ffl

(i>

(IL) OH-)

(IV.)

C-}

0-5

■■38s

l-OII

0730

0-598

0-518 0-4SS

0-404

0-36;

1-

I -56*

1-6.5

0-860

071 s

0-6JS 0-S54

O-406

OM'.

1'25

1614

i-iii

0-901

07S^

0-660 0586

0-527

0-4I!

H

>6ss

l-*49

0-933

07SJ

0-68S 0613

0551

05™

i-n

i'6SS

1-279

0961

O'SoS

0712 0-635

OS73

o-sis

i-

1716

1-305

0-984

0-829

0-732 o6ss

o-S9»

0-4SI

1%

1740

1-327

I-OCH

0-848

0750 0<73

0608

o-55!

?■&

T7f.T

■■341^

1021

0-S64

o-;65 0-687

o-6z:

o-in;

275

1779

'-36i

1-OJ7

0S79

D-779 0700

0-635

Oj5i

3'

'795

■■378

1-051

0-892

0-792 0-712

0-647

050:

325

1-809

1392

1063

0-904

O-304 0-723

0-657

o«:

3'5

l'?2J

\^i,a^

1-075

O-QIS

0-S14 0-733

0-667

0-*i:

i-

1VS.1S

r-i^O

.-093

C-935

"-."33 075'

C.-6S5

O'o;.

4S

fSos

I'+l-J

1-113

0-951

0-S49 Q-;57

0-700

o-ey

S-

rSSi

1-460

1-12S

0-966

0-S63 0-7S.

0-713

OH-

5-5

t-S(i!i

'■474

1141

0-979

0-S76 0-793

o-rzs

oM

G'

[■.J09

'■4S7

'■'53

0991

0-SS7 0-S04

0-73S

□ «:■

G'B

f92l

■ ■4'38

I -.64

i-ooi

0897 0814

0-746

06SJ

!■

1-9J1

l'3oS

1-174

i-oio

0-907 0S23

0-754

o-w

H

I gao

i'5«7

1 .S3

1-019

0-915 o'83i

0-763

070

8'

'■949

.■526

1-191

1-027

0-913 oSjiJ

0-7JO

071

8'S

'■957

■531

i-igS

I-034

0-930 0-S46

0777

071'

9

■■9b4

i';4T

1-205

I -041

0-937 "-ssj

0784

OTit

10

'■977

'554

1 21S

1-054

0-949 0-865

079;

07J

15

2023

•599

I -263

1-1x8

0993 0-90S

0-838

o-r&

ZO

2051

■627

1291

1-126

.-021 0-936

0-866

o-Sol

^^m^^

I

Kii. PAW 4] HYDRAULIC CO-EFFICtENTS. 139 H

4<fl«i/.

, — Ce-tffUUnU of mean velocity suited to varioui ^|

1

malffiah, eakvtated for a fixed value of^=

0-0001.

■010

■013 017 -oao -oaas 0250

-027B -OSOO

(»

0 13) (T)

(U.) (ID.)

(iV-) (V,)

^B

1-263

0-916 0658 0-S39

0-467 0-410

0365 0319

^B

H78

i-o<)7 o-go6 0-669

O-58S 0518

0465 0-411

^^m

i-HS

1-155 0855 °-Vii

0-625 °556

0-499 0-4S3

^^M

I 598

i-aoi 0-895 0750?

0-659 0-587

0-S19 0-4S0

l^p

1-643

1-740 0-919 0-780

0-687 0613

0-554 0-504

1 >

I-680

1-174 o'gSS o-So7

0711 0-637

0-576 o'i^S

2'K

171a

1-303 0-9S4 0-831

0-734 0-658

0595 0543

?S

1-741

1-319 t-007 0-8SJ

0754 0-676

0'6j3 0-560

i-75

1766

I-3SI 1028 0S71

0-772 0693

0-629 057S

3-

■ 78a

i-37i 1-046 0-888

O-78S 0-709

0-643 05S9

32$

1S09

1391 1-063 0904

0803 0-723

0-657 0-602

SS

1-827

1408 1-079 09'8

0-817 0736

0-670 0-614

l-86r)

1-438 1106 0-944

olifi 0760

o-6gi 0-636

*■&

1-888

1-465 1-130 0967

0864 0780

0711 0-655

i-gij

1-487 1-15* 0987

0-883 0799

0-730 0-671

6-5

•9J3

1-508 1-170 1-005

o'9<» 0-816

0746 0-6S8

.■9Sa

i-5ii6 1-187 '-02'

o'gi6 0-831

0-760 0-701

'-98S

1-557 1-217 o'OSO

0943 0*857

0-786 0727

2 -oil

V583 1-14* 1-073

0-966 0-S80

o-8o8 0748

^■(iJS

1605 rs6j 1-094

0986 0S99

0827 0767

ip;s

.■62s .-.82 i-n2

1-004 o-gi6

0-844 0-78J

a 073

1-642 1-198 risS

1 1.20 0 93'

0-859 0-798

s-oS8

1-657 1-313 »i«

I-OJ4 0946

0873 o8ti

z-:oi

1670 1-316 i>S6

1 047 0-958

0-8S5 0-82J

2-114

.-68j 1338 ""68

1-058 0970

0896 0834

1-II6

1694 1-349 fr78

1-069 0-980

0907 0845

i-t70

1-738 '393 '"»

nil 1013

0-949 0-886

L

_^

_J

1

^^^^B^^H

1*0

HYDRAOUC CO-BPFICIEVTS. [tuU

1

n

Part 4 {cenll—Ctniguunt (e) of Aft

«=

Corresponding to Values o/R,t/u

JlyJrOMli

£ perlhouwid

ii>rw

1-0

oa

OS

0-5

0-1

O'l

0-93S

0-931

0-923

0-916

0-905

0-2

1131

1-126

1-117

0'3

'■^45

1141

1-233

I -216

I-2I7

0'4

133s

I-320

'■3'3

1-307

119}

0'6

.■38s

1 38.

'■374

.369

I-Jtt 1

D-6

"■433

I«0

I-.423

1-419

t-4ll 1

0-7

'■471

1-470

1-464

1-460

i«3 1

CM!
D9

i-S»7

1 -tje

1-504
' -533

1 -4'Kl

1-4SS
1-5.9

''

.■50J

i'559

'■554

J -55'

.546

2'
2'6

1-&5;

' '^:^i

'■713
1 ih'i

.■64S

1-644

3'

1 7(.;

'715

17'H

1-794

1-794

a'5

1-SJj

■ ■S23

■ ■S23

J -823

I-S2]

i-i
5'

1 -S-lli

1 '^47

i'M'7

I-S47

1-S67

.■S4S

1-S69
1-SS7

6'5

l-S.,6

1 -.'<'i7

1 -S.,g

I-9CO

S'

I-IJ09

rgio

i-yi3

1-914

1-917

?■

1-951

''53,i

1-135

'■937

i-n4i

&

1 -1149

i-ySi

"■9f;7

5-

1 'OIH

I -.jb6

'■973

i->ir7

10'

1977

l-9fto

1-084

'■9S7

It'

. ySq

1-991

1 '095

1-999

2-c<H

12'

I 'yog

2-<.«6

S-»39

!-0[5

13'

2'OOS

2-QlS

a'oig

14'

3-019

i-OZ^

I-DJi

16'

2-o:!3

3-02S

a'041

IG'

2-030

=-t>33

2 -033

2-0^2

2-04S

■m-

2-051

2-055

2 -061

2-06S

2^7i

■

■

^H

■

^B xit. PAUT 4] HYDRA UUC COEFFICIENTS.

n

^Ktm/ and GUiti Malmul (Nm'),

1

^B in ftel, and of S per thousand.

^^H

"

-o-oio

■

P

'-—- '

1

0-8 ] (ra 1 015 1 01 1

0-06

fri

o-8Sg

•■■858

0-8 JO

0783

0-682

0-!

10S5

i-ojs

1-018

0-980

0-875

D-3

1-149

1 104

I'OOl

!js|

1-259

1-236

1-193

I -09s

I-.MQ

i-3»S

l-joj

1-263

1-170

1-400

•378

1-357

1-320

1-213

B-7

'■H»

t-4aa

1-403

■ -368

iM

PS

1-478

1-463

1-410

1-33*

'-a

1 Sio

I-49J

1-476

1-446

1-373

1-537

i-Sii

1-S06

1-178

I -410

■

1:.

1 'fije

1-628

1-618

1-598

i-SS"

■

.■7S6

1-699

1-692

1680

1-649

H

■:5

'7SS

1-751

1-748

1-741

1-733

1793

1-792

1-791

1788

^m

I'S

lSi4

x-iii

■ '836

1-8J7

>-S3> ■

l-BW

i-S:l

1-855

I-S60

•'873 ■

1-871

'■S7S

iSdb

i-SbS

■-909 ' ■

I-80O

1-B96

1901

1912

1-940 . ^

1-906

1-920

'■953

I -968

^

1911

t-939

1-937

1-952

1-993

■

1-946

1-^56

.■966

.985

2036

■

'■978

1-990

^m

I-0S4

1-997

a-03s

^m

1-999

2-CI3

2-028

2-oss

■

»t)i7

2-043

'.SI

1 ^1

a-0!3

3-040

2^56

H

3-033

2-051

2-068

1 ^1

2-079

2114

1051

2^

2-126

^1

.-ols

a -(^8

»-o9a

2-136

■

a'083

3-IC«

2-127

2-170

: ■

^^H ^^1

HYDRACUC COEFFICIENTS, [tawj x

Part 4 {ix>nt.).—Ciht£icuntt (c) ef Mean Veiodty for BriJt^

Corresponding tg valmt .■' !

^puihou^d

,.f-

10

OS

0-6

0-S

0-4

Q'l

0-650

0-646

0-6J9

0-634

0-61!

0-2

0S02

0-798

0-791

o-rs6

07W

»3

0-S9S

0-891

o-SSj

oSSo

o-SjJ

0'4

0-961

0-957

0-951

0-947

0-94U

06

1-008

1-003

0-999

o^j 1

O'B

'■OS J

I -050

i-ais

IX»+I

I-OJi

07

1-087

I-oi4

1-080

i«76

i-o;i

D'3

1-117

I-I06

n

i:iS

I -143

.136

i-ijj

fllS

t-fl

1-163

I -155

MS6

I-IJJ 1

1-6

1-149

1-147

1-147

l-»43

VW> 1

2-

'■30s

1-304

1-301

1-301

!■»» !

2'e

'•346

<-34S

'■344

"■344

i-3«3

3'

.■378

1-378

1-378

1-377

i-jn

S'S

1-404

1-404

1-404

1-404

:s

4-

14J6

■ -416

1417

1-417

i-h

1444

>-44S

1-446

1'447

1443

fr

.■460

1-461

l-4f3

1-464

^4^5

5-5

1-474

1-475

1-477

1478

1-4*0

B'

1-487

l-48if

1-490

'■49*

I-494 1

7-

I-SOS

1-510

t-5"

1-514

1-5'J

8-

1-SJ6

1-528

1-530

l^iS

9-

"54'

■-S43

,-546

lo-

'554

1-556

I '559

1-561

ll'

I '565

,567

'■571

1-574

\2-

'■S7S

1-577

1-5S.

1-585

13-

.■S84

1-586

I 591

1594

1*

1-S9J

1-594

1-599

I-60I

Ifi-

1-599

I ■601

l-6o6

1-610

16-

1-606

l-6oS

1-613

1-6:7

i«ifl

20-

1-617

1-63°

.-636

1-540

■ 4llfl

^^^^H

f«au »r. PMT 4] HYDRAULIC CO-EFFICIENTS. 1U ^^^H

Ashlar, New Cast and iVrought Iron, and Unghxtd Stoneaiare H

n = oot3

i pra IhouMfld

■J^

0-3

oa

018

o-i

0-08

W

o'6iS

0-S93

0-374

0541

0-473

m

0767

0745

C73S

0691

0-617

0-3

0-S6I

0'840

o-Szl

07SS

0-714

04

0-539

o'gio

0-891

0-859

0-788

0'5

oyS»

0964

0-947

0-916

0-847

06

1 P26

i-ooS

0-99*

0963

0-898

07

1-L«1

1-046

I -031

;3

0-94I

0'9

logj

.■078

1-064

D-979

U-9

1106

1-093

1-069

1-013

1"

1 MS

ri3i

1-M9

1-097

1-044

IS

lajS

tn6

I-JI7

i-aoi

1163

r

1196

I ago

i-a»4

1-374

1-249

7-i

'■.«i

<-338

1-335

1-329

i-J«4

3'

■ ■376

'■37S

1-374

i-37»

1-367

3-S

1-405

1-406

1-407

1-408

1-411

4-

1 429

"■43s

1-434

1-438

■ -■45°

4'5

t 450

1*454

1458

1-465

I-4S3

5-

146S

1-473

■-487

|-5'>

5-5

;a

1-490

\%6

rjoS

1-538

6-

1-505

i-S'a

,-Si6

1-561

^

ISM

»S3i

1-540

1-557

I-6oa

»

1541

1-553

■-56,

1583

1636

9-

>Si9

1-571

•■SS3

I -605

1-665

ID-

'"573

1-587

i-eoo

1-6IS

.■691

11-

rs86

1-601

1615

I -641

1714

B-

1 -$"7

1613

1-657

1735

O-

1607

1624

1-640

.■670

'-753

«■

I'M 7

1-634

1-650

1-683

1770

IS-

rtijs

'-643

■ -&60 1-694

1785

«■

.■63J

1-651

1-669 '-I'M

1-799

20-

..57

1-678

1699 1-738

1-846

B

GO J

_4

i

^^

^1

HYDRAULIC CO-EFFICIENTS. jTAi

Corresponding to values */B

i*-o-oi7

£ per Ihouund

Dfc..

10

oa

O'S

0-5

0-*

01

0-445

0-443

0-438

0-434

0-429

0-2

OS61

o;S58

0-S54

0-550

0-S4S

03

0-6J4

0627

0-623

o-tiiS

0'4

0-6S8

0-68S

o'68l

0-677

0-672

0-7

0-730

0-717

0723

0-720

071S

O'E

0764

0762

075a

0-7SS

SS

07

0793

0-791

07S7

0-784

08

o-SiS

o-Si6

0-81 J

o-8io

0'So6

0-9

0M40

0838

0-835

o8jj

0-3J9

'■

0-860

o-SiS

0-855

0853

0-849

1'S

0-933

0-931

0030

0-923

0^^

2-

0-9S4

0-98J

0-982

o-^

0-979

2-5

1-019

1-OI9

3'

1051

1-051

1050

i-o;o

I -op

3-S

I '075

I-07S

1-075

1-076

1-076

4'S

i-oys

1-096

1-096

1-097

1W7

Is

\\'^%

1129

i-ljo

1-131

vni i

1141

1-142

1-145

114- 1

6'

>"53

I 1 54

1136

i-.SS

1160

1-

I -174

1I7S

1-177

1-179

i-iS:

8-

i-tgi

•■'93

1-'9S

i-[.i7

9-

120S

I -207

10-

1-218

1-223

I-2.JD

11-

(■«9

:-2ji

1-2^5

1-237

1-241 ;

12-

1*39

1-J41

1-245

1-2+S

.■2S2 1

13-

1148

r-2So

I-IS4

I-2S7

14'

1'2S6

1-2^8

1-262

■ ■265

IS'

I-26J

1205

1-270

1-273

i-i;8

10

1-269

1-272

1276

1-280

1-2SJ

20

1-391

•■294

1-299

1 303

'"_-

■

^H

■

^njUt. fAliT 4] HYDRAULIC CO-EFFICIENTS. 14G ^^^^H

GId BrukwoTkcrAskhr.and Old Iron and Unglaztd Stontwan. ^|

inful and S pfr Ihousand.

n = 0-017

J ,«. .h<.i,«;.d

It
is fed

0'3

0-a

015

01

0-08

EM

0421

0-406

0-J93

0-371

0-316

0-2

0SJ6

530

0507

0-483

a'433

03

0610

594

0581

t>-5S7

0-506

0-4

ofi64

650

0-636

0-563

0'&

070a

693

0'6Si

0-658

0-610

0-6

OT43

730

0-7.8

o-6^

0-649

0-?

0773

761

0-749

0-759

0-684

D-B

o'Suo

788

0-7J7

0-7S8

0-715

0-9

o-Saj

S13

0-801

0-783

0742

'■

0S44

0SJ3

0-83*

oto6

6-76?

1'B

o,«

o-9'S

o-9tJ!

0-895

0-867

2-

0976

0-y7I

0-967

0-959

0-939

?S

1017

1-0(4

1-007

0996

3-

1-0(9

049

1-048

1-046

1-042

s-s

l-o?6

077

1-077

1-079

4'
4-5

'■099
l-liS

1°{

flOJ

riJ4

i-io6
1130

i-iij
I MS

fr

'■'35

■39

1-152

1-171

6-6

1150

'55

r't6i

"■>9S

&

I 163

170

.176

i-m7

1-117

7-

i'i86

'94

1-301

1-317

I -334

»

.-IDS

2'S

I-J34

1-342

1187

9-

!-"fi

m

1243

1163

1-314

W

34B

t-iSi

"■339

ti-

1-M8

361

|-*74

1-198

1-56.

c-

1-319

ars

1-187

ijij

.-380

is-

1-369

384

iw»

1-326

'-398 ■

M-

1-278

394

1-309

'■338

■

Ifr

1-387

303

1-319

"■349

1-419

»

lag*

1-311

i-3«

1-359

"'443

H

»

i-3«9

'-33a

I 357

1-393

1-489

1

1

■

1

■

■

■

■

■

US HYDRAULIC CO-EFFICIENTS, [tabix wi. r*M ,

^m

I'ABT 4 {fimL).—Cotffidmls (c) «s/ ^lA-<m rrftwyv /or iilw-;: .

^^B

ff«^/,f. or for £ar/Auvri in Class I. of She Ixsi cr. :

^^H

eomspondin^ to valuts of '& in fett, and of ^ per thouiar .

1

■wktn n=0-020.

la 1^1

10

0-8

o-a

0-5

0*

04

OS^I

0-5J9

0555

O'SSJ

D-549

O'S

o'6:9

o'6a7

0-623

0-61 J

0-a

0.677

0-675

0-672

0-670

0-66?

J-

0-715

0-713

0-709

070'

n

078a

0-78.

o'779

0'778

'X

1-

o-Big

o-8>8

o'S37

0-SJ6

?5

0'S64

0864

0863

0-8&3

a-U;

3-

o-B9i

0-S91

•■89J

oSga

o.&)i

a-

093s

0-5.15

■ o'93s

0-936

0-9 ji.

6-

o,&6

0967

o'9r,S

0-969

09:0

^H

6-

0'99'

0'99i

o'99J
i-oji

0.994

0-99"

^H

8-

1'0I7

1-019

1-033

\T,S>

9-

1-041

1-043

1-046

1-048

lt>Si

to-

"■054

.056

1059

i-o<5i

I-06S

1-067

1-070

1-07 J

12'

l'074

1076

loSo

loSj

l-oSTll

13'

1083

i^S

10S9

l'09J

>«9CM

M-

1091

1-093

1-097

"<^H

16'

1104

i-io;

I-II5

ri^H

1

20'

lllS

1-139

'■"34

I-.3*

'-<«

,.?,.:

0 3

0«

0-16

&l 1 005

U4

o'542

o'53o

0-519

0-500

0.41.'

O'B

0590

o'57a

o-iJl

n'B

O'Mi

0-651

0-64J

0626

O'S'.i

\-

o'70i

0-69*

0'6S4

0669

o«i;

1-5

o-ili

0-766

%Z

0750

07' i

!■

a-U%

0-3 18

0807

;s

25

0S61

0-858

0-8S6

s:yi

3'

0891

0-890

0SS9

o-SS*

4'

0-937

0-939

0-941

0-9M

0-95;

6'

0-971

0-976

o;98o

0-987

it«5

^1

6-
7-

0'999

1-005
IOI9

!^]6

1-050

13^

8-

I-O40

tO|9

1-058

1T>74

»

1^56

1-066

1-076

1-094

1140

10'

I-OSI

ii>)j

^^H

11'

■ ■oSj

1-095

I 106

i-tia

riS;

12-

I-09.1

I-I07

I-l«

J.»i4

13>

1 103

I-II7

)-iji

"S

l-UI

14'

I-IS7

ri4i

I'lM

i.»J7

16'

I-liS

ii«

"59

i-m

l-ftS

^^1

20-

t'.ss \ 1-"^ \ ^'^^ \ *■•« I i-J'-'

1

■

■

■

^H

^^^^^^H

X.I. fAKt 4]

HVDRAULiC CO-EFFICIENTS.

1

..-orkin CJas

Co^atnlj (c) of Mean ydodty /

r E<,nh- ^1

//. in alxnt-averagi ord<r, <orrf spending /« ^B

lalufi fiJVt. in

feet, andof^ptr thousand, when n

=0-0:^35.

■

,X.

»„,.„„.

1

O'S

0^8

06

04

V*

0-484

o-48a

0-479

0-477

0-473

is%

0-54S

0-544

0-5*1

0-539

OS3S

IK

OS90

0-588

0-586

0584

0581

r

<,«iS

o-bzi

0-61 1

0-619

0-617

1-5

06*1

0-687

0685

O-6S4

0-682

t

o73»

0731

0-730

0-729

0-728

2-6

<.763

0765

0-764

0764

076J

»

0-792

0-792

0-79J

O-79J

0-791

»

0-8J.

o-8l3

0-834

0-834

0-835

fi-

o-sij

o-S6i

o-slt

0-S66

0-867

ft

08S;

o-SSS

0S90

0-891

0-893

7"

0-907

0-908

0-910

0-911

0913

»

0-LI23

0914

0-9J6

o-9rf

0-931

1

0'9i7

0-9J9

0-941

0-943

0-946

to-

0-949

0951

0-954

0-956

0-9S9

ll-

W960

0-96*

0-965

0-967

e-971

B-

0909

0-971

0-975

0-977

0-981

0-

OQ?8

0-980

0-984

0-987

0-991

It-

09M6

0'9SS

0-99*

0-995

0-999

tfr

0099

1-006

I-009

1-014

20-

1-024

I'OiS

I -031

,■037

1

5 per iIwubhiI

03

oa

0 16 1 0-1

0-06

0 4

o-jl.;

D-457

o-44»

0432

0-39S

O'Sjo

o-SJo

Dsia

0497

0464

-;S76

0-567

0SS9

0-S46

0-515

0-605

0-S97

0585

0-SS7

0'h79

0-67J

0-668

0*59

0-638

0-J16

07Ja

0-719

0-7 1 J

0698

076J

0-760

07S8

o^M

0-746

0-790

0790

0-7S8

0-785

0-836

0-S37

o8j9

o-84»

0-849

0-869

0-873

0876

0-883

0S99

OS9S

0-901

0-906

0-916

0939

l

0917

0914

0931

0-943

0-973

1 *

O'OJS

0-W4

0-95*

0-966

1-003

9-

0-95'

o-u6i

0970

0-986

1029

lU-

o9ft5

0-975

0-985

I-O04

1-051

0-977

0-9S8

0999

1-oxo

I -07=

1!-

0'9S8

i'034

1090

13-

o'9y7

1013

1-047

1 107

14-

I-C-J6

I -033

1-058

1-133

1-037

l-oji

1-079

IIJO

wL^

1-046

1-064

i-oSo

fl95

^H

I

^^

J

^^^^i^m

118

HYDf:AUUC CO.EFFICIENTS. [TiHL* Sll. r±M«T

Tart 4

{cont.).—C0-effidattsic-\ of Mean VdoHty.fitr Eof&K'-

in

Clan III., in good average order, eomtpondingU noAicv .,'

R

in feet:, and oJ'Aper thousand, wktn d = 0026.

j;pu>hoa>i»d

10

O'B

0-«

05

M

04

0-424

0-422

0-420

0-418

0-4U ,

0-6

0-480

479

0-470

0474

0-4II

08

osii

520

0-518

o-ii6

0513

0-SS4

SS3

0-550

OS49

0-54*

1'5

0-6.3

612

0-6II

0-609

o««

2-

o-6/s

6S4

0-6S3

0-6S,

0-651 .

7-i

0-687

6S6

0-6S6

0-6SS

0*44 ;

3-

0-71*

712

0-712

0-7II

0711

t'

0751

75*

D-7Si

07S3

0753

&

.^-78.

781

0-781

0783

07S4

B.

fi-«04

80s

0-806

o-8£^

0(09

6-

0-8J3

8^

0-816

0-827

oSp ,

8'

0*39

840

0-843

0-844

o-«»r 1

9-

o-Sij

SJ4

0-857

o-8i9

u-t&J 1

10'

o-8bs

S07

0-869

W-S7I

oS;5

(1-

0-876

877

o-HSo

0883

o-SJi '

12-

0-83S

8Jt7

0-890

0-803

0S46

IS'

0-S93

89s

0-899

OW

14'

0-901

903

0-907

0-910

16>

0-915

917

o-9;ti

0-924

0-910

2G-

0-910

0939

0-943

0-047

o-fS-'

i„l.

0-3

03

0-lS

01

ODB

0'4

0-409

0-400

D-39J

0-379

0 35"

0'6

0-467

4S»

0-4^1

"437

0-410

08

0-509

SOI

0-494

o-48i

o-4<6

o-S«

53*

0-5M

0519

0-49*

1'5

0-605

600

OS9S

0-587

o-Sto

7-

0-649

■646

0643

0-637

0<»4

2-i

o-6.i3

6St

o-6Sa

o«TS

0-669

3-

0-7I1

710

0-710

o-;«9

o-;o6

t-

V-S,

755

0-757

0760

07«

s-

790

0-7W

0799

OSlj

B'

o-Sii

«17

o-»ii

0-631

<»«H_I_

7-

0-831

D-Sst

0

840
859

o-ai6

0-806

oS

^

9>

0-S66

0

87s

0'8S4

0-609

o-a^B

10-

890

0-899

0-9.6

°^H

tfli

0-9IJ

o-93a

"■•■W

1Z'

0-9OJ

9"4

0-915

0-946

«w« 1 1

13-

0-911

014

o-wt-

0-9S8

lOIJ

\i-

0-9)1

0-934

o-«6

0-970

IT.3D

1&

0-936

0-9S0

0964

O-990

i-»57 1 1

■'.fr

o<X>( a-ffit

0993

1W23

""M

B

^

■

■

^H

XIU PART 41 MYDRAVUC CO-EFFICIENTS. US ^^k

: 4UonL).~C0-<8iei€n(s(c)qfMtanVeloaty,for£arH,KVri ^|
!•! Class I v. in bf!<mi-eiverage order, corresponding to values ^^|

=/R in (eti, and of ^ptr thousand, a-A^w n=00275.

<ar«c

i-t«.hou^d

10 0-8

06 1 05

0-4

'i.

o-3;6

Q-37S

0-371

0370

0368

o-4»8

0-417

0-424

0-4J3

420

o'466

0-46S

0-463

0-461

459

0-496

0-45S

0-493

0492

490

0-551

o-SSi

0-SSO

0549

S47

t

0-591

0-591

0-590

0-589

588

?S

o-gza

0-6ZI

0-6JI

680

3-

o'647

0647

0-646

0646

646

1-

o-Orts

o6Ss

068s

0686

■686

S-

0713

0714

07 IS
0738

0715

7.6

ft

0736

0-7J7

0-7J9

741

r

0754

0755

0757

0758

760

»

0-770

0771

0773

0775

777

9>

0-784

07»S

0787

0789

792

fl

079S

0797

o-8oo

0-B02

805

o-8o6

o'KoS

0'8io

o-8m

816

o'Sis

0-817

0-820

0-822

S26

o»24

o-Sl6

o-S»

0-831

83s

;i

o»3l

O'SjJ

0'8j7

0*8 J9

843

16-

0'84S

0-847

0-85.

0-854

858

SO-

0S66

0S69

0-873

0S76

08S1

JL.

Jp.,.h^>..^«i

0-3

oa

0-lB

0-1

0-06

0-*

o-lf'l

0-355

0

348

0-336

0311

0-e

0.1 16

0-408

401

0-J90

366

M

0-455

044s

o'43>

40S

!■

04S6

O-4K0

47S

0-465

444

I-S

w*S4S

0540

5J6

o-5'9

SI*

f

0S»7

0584

581

0-576

564

2-S

oi:'i9

o«i7

616

0-6.3

606

3-

;a?

0645

■64s

0643

641

*

0'68S

690

0-69*

698

s-

o7>8

07 J 1

7*4

0730

743

e-

0743

0748

75*

0-760

;8o

V

0764

0770

■76

0-786

8ia

»

07S1

0788

79S

o-8o8

839

9-

0'796

0*805

i:i

0827

863

«•

0'^

0-819

0-844

ssj

1*

oair

0-83.

S41

0859

904

©

0833

0-843

853

0*73

o-gii

13-

0S4I

085}

8S4

0'NI45

0-9J7

u-

0-S50

0-iU>2

S74

^■S96

0-951

.J£

C-S6S

0'B79

0892

0-916

0-979

y£r

0-889

0905

o-gw

0-949

COM

^

■

■

q

^H IM HYDRAUUC CO.EFFICIENTS. [T*K^

^H V\yn A,{eoni.\—Cif^fficimH{,<:)ef Mean Veloaty.foF

BofOr^s

^H in aass K. ia tad ordtr, parity pvergrmm, vr

Porm :•

pededby detritus, when n=003a

inf«<

1-0

0-8

0-8

0-fi

04

w

0-337

0336

0-3J4

1%

0-33S

0-6

0'38s

0384

0-381

o'37»

0>8

0-41I

04M

0418

0-4.6

1-

0-449

0-448

0-447

0-44S

t'S

050a

o-soi

0-500

0-199

049t

2-

0-540

°m

0SJ8

0-538

»JJ7

?5

0569

o-ifla

0-568

0-S68

o-SW

3-

OJQJ

0-59J

0-592

0-591

OT^

*■

0-619

o-6i9

0-630

0-630

<.«J=

S-

0-057

0-6S7

0658

o<59

0-6W

fr

0-679

0-679

0-6S1

0-0^

0-6S1

?■

0-697

0-698

0-699

0-70I

0705

B'

0-711

0-713

0-715

071?

07"*

9-

0-7M

0-717

0719

0731

o-;.y

10-

0737

0*739

0-I4I

0-743

0-7*'

If

0748

07^9

0'7S3

o-?S4

07>:

1?

0-757

0-759

0-761

o-7<4

07«

13'

0-765

0-767

0770

X%

o?:*

U-

0-773

o-7;s

0-778

07&.

IS'

0-7S6

0-788

o-;8i

c-795

o-jin

20'

0-807

0-810

0-814

0-S17

o-Sji

,.1,

iperlhon^d

0-3 0-a

0-16 1 O-I

0^09

0'4

0-3^6

0-319

03U

0-30J

02S1

O'B

0-374

0-36S

o-j6i

0-3S1

o-3y>

0-8

0-405

0399

0-J90

0 3?3

0-440

0-43S

0430

o-4»i

0-401

I'S

0-495

0-491

0-487

0-4S0

o-4«

2-

0-S3S

0-S31

0-539

0-515

0-514

!-S

0-566

0-564

0563

0-560

3'

0-S91

0591

0590

0-589

4'

0-631

0-6J1

0-634

0-636

£■

0-661

0-664

0-667

0-67J

6-

0-6S6

0-690

0-694

070J

o-rni

1-

0-706

0-711

0717

0-717
0-748

07 JO

e-

07S3

0-730

0736

o77e

9-

0-738

0-74S

0753

0-767

o-Sw

to-

0-75:

0-7S9

e-7t8

;3

0-81.

ll'

0-761

0-771

0-7M1

o8j9

!!■

0773

0-783

0-793

0811

ofiji

13'

0-7S1

0-793

oSai

o-S»3

0S71

14'

0-790

o-Soi

0-8,4

0-8.14

08S;

16'

0-806

0-818

0-831

0-854

o-?u , ,

20>

o-8jo

0-S4S

0-859

o-m

o^^J

TABLB xn. FA»T 5] HYDRAULIC CO-EFFICIENTS. 151

Part 5. — Co^ffidents of Discharge for Orifices^ being values of
ofor the formula in Table X,, and given in the Text,

r-<»x 8-026 V^

Appfied Acoording
ktlw to Ex-

TaUc periment.

55 '572 I Rectangular, width 7 depth, ( IT? -D) ; see next page.

*62 *62 \ Orifices generally.

66 *66 I Sluices without side walls.

7 *7 I Canal lock gates and dock gates.

727 •da J Undershot wheel gates.

'84 '83 Sluices in lock gates.

-84 '84 Large vertical pipes.

•9 '9 Narrow bridge openings.

-96 *94 Large sluices.

•96 -96 "Wide openings from reservoirs.

•96 '96 Wide bridge openings.

-96 '96 Orifices with converging mouth-pieces.

I * I * Large orifices with diverging mouth-pieces.

I *3 Attached diverging mill channels.

Modification of the co-efficient so as to include the effect doe to
^ocity of approach ;

Let A ahead due to this velocity only,

then^,»<?^l + A
Mad 0, is the new co-efficient to be used.

152

HYDRAULIC CO'EfFICIENTS, [table xiL PAIT5

Part 5 (con/,), — QHefficUnts of Discharge for Orifias.

Table of Co-efficients of Velocity or Discharge for Rectangular Orificts,
when the depth {D) is less than the width ( Tf^ for a head (ZT).

H

W

10

n

0-6

D
0^6

D

W

016

£

01

D
w

0-05

Values

( of «

;05

•709

•10

•660

•698

•15

•638

•660

•691

•20

•612

•640

•659

•685

•25

•617

•640

•659

•6S2

•30

•622

•640

•658

•678

•40

•600

•626

•639

•657

•671

•50

•605

•628

•638

•655

•667

•60

•572

•609

•630

•637

•654

•664 j

•75

•5S5

•611

•631

•635

•653

•660

I'OO

•592

•613

•634

•634

•650

•655

1-50

•598

•616

•632

•632

•645

•650

2-00

•400

•617

•631

•631

•642

•647

2-50

•602

•617

•631

•630

•640

•643 '

3-50

•604

•616

•629

•629

•637

•638 1

4-00

•605

•615

•627

•627

•632

•627 ,

600

•604

•613

•623

•623

•625

•621

8^00

•602

•611

•619

•619

•618

•616

1

lO'OO

•601

•607

•613

•613

•613

•61J

The above was deduced by Rankine from results of experiments by
Poncelet and Lcsbros.

N.B. — When lIj'iiD, the centre of figure may be considered the
centre of motion.

I

;n. r**.j 6] aVD/lALrzrc CO-£FfiaEXTS.

CO'ffiaenIi ef Dhchnrge for Orerfalls, biing values of
•- Ikt formula applied in Table X., andgixien in the Tex/.'

F"J«. 8-025 v'fl

.:t !■• length of weir sill: £- length of ilam, or bteadlh of channel :
lii-atl on sill: i>sd«pUi ofootch.

Bjl.<

jWntt with 1-inch cresti when l — ofj-^% the tmsX
I viiue of 0 being— *6T x —^

IOveifalls when I7 — and < —
V-shaped nolch, when i - —
V-shaptd notch, . when I=—

rWdn when l~L, and H7\ heighl of the bamci ; in
S thi( case the velocity of approach must be considered

Weiri generally when (i L and B<. \ the height of the

Bmodify (he cu-efEcieut a »o u to Locluile the effect due lu velocity

Vuh.

■ A— head doe to velocity of approach only: —

•{(■4)'-a)-}

k th« new co-eSdcDt to be used.

I nting Ta'ite X. for overfalli, always diminish Ihe Telocity of
t there given by one-thiid ; this slune admili of the nte of ih«
le for ditchoiges Loth of oriRces and overfalls.

155

APPENDIX

OP

MISCELLANEOUS TABLES AND DATA.

Masonry Dams.
RriAiNiNO Walls.
Weight of Materials.
Thickness and Weight of

Water-pipes.
Absorption and Strength

OF Stoneware Pipes.
Ovoid Culvert-sections.

Table of Arcs and Sectors.
Tables of Powers, Roots,

AND Reciprocals.
Duty of Hydraulic Machines

AND Contrivances.
Constants of Labour and

Cartage.

Lofty Dams.

poljrgomd section (No. IJ) applies to masonry having
ilduilj of WBter, or weighing 3 foolweight per cubic Tool, and
tcrifting ■ pressure of nearly zoo foolweight per squure foot.
;s alio auiuned lo be the limitinB pressure allowed on lie foun-
lie co-effidenl of friction for the sliding of the courses on each
.<.n >l 073 ; (he effect of cohesion of the mortar being neglected.
ite ii polygonal on both faces, thus consisting of four rectilinear
ind is thus R practice ip proximal ion to the Iheotelical double-
n without any top-thickness ; the Hatter curvature being on the
or outer face. The followint'

tlbe greater cwalare 01
^oas in fecL
H.!gh..
^. . 0

39-3G
1 6E-B0

W . .164-

168 '96

1 is obtained by ordinaies :

oorretpooding carved si
twvlj ihm ; —
limiting pressure in footweighl per square foot
I top width of dun

width of dam at any depth 0 from the top
I depth from water sur&cc

" from vertical line to outer face at any depth a
lOfot (rom vertical tine to inner face at any depth «

Lo-96(^^'; 1- JLy; alsni-OfiSv; and

»t-ljr when a = \n, the total height of the dam ; but no
nJnc of y less than ti'tiv a admiuibte.

y krfky dams the value of P should be •jiminished by subsli.
nJ^l-O-OOlSir).

Ftrm^ and Dat»M Xt^i*m "^

Vkeic ir-UUl kafaHUi pcMBK ifriM tke l«fc d At tiA

■ MthEMiOBr iteiirtitwl Mn to Ok if a mh^<

UfhtaailfcRiidlk.

■ - the awitlht «r k ofak faoi of tbe aal.

Wiib nnkd ncla«K«I>r KdiooK a — I, f'^t^ r' a/(s
Wii^ pl^b-faod Uspooiial Mctions of ■ top tUdb^ |l)

,j'^^^^:®c

°»"';;'r,::~~'"

J M>i^:uj. Thclimiiing lalui of j lo avoid icniion In Ihemi!
? -. ': .: ■.:; hm]iing value in aciual praeiice is \. In spixiil cjsf.

■■* I sie reais^ajiee (fj lo crushing of the ni.i:eiiil, iis values coctcswi
■ ii A-i :i> ihc values of _, where ^' = lhc me.in prci*ure pi'i unit of y
:•■ r^-c. ^ rem of the venicaHotces + arca of ihc Iwsc ; imi/'isl*^

„ !'

,v I u i, ,

liKh.itjt. If j- = lhicliness of a vertical rcclangul;!! siajl losi
1 h. >r.:o n I il- topped bank,

,:,% for in incielinite surchii^e,

d.i. for a surcharge of a heighi c,

j^ - ./.T— — i; wliete k — heighi of the wall

AND DATA,

AdiiHmal ^rmtiite fir Retaining Walls.

d thrust (ff] for a lection whose brcadlii U tmity.
li luving vertical backs, and for earth with varioua angles of

=• oo-eScienl x weight of l cubic Tool of eartli i h*.

W 30° Si" 38" 39° 42" *6° 48"
Co-efScienis of earth ptessure.
W;Kmlal.lthele«dJ.,gg .jgj .^„ .^g^ .j,^ ^gg ^g. ^^^

re^****^ "^VaST -375 •361 -387 308 ■»7I1 ■2S0 -m

' ill) with aloping backs, having deleimined the position of thp

.:..i>iinuin pressure, and hence also the valaes uf • the incliaaLion

nc with the anRlc of repoic, unci A the scclionnl areaof cffeciiv*

, ilico H—A tun * ■ weigbl of 1 cubic fool of Ibe eaiih.

:, U^^Kyk'-ZVihKk^, when TT, ''62-d.

(3) Anowuce for limiting mislaoce to cniihing.
% cnkulaled x, ihe bollnm Ihickniss, in the ordioaij way, obtain
fldonki bollom thickness necessaty, as follows.

- lautancc. which is loughly B ions per square fwl lor bricliwoik

and 4(1 tons per square foot foi the heaviest masinry.

- irrrigbl of wall per unit of length, also in tons.

. liiickwork wall of hei^jhl k, anil mean thickness t in feet,

ht

'-' r ' 30 a 3 H 8 3ai1
I case the whole ihickneu f — r,

''V'32<j}

nf wall nre from BO lo 100 Ibi. per cubic fool j the
gTMiiie rubble UU ; basalt nibble 160 \ nshtai from ls!0 Vt

(J) AUowuiec for Ihe effect of batter in a wall.

a iccianguhu wall the suilsble hollom thickness \ but a»
\ the horiiontal thrust would be greater, and In re-
it would be less, the altered thickness may be obtained by
li dbgnun to icalE, ami .illowing the pluoili-facE (o ifvoIvm
«-tbinl uf the height. Undci that con<liIitin Ihe
ney lie lealcii ; for the hoiiaonrsl inoveineni uf ihe centre 'A
ilie wall U not aKecled, not in iWbilily.

j^Mx^ocs rdai£s

>-xiMi m^ mm.

:; ;; j^^' . '. . . s-;u!-^

;, L..!;-i-.

; iv:.-.i.- in ccmw^ii. Chiririg Cr.-.f. liri.lgc IJ

b:a3..r

>hiii.- i-liic Mkk in >:emeiii. Ctilion Su.^ivn-

red L.[

ninyh.im in lb, lime. Railway Viaducl 7

mM.k' In

V working load foi masonry' and brickwork 15 Ihil t«
In ....im.ir)- calculation. 5 ions per square foot forbnd-
••M. ;i.i.l ;0 fur aslilat in Cfnifiil. is ijoneraUy iHomL

AND DATA.

J

^H PrtpoTtions

of Seetiom of Ovoid Culverts.

^1

(By the Author,)

Feclop

Ibuicne diarowcr or-.
ntnanciDsidc widlb/

R..(i.«orwpcin:le

I

1

I

■' vfrticaJ deplli

3

S<S8GS

3

of curved iidc .

2

-finvat . .

0-5

O'SSBS

0-375

»utLl. of tide, oi uc .

Z6- Si'' ir

45"

1-5

«M«fMpaKlo .

I8tl"

180=

220'>

ItKoriKvcrt. . .

IIW' Iff

90°

140°

klMofFallSecliDa .

I'sei

3-9820

4-ia4C

Am, SUM to § d<rpih .

3'023

2-6868

a -6834

k». filled to) depth .

1-136

1-0278

0-9637

[■mnirtet of Full Seclion

7 '930

7-W3i

T-7660

filled 10 S depth

4-788

4 -3376

4-6144

filled lo ( depth

2'7S0

S-BHET

3-S413

; Kul.foi Full Section

0-679

0-6iS8

0-esB

.. filled to ; depth

0-631

0-B20

0-G60

„ filltd to 1 depth

0-413

0-396

0-381

Msed oo AQ equ.1 tnic

werse duune

o for each

iwrnofcutveit.

ir ilie <™l*ert» are >s»i.med to be of equd

Kction when

Died, tbe celAtive dumcM

s for the different forms of cul»ert ar

ethu.-

CylindiKul Section

t-lSS6 ^1

Phillip.-s Melntpolilal

1-0003 and

■2<)30 ^H

It«»ksley'i Ovoid

O-USSland l-39ue ^H

jMkwn'i Pee<op

0-9818 »nd

■

riM P«glop iMlon flushes highest with Ike aam

quinlily of

iquid i but ^H

• tUc* muii be of itiehtly increased tbickacM

when mbject to much ^H

^UIB

■

■

1

■

■

^^^^^ 192 MISCELLANEOUS TABLES

^H CatI Iron » ttter-fipts ; »4opttd in the Rio d€ jMiko

^^B

Wattrworki.

^^B Lcnglh

Wdctil

TH^>n"

^^H t)in«»r wiltaZul

■ilh.'ui

^^H oTpipc IbJlkflgn

ocJka S«kt< or iDchci

^^H incha in.

fn ior

IhL

^H oSoorjIi i;^

iz SH «0 J

« i -

^H 0'Saor3.4 t^

9 Stt JO I

17

33 3 ^

^H 050011^ 1

la sft »i 1

»3

aa 3 :-

^^B 0-5QC119;],

9 5ft 16 0

^H °'40«isU H

«» Sft '5 0

13

16 1 i<

^H 0-40 «ts» ti

9 Sft >« I

^H 0-^o.nH tt

9 +

; 7 J

S 3 1

^H ojoorll^' ]}

9 4

6 3

»7

^H oiSor 911 II

9 4» S o

s i

^H o-^o TU ft

9 4ft 3 a

^1 >>'>S«' SM ft

9 4ft

10

a 3

^H o->o»r VA ft

9 4ft I a

16

1 3 !■

31J" pipes 20

ainweqihcm; v^.'-

^^H gtaviiy of iioD uJcen U 7-30.

Gtatg^

^^1 Caitlr»n Waltr-fiptt adopud at

^^1 -niiik- wtigtu i»i.

W«li.g

Tliici

Tortadat. «

^^M tTph K» SoHlM

hud

L«sA »«

»M

tin..v..lb»

^V 3J' 39 ' IS

■« H

3 »S

^B 30 ti 44 o 3

300

|< B

0 IS

^K 30 IS 3 5

130

>4 5

^H M 28 ■ >J

JOO

" 1

3 IJ

^H 16 0 4

270

«

0 16

^H »> 13 3 35

»40

'" «

0 16

^H H u 1 '3

300

9 A

a *«

^B ii I .9

ite

» 1

1 as

^H u •> > 17

330

7 i

t 1

^H 10 3 37

300

« A

1 a?

^^1 H 10 0

ISO

s U

3 >4

^B 9 > 9

aoo

t so

^B H 9 > 3

J70

3 1

0 la

^H ft T 3 35

iSo

3 1

1 4

^^B Testing sln^a double Ihe working pre

isure.

^H Tlie loigthi IK 9 (Mt

cduJing

Bx-M) but lac 14

pipcM^

^^1 «»di ibt Unfith te ta («et

udtoia

>p.6fc.L

J

d

n and Strtn^h of Cylindrical Stonnva\
(Bf Baldwin Laihaoi. C.E.)

: Pi pa.

075

in"

31

3 '■as

0-Sq6

■ 6'

07a

t II

29S

»97S

0-85

0-63

i8

rf7S

»-6S

074

1 fi

30-S

31 7J

4-10

1 0-87

57 7S

587s

"73

; f

0-93

n

737i

1-03

o-Si

60s

632s

4-S4

■ ■00

58

£1

6-S9

I -OS

96-<.

WS

iS6

34

ss

476

"

ita

I 10

«is

67-s

i-SS

I -03

I II

79-S

8a-s

377

ro6

U6S

117-0

«-43

:}■!•

1-36

13a

■39

5 -30

171

130

'37

5'3S

-31

165

174-S

S7S

■ I8"

1-43

aa6

3-l6

1-38

a.o

ai7

3 33

TJiinlr-

BucaiDc

TwOt

Dim.

L.ng<h

tvoiun

rangifc

U, cru.hu,.

B.

T.

c

■ *"

07»

JO

1307
416

"74J

0-48
0-69

70

as

J043

2956

0-84

40

iH2

■ .^

079

>o

113-9

»470

0-S4

4S

60

aoi-s
3a»-4

3Sfii

•)..

107

7

39-3

2834

0-94

7

44.6

WJ9S6

1

119

3J

ao7-9

X"

IIQ

M

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MISCELLANEOUS

TABLES

1

Pewers, Hoots, and Rmfrotals

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Fifth

p™«

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Numlxr

Si«n«

Rm

b!»i

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3-8015

13964

1-1493

1-1419

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13061

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1-2599

1-1487

5-6569

1-3195

2-1

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1-4491

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I -■600

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1-4833

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11914

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10-5615

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1-3510

41-9561

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1-1794

1-3656

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1-2361

1-7099

1-3804

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3-5652
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0-047 619
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2-9625

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1-9473
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3-7372
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0-037 03'
0-035 714
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5-7746

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6.2449
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2-0699
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0-027 778
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6-4807
6-5574

3-4482
3-4700
3-5034
3-5303
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2-1217

i-'3'5

10763
1 1432
12124
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4-4596
4-5018
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0-022 727

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3-6593
3-6840

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2-1689
2-1779
2-1867

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4-6249
4-6649
4-7043
4-7433
4-7818

0-021 739
0-021 277
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7 '3484
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3-7084
37325
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3-8030

2-1954

2-2039

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48574
4-8945
4-9313
4-9676

0-019 608
001 9 231
0-018868
o'oiS 519
o'otS 1S2

Hi

7 '4833

7-S»9o
7-6158

3-8709

23468

245^

25619

5-0035
5-0391

5-0742

0-017 857

0017 544
001 7 241

1

^

A

1

i

^H

■■

^H

■* -r

/ -■ i:

-J,

I:

'A

f;
K7

'/J

/J

71

n

/4
7^

n.
II

n

n\
'if/

hi;
I'./
iiii
ji'i

WW

!)!)

'Hi
9/

Hrt
nil
mo

'/>■-

^ -

4:'/j

S^'4l
51-4

S17''

5';25

-77'''
O241

f.724
7-^25

Tx-"^!

• :2,-

« • ^ « -' -

% i.^53

^■544"-'
S'>-^25

S Vy.3

S717S
". / 1 - J

■S-94'»3

9"

9''''5=>4
'y"i 104

9-1052
9 "2 "'95

;i.

" — ■* V -

I T-i--

i i-»:-2

i I • :

4 2172

42 ..^
4 _'!"'-,-•
•i "267

4-34;5

4r':i'

4 -37^'?
4-396.S

;■ - -^L

- . - »,

■^ - — •

^ ^1 * ■

■»■-»•

-I'-'Jt

f » — •

: ■ : :^

_'«.•.> %

2 .:':>2

2UliI

2-4:0?

2-425>

2-4315

- 7 ri; 1

: I : :a

■V ■

p - X

; "->:

;:I2":

??>i

UK

::3

- -i«

•

:-:i:

■; :i:

7 i'">

92736

4-4140

2U372

6S 5 S9

^■-.1C2 coil

7S''9

9-3273

r4>io

2-4429

70550

5-G?77 ccii

7744

9-3«o.S

4-44>So

2 -44^5

72045

^■co;i o-:"!!

7W2I

9-434''

4 -4' -47

2 4540

74720

0'C222 00' I

Sl(M)

9*4iSoS

4-4814

2-4595

76S43

00492 0 01 1

.S.'Si

9*5394

4-4979

2 -4650

7^'^995

6-0760 1 o-oio

K^u^

9-5917

4-5 '44

2-4703

81183

6-1026 i O-OIO

K'M'J

9 -"437

4-5307

2-4757

8340S

6-1201 ' o-oio

SS.ic

«>'6.j54

4 •540s

2-4810

S506S

0-1553 o-oio

'X>25

(>740S

4-5029

2-4863

i>79t>4

6-iSi4 ; o-oio

t;.'Ifl

<)7()S<)

4-57S9

2-4015

0029S

6-2074 o-oic

«M»»«)

9-S4SW

4-5947

2 -4966

92668

(>'2^^2 ' 0-OIC

<)<"t'4

()-Scj«)5

4-0 04

2-5018

95075

6-2588 ' 0-010

«)S«)|

tr«M99

4-O20I

2-5068

97519

6-2843 i 0-OIC

lIXMM)

I •()

4-6416

2-51 19

lOOOOO

6*3096 001

NoiK. This tabic admits ol finding the fuurth aiid tifth powers o\ num

1

^^1

1

1

1

^H

■

^^^^^^H

■

^^^^^H

^^^^^^ 171 ^M

Hydraulic Machines :^Reiurn of Motivt Power. ^|

U«iuM<i fro™ Morin'i eniwrimtnls.

I^n

&f

u/ Mulivi

y;.;l<ltd

ri^d^

n>^'

\ ..rte pump

■5 '6

Fi>e £«^»/i.

1 lie enpae

■«33

■S7*

■9M

1 hincie wheel . \

■36

Tjlo. ....

■6.S

■8S7

■59

LtlL-^tU

'452

■910

I'luh wlicci

75

!;«ry ....

■300

■91a

Wmi l«mp . {

■640

Maud ....
Ferrir ....

■210

■930
■900

<?^a-y.

Drainagt Piimfs.

Stou pump

■*3

Deniiol

■690

■930

Uclere . .

■J07

Uelpcch

■too
■S'3

■9J6
■940

Cm/VW^

Millus .'.'.'.

■Soa

VpJ^id ; :

70
■190

Suff/y Pump!.
At Ivry (fccJer alone) .

■ajQ

UmfKOt . . 'i

■300

At Ivry (three pumps) .

■5JO

<.if«d

■jOO

At Si. Ouen

■696

\ citidl helix .

■19

At Dsbon (Farcot)
Solid pi&ion pumps

■651
■900

fKibr Xami.

Monle«Ifier . /

■80

VsKiJe's fire-engine .

■50

'->ligt,]r . .

■43

;55

Gniy'$ OBCillaling .

■45

iJirtige's babDCe

lltlJor .

not used

l<»eleMl .

■4S

riclKh .

771

Hydrasdie Contrivances.

(B; Ihe Author.)

Cotlfcicni

C«fl!«o(

(orpDwtr

forpowB

JWing . . .

075

Single choiQ nf pots .

OSS

o-;a

Double chain «( pots .

0-60

^■Dd (lndi^l

070

5meleM6t (Indi^l .

070

Hmn ISmiib Indin) .

070

Double Mi5t (I tidi«n).

0-60

HJBcHn xxl Inickcl

080

ComoioD panip .

O-TO

n»i>h IS. iDdi^) .

o'So

Lift and (OTCf.pump . o-&>

t^. .

^

^^^^^^^■1

172

MISCEU^HSOPS TABLES ■

Ma

-^

Feet - D-OIS -GuDUi't duiu.
Feel X 0-00019 -Milei.
SciiiMefect . 0-m -Square yards.
Squi>rcrecl - O-OUOOSS -^hcta.
Cubic feel « 8-23 "CUoijs.
Cubic feel ■ O'TTS *Bu<Ach.
Cubic leet >• 0-037 -Cnlnc jmcdi.

„ of Ifa .a. If

, KAIHTAU.

Feet of down

ponrx 193600- -cubic fe« pet

«ia«ieMD«,

;l of downpour m 302-B =

J will irrigate 176 a^re^a'ji-.i
20O acres pet cub c fxi pei -. 1
will supply 47, jSo inVi u >"
colU-ctiiis; 1 fuot in Jcplh yearly | duty of 10 gilluns di h f. \^
■S8j3 cubic feet pel sCT.jnJihi'.u
\ out Ilie year.

IS per s

cond.

■z gallons per 1

e thousands of gallons pei houi.

■e thousands of gallons per day.

6-Si2

and weight C9'32 Ibt.
1 aaii weighs 10 \hi.

11 '2 gjid weighs I cwt.

!31 and weighs 1 Ion.

-00.11) and weighs '0361 Ibl.

437'5 grains^
H fluid drams, t6 minioti,
s S Quid dums.
c^ S319'G4 miDims of wnter.
i - TOOOO gra. of ?rater.
h, Anrir. - 7000 giains - 7680 minims of waler.
All comparisons between measures of capacity aod thOK of wdght an
de with distilled watei U. a maximum density, at a specific gntnly of 1 ;
, » coDmetdal mcatore, the vessel 'u at a lemperatuie oC^H" Fihr.

35-0f3
1 cubic inch
laid etDct weight

l*oifdupoU ounce mi
it. Trojr - 6T60 giains
Sllon cTGSOOin

\

PRESS U BE 0

had of water in feet

isof<

JHF =

n Us. pa square foot

HORSB- POWER.

' water laised 1 fool in t mini:
rater nised 1 fool in 1 hour.
SQxfallinfeet.

10 square milM collectin]

g 12" yearly gives 1 HP for
:h fool of fall.

Koi pumping engines of the best class, allow HF<
■quintity niwd in cubic feet per second, H-> height i

'143 QQ where

The gcDcrat fonnuU rcfencd to in the text il

irtcre n^the pull on the rope in pounds,

T-thediiplacement of tbe barge in tons,
K>thc velocity through ibe water,

t *a coefficient varying with the fonii of the biigc, from
■109 to -369.

g^^^^BH

in MJSCEUJiyEovs tables ^H

Constantt^laiour.

■

(Hnai-J

^

URTHWOEE.

Dapa(>Ub«ni.

S«I

Eiovaticg only .... percob.)nid

-050 -K»

„ in rock reqmriiig bhwiag ., „

'■

Lwta Han

Thiowines feet high, or Gtru^ [rack* „

■«*S -OiS

Filling barrows . . , „ „

"CMS t»S» -'

inKdi- dktince . . .,■-■.

^ -CJO .-

Filling at back of mill . ■ .. „

■04! -ojs «iS

Rammiof; euth in frincb layen ■ „ ,,

^ JH

,. la-iDch . . ,. ^

■

Levelling eaUh frnn bunxr-taei^ i

-,- ^ ■

«iihoaltbrowi>e. . . ) - "

..;■

Lnclling and trimintne slopes . - pel t^ Jtti

Tuif 4 incbei tbick, cnlting utdi

^1

wackingoni, . . . i " "

^ ^

■065

Days of drirer. hone, .ndcwt. (SeeaLo

CMtaee Tabic)

«»»«*(•

•a» to ttts

N.a— The wliol tnaspon of euth is cqaal

to IS tMMs the Ed

(hnes wba hem*^^

<ara.«anploj^

^H

DijioTuIndimCoolk.

^H

%Bi On-d ^^1

Ewa«line do»a to 9 feet, anying to as ydi to a

basket auA .If (untiiig up to G b., pel cob. pid

1-35 sto ^H

Evcnaneedownui i5bci . . .. »

>«<> *?i ^H

AJJ for each J to moK of •lepA « Mehi oT

^^1

>-« p««Ur>rf

-^s ^H

AND DATA.

Constants of Labour.

(Hunt.)

Bxprtsstd in term! e/a day's taimtr of lO houn.

One Biickliycr'* Labinucr.

1
MiiiDg eoDcretCi wheeling xnd throwiog trota ■ stage, per cub. yaid

Mixine mortar witb a i^hovd ., >,

A two-hone puK-mill idUcs IJ cubic ysHs of inortEC in . • I

Picking up and slacking bricks without moving . . p;r i.ooo

„ ,. if handed to him „

Sdwting bricks fix fucings ..... „

Taking down old brickworit in monar, cleaning and slnck-
ing pec cub. yaid

One Bricklayer uid Labourer.

a moitar to walls, exclusive of face traik, pet ci

I, in c«m«Qt

„ in mortat to covering arehes
fatil% Aat joint in mortar and taking out mortal joints pi
ifalttng flat joint in cement and raking out ccmenl joints.
ating luck in cement and lakiog out cemcDl joints
~ Ig with (lock bricks on edge in mortar .

id jointing ID

One Bricklaj-er onl; .

Istklng each fair (ace lo brickwork and p<Mnting . . per a fd.
bckiog each fair (ace in malms or bdng of tupcrior b'icks
per*, yd.
g each fair face in malnu, eircniu lo tempbrie „

mSCELLA.VEOVS TABLES

Conitanls of Labcur — (continued).

(Hum.)

masons' work.

Days of a Labourer.
Rubble stdcc. — Filling batrowi . >

,, RcmOTiag aj yards and letuini

,, UnlcAding tnnows .

1, Taking down old niBsonty in o

cleaning and slacking
Breaking slone to ij" ordinary limeslone
,, granite en very hanil slone

Spieading the ^mc for metalling 3'' deep

Days of a Mason and Labooret.

Kubble masonry, dry in foundalioiu . . . p«r nilric ]>ud '

Ashlar masonry, ij" (hick and in IZ

rubble wilh chisel-drafted margins .

Cubed stone hoisted and set in roortir .

Dijs of R Mason only.
Add to nibble masoniy for each fair face
,1 „ if hammer dressed

„ „ if carved .

SqtuiriiQ 1" flags for paving . . .

"4'

Days of a Mason on aionB of vj

ir axing, per square yard

■J70
■S40

■540

■900 I-39S

-67s 1-080

lojs i-STS

i-Soo STOO ♦■pej

AND DATA.

CmsUoits of Labour — (continued).

^^V Constants

^^k MVIOSS', PLASIBREBS', SLATKBs', AMD rAINTEBS' WORK.

^ Daf a of a Pavior end Labourer.

Couned pilcher paving, 6'', in gravel, &" deep . per squate yard

Add Tor grouting Bod setting in roorlai . . ,, „

Days ot a Slate-mnson.

Planing slate slabs pet square yard

~ "ihing slabs with Tciy fine sand ... ,, „

ring oD.nnder side of lUting ... „ „

Da.ys of a Slater and Labourer.

per iquaie

Days of B Lsbourci.

per cubic yard 003a

Dayi of a Plaslcrei and Labourer.

setting or floating

il)i double lit tatbx ....

Kendcring with cement and sand .
Rough casting In line and fine giatrel

Lime wbiliog

Whiting and site, two eoati, eic. tcounng
Oiluuring, done 01 buS, two cosu . , .

Days of a Painter ot Gluier.
rrxiiting. sifipping, and painting, 1st coat . . f

i>nd or following coats, each
I uriing "rilh Stockholm tar, iil eont .

Sub tqiutei, each side, i coatt

pel square yard o'ojo

^^^^B^I^B

1

«K MISCXLLANEOUS TABLES

d

1

CAinsnu- vraKK.

■

^

Smi^. Pncorrn paiqHRbU

Ad^ fc«ch, tla. Indi

£Dgiiih<»k,mk ,

Foe «!»■«« ««i« *M Iwo-tLirfi.

Eton of a CuptiUa.

0-oto 1

W«Aiae fir iDtD Bft.li. [»&<», ioiMs, .ha

ndal6>q.i>cfaa^«ti« . . . p« «l«c foot
rote 36 Ki- ». o^rf9i —a- ««. <»«6". ora

Si

Wnking Sr into K-u^b frames u naked Soun
=.., 16- H- "- ...

W .':l..r^ r.T' ;r.:j ^r-iises, section 15'' ind O'

invu^ht iwo iijes under 16"
,. itA->^^b; 1:1 tound undei 16'

per square foot

AND DATA,

Cartage Table.
(By J. H. E. Hui.)

■

C«tof

Co™^„f«oo..o,

U.P

Bcw.

ei cwi. ,

^

..™,.

l'.M;:S

■063^

■IS6

■"49

'39

■las

■08,

■196

.as

-.67

" 1

■25

■335

■2

■Its

■3' 3

■294

■25

■417

■39J

370

■333

■6»S

■J88

IS"

-i

■J33

'5

■S33

•784
i^i76 1

■667

It

(■67

I 57 >

IJ3

■ ■»8 1

>; ,. «

1 ll-o

=■5

2>35 3

22

20

1 1

CoDMnU

Of .0= cubic l«l

tnp

1

8

S

9

10

la

IB

le

■ 1 16

■Tfii

■63^

\ \l

■0S3

1-389
■ ■667

I ■041

■926

-833

■694

s;

■S2I

•62s

■ris

3 '083

rjSg

I -25

f042

2.0S3

1-852

;:s?

(■a42

277«

1-oSi

1-01

Vis*.

2 ■112

2 081

4-lt.7

.4 Ij

■667
■3

'3'333

S;333

7-407
8'B«9

..«,

S-SS*'
6-667

4-444

5 333

4-167
5-

■ * ' '

16667

■ 15

IIUl

lo-

6-667

-"

D&ily discharge method . . ,

I, See ttlsa JDcluded with Humpbrcf .
lenoa and Appold. Module . .

icttoa and Stevenson. Observations on the Tay
Ucy, Velocities in pipes . . ,

„ ■Walet'level gauge
., See alio included nith Buio.
tabuitKni. Gnvily foimuia , .

„ General reference

„ Ixieki, baiins, &c., formutz .

„ Velocilj forniula

dwui and Whistler. Surface velocity ganging
elnan and Thomson. Thickness of wa[ei-pipe*
in and D'Aicy. Geneid reference .

„ Four categories of co-efGcienti •

„ Maximum velocity formula

t Velocities in cbanseU .

Velocities in large channels
Reiulli of cipeiimcnts on alui
Sluice -gauging . .

Tube cunent-meler
Telling lube currenl-melei
Observations on rigoles
Deductions from obseivationi
Old velocity forrnuta .
aen, TraiuUitoo of D'Aubuisson'a
DM^ OlMFrvationi on supptessed ci
iMO. Bubble cuirent-meler
iM. Orifices in compound planes
liai. Hook level'gauge
nlngi. Tnchomcler . .

Iffi INDEX.

ttnmCon. Piiton witcr-meter .

Hurges. Flood disduige fbnniiU .

Bytnc Dual togirithiiu
„ Weight ormatenil, Spon's IKcL

Carroll. Module

Cutd. OrificFS wilb i
„ Overalls and weirs

Cheif. Velocity rormula .

Crostej. Trough woler-metiis

CuDDingham. Deduclions on verticalic veli
„ Conditions or obsetYatioQ

„ Moitet of observation

„ Surface convexitf

„ Verticalic velocity ,

„ Transvcrsalic velocity .

„ Mean velodlji

„ Remarks on hydraulic roitnulx

Delocre. I^ofty dam of polygonal tiaee
De Ptony. Old velodty formula
De^rEiB. Observations on Great Nevka
Dickens. Flood waterway
Downing. See also fonnula of d'AubuiiSon
Dubnat. Obstniciions lo velocity

,, Old velocity fonnuU

Pupuil. Mean velodly IbnnulB .

Ellet. Old velocity fonnula .

Eyielwcin. Old velocity bnnuta •

Fowler. Forrnula employed ,

Francis. Weir formula

„ Gauging weirs and canal*
Frost. Piston water-meter , ,

Gttlaffe. Piston water-meler
Ganguillet and Kntlcr. See Kutter.
Girard. Old velocity fbrmuU .
Graeir. Contents of teservoits
GrandL Bfnt current -meter .
Gunter. Ilie 6G-reel chain
Hart. Retaining walls , . .

„ Cartage table . . <

Hawluley. Ovoid culvert section •
lliggin and Higginson. Module
Humphreys land Abbot). See also Abbot

Veloc

G«nenJ foimulie

.□ very taiEe nver b*dt

INDEX.

Ilnmpbteys. ^tade of gaugii^ the MUiiiiippi .

., Gauging ctevasses . . . .

„ Mid-dcp(h Tclociiy, mode of gauging

„ Reference lo Iheiv obaennitions

llunL Constanu of labour in daj^i work
Jicksan. References lo special subjecu.

„ RedcleTTniaitioii of co-elfidcnti of roughness

„ Re-innngement of Telocity co-effidenci .

„ Ovoid (pestop) cuWen Kction fai- bigb DushiDg

Spring cunenl-mder

lirge waler-pipes of minimuin safe Ihickaeu
Eqnilibrinm module . . . .

. PUion wster-mcief . , . ,

X ind Gangnitlel. Generil reference .

„ Ten Mtcgories of eo-elfieienU .

„ Velocity formula

„ The tame in form uicd by JdcIhod

Scvri^e form tx Daniig .
Abioiplion of ilonewaie pipes
Strength of slanewait: pipes . >

Old wloeity formula .
le and Pin. Sluices

„ Orilices with mouthpieces
d Poncelet. Rectangular orifices

„ Attached channel

On water-cushions . . •

pddier. Module ....
iroith. Lofty dam-secljon

Hydraulic machines . .

Hi. Circulai oiilices ; also with mouthpiece*

odiJ. Ton
CuItc

o Metropoiitan ovoid

Taben
Sec included with Leipinasse.
See included with Lesbros.
Deci 011,1 chaiD of k

Mode of gauginc

Screw CI

. Module

Old vclociiy lonnula
Turbine wnlci-meler
ObservalioDs on unall

Miic. Tables
MiJC. Tables

J.VDSX.

See Balnnan.
Tylor. Fui wMei-roelef
St. Venam. Old velocity formulA .
VeoluiL Mouthpiece of mmii
Wettboch. Fonnula for beodi adopted bj hi
Whisilei. S« Btldwin.
WoUmBiin. Hytlrometrie miU .
VouDg. old velodtjr fmnolK

^^^^^^* Xavemhtr, 1SS2,

W % €atitl0guc 0f goiihs

H ISCLLTJISO ILVSV NKW AND ST,l_VIIillD W0HK3 IN

BNGINEERING, ARCHITECTURE, AGRICULTURE,
_ mTHEMATICS, MECHANICS, SCIENCE, ETC.

2ROSBY LOGKWOOD & CO..

7, STATIONERS'-HALL COL.RT, LUDGATE HILL, E.G.

ENGINEERING. SURVEYING. ETC.

Humberts New Work on Water-SuppTy.

A COMPREHENSIVE TKEATISEon the WATEK-SUPPLV

of CITIES and TOWNS. By William Humbeh, A.-M. Inst.

C.E., and M. Insl. M.E. Illustialed with 50 Double Plnles,

t Single Ptale, Coloured FioniisjiiccCi and upwards of 250 Wood-

— md containing 400 pages of Teil. Imp. 410, 6/. bi. cJeganlly

Mbstuitiiill}' hair-bouniT in morocco.

LUI </ CiMlnli I—

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rf WUel.—

I Cantabiiiy, :

uodK, Hijibi. LinibcUi,

Mil. Rawvoin.— 'iiitf'TbtPuost ,_. . _,.. .. .

- — " - — - ' •■ ■ ■ 0. Dublin, uc

■t tyiHma^c uid valoable vork unm water njpp^r iittHctto produud
10 tny otlwr buiffua^ . . . . ATr. rluiDberiwtn-kurhanci^icd kIrm

0( £nElu)i udtniul Iculiio."— £ii/iiuir.

Huntbef^s Great Work on Bridge Construction.

A COMPLETE and PRACTICAL TREATISE on CAST and

WROUGHT-IRON BRIDGE CONSTRUCTION, including

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,E. Third Edition, with 1 1 J Doable PUtd In 1 voli. imp. 4I0,

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D Duf t*ii«ifflT bv did to lisve ctlabEisUnl ttt dwd

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WiLiOAU IIunacB, A..M. :

«V Ihiolile PlUes dnwa u 1 ' ^

n.,«;..!,.„.,CE,.i'.k.s..4^. .■ i.r

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pbcawn, CF-. he., and descriptive Lelttrpie;
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HYDRAULIC TABLES, CO-EFFICIENTS, and FORMUL.*

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cdly «■ ex«HltPxly uicfbJ kjid eUboraic compilnti-.-.

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Xiver Engintering.

RIVER BAR.S : Notei on the Causes of their Formnlion, and on
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fydraii/tcs.

HYDRAULIC MANUAL. CansUiing of Wottinj Tables and
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4 WORKS IN ENGINEERING, SURVEYING. 1

Leoelling.

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F.G.S., M. Inst. C.E. Sixth Edilion, Tcty carefully rcroti mlh
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and the Construction of the Brickwork of Tunnels nith theamairat
of labour reqiured for, and the Cost of, the vniions poiliaiu of the
work. By F. W. SiMMS, M. Insu C.E. Third Editioei, Revised
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Steam.

STEAM AND THE STEAM ENGINE, Stationary and Pbtt
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Civil and Hydraulic Engineering.

Cn'H, ENGINEERING. Hy Hesrv Law, M. Inrt. CE.
Including a Treatise on Hydraulic Engineering, by G(
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Gas-L ighting.

COMMON SENSE FOR GAS-USERS: a Catechism cfGw-
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Bridge Construction in Masonry, Timber, & Iron..

EXAMPLES OF BRIDGE AND VIADUCT CONSTRUCT

Worki. By W. Davis Ha-^kou, C.E. Second EdiUo*. wU

theadditionof 554 Estimates, and the Practice of Selling out Woria

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Earthwork.

EARTHWORK TABLES, showing the Conletvts in Odiie VanL
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By D. KifJNKAK Clakk, M.I.C.E. Supplemenfaiiy Volume;
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■ TRAMWAYS: their CONSTRUCTION and WORKING,
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fiit/uer Engineering.

' PIONEER ENGINEERING. A Tteatiie on the Engineering
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fluiunliLe productioD, and ane wiihoul poncBion of vhich dO man tliQuld
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Jffeam Engine.

TEXT-BOOK ON TflE STEAM ENGINE. By T. M.
GOODBVE, M.A., Barrisler-al-Law, Author of "The Principle*
of Medianics,' "The Elemems of Mechanism," &c. Fourth
o. With numerous Ulusinitions. Crown 8vo, bi. doih.

il Steam Userx. Byan EHGlNKEk. 4U1 Edilion. Sewed, &/.
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Wechanical Engineering.

DETAILS OK MACHINERY! Comprbbg Instructions for the
Exectttioo of various Wiwks in Iron, in llie Fiiting-Sliop, Foundry,
uid Boiler- Yard. Arranged expressly for the use of Draughts-
men, Siodcnts, and Korcnen Eni;inecrs, By Fkancis Campin,
C.E. lamo. 2>- W. doib. {JhsI faMiihtJ.

Mechanical Engineeririg.

MECHANICAL ENGINEERING! Comprising Meullnrgy,
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facCHre otthe Steam Engine, &c. By F. Camfin, CE. y. dotb.

Works of Construction.

MATERIALS AND CONSTRUCTION: a Theoretical and
Practical Trcatiw on the Sitaios, Desi|rning, and Erection of
Works of Construciion. Hy F. Campin.CE. iimo. }j. &/. cl bnls.

Iron Bridges. Girders, Roofs, &c.

A TREATISE ON THK APl*LICATION OF IRON

TO THE CONSTRUCTION OF UklDGES, GIRDERS,

^^ ROOFS, AND OTHER WORKS. ByF.CAMPis.C.E. iamo,3/.

6 WORKS IN ENGINEERING^ SURVEYING^ ETC,

Boiler Construction.

THE MECHANICAL ENGINEER'S OFFICE BOOK:
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Manager Ftlmcr's Engme Works, Jarrow. With 29 full-page
litbographk Diagiams. Folio 2Lr. half-bound.

Oblique Arches.

A PRACTICAL TREATISE ON THE CONSTRUCTION of
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OUique Bridges.

A PRACTICAL and THEORETICAL ESSAY on OBLIQUE
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Buck, M.LCE. Thud Edition, icrised by his Son, J. H. Watson
BrcK, M.I.C.E. ; and with the addition of Description to Dia-
grams for Facilitating the Construction of Oblique Bridges, by
W. H. BaUjOW, M.LCE Royal Siro, 12/. doth.
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Gas and Gasworks.

THE CONSTRUCTION OF GASWORKS AND THE
MANUFACTURE AND DISTRIBUTION OF COAL-GAS.
OriiT-nilly written by S. Hughes, C.E. Sixth Edition. Re-wiittcn
and er.'.arg\?d, by W. Richards, C.E. i2mo, 51. doth.

Waterzi'orks for Cities and Towns,

WATERWORKS for tiie SUPPLY of CITIES and TOWNS,
with a De>cTipiion of the Principal Geological Formations of Eng-
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Locomctii't' Engine Drizifi^,

LOCOMOTIVE-LNGINE DRIVING: a Practical Manual for
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Reyn.'LDS. M.S-E. Finh Edition. Comprising A KEY TO THE
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•' Mr. Re\-ri>:.d> has supplied a vxnt, and has supplied it well." — Engineer.

The En^inecr^ Fireman, and £nfn?ie-Boy.

THE MODEL LOCOMOTIVE ENGINEER, FIREMAN,
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S/a/i.^nj/T Enip'ne Driving.

STATI''NAKY"ENGINE DRIVING. A Practical Manual for
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Engine- Drivinc!^ Life.

ENGINE-DRIVING LIFE ; or Stirring Adventures and Inci-
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Continuous Railicay Brakes.

CONTINUOUS RAILWAY BRAKES. A Practical Treatise on
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Tables. By Michael Reynolds. Large Crown Svo. 9^. cloth.

\yusipubiishcd

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CoHStruction of Iron Beams, Pillars, &c.

IRON AND HEAT ; exhibiiiiig tlii: Princliiles conctmed in the

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^ ActknofBoHmlbeSmeliingKurnnce. ItyJ.AKMuuN, U.E. 3/.

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FIRES. niiE-ENGINES. AND FIRE BRIGADES. With
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ment; Remarkt on iuc'Ptooi Buildings, md the Presemuinn of
Life from Fire ; Suumics of the Fire Apptlatii.'es in V.ag\\ib,
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»BrCHA>LC!i !■. T. YoiiNG, C.E. With numennu lUuiOWJoiis,
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■nd PrscticiJ AsiRinoDi]', Bj LiBvr. -Cen . Fbouei, R.E., laie lo-
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partly Rr-wriiten. By CAFTAi.t Chakles Warren, K.E. With
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Tables of Curves.

TABLES OF TANGENTIAL ANCLES and MULTIPLES
Ibr Kliuig out Curvet from 5 to too Radius. By Alexandbk
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" ■ in « cloili ben, waiMcoat-pocket aiie, y- ^■

nneering Ficldwork. M/vwr—.

THE PRACTICE OF ENGINEERING FIELDWORK,
implied u Land and Hydraulic, Hytlrogtaphic, and Suhoiarine
Surveying and I.etelline. Second Edition, revised, with consider-
Blileaddili<m>,Bn(USB|.p1emenl on WATERWORKS. SEWERS,
SEWAGE, ami IRRIGATION. By W. Davis HAsKOl.^ C.E.
IS folding; I'iatos. In I Vol., deniy 8vo, iL 51., d. Iioards.

Tannel Shafts.

filE CON.STRUCTIO.V OF LARGE TUNNEL SHAFTS.
I A tnaiaX ind Thcotci.cd F-siay. By I. H. Wats^.m Huck.
■ h. In«. CE- Resldcot Engineer. Lon^ and Nortli-W«iem
mftdtway. Illiutntied wiili Adding PLUcs. Royal Svn, 121. doth.

S WORKS IX ENCINEERTNG, SURVEYING,

Surv^ Practice.

AID TO SURVEY PRACTICE: for Reference ia S
Levelling, Sttting-mit unl in Route Surrejs uf Tnvellcis by 1.
and ScB. Willi T&Ues, lUaitniiocs, and Reconli. Bjr L~
U'A. jACKsoK. A.-M.I.C.E. AuihorofUydtaolicM

Smtiatfcs." &(:. I.lrgc crown gvo, I2J, W,. doth.
' ■ ■ ■ (« ihe I

Sanitary It ork.

SANITARY WORK IN THE SMALLER TOWNS A!M
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Supply. BvCitAs. Slagg, Assoc Inst. C.E. Crown 5TO,f- -

pii/ti^ UF^tiHifc in tlie wuju of •riiieh he tmu.'— ifcinJifr.

Locoitiotivcs.

LOCOMOTIVE ENGINES, A Rudimentsry Tnaliieoi
priiing an Hi^toricai Sketch and Description uf the I
Engine. By G. D. Dehpsev, CE. Wiih large aiMii
ingof the MooEHK Locomotite, bjt D. Kisnuu Clamc, C^
M.LC.E., Author of "Tramways, thcu Conainictioa and WmI'
&c, &c With numerous Illustrations, iima ji. bd. doth Ix
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Fuels and their Economy.

FUEL, its Combustion and Ecooomy; conHStit
mcnt of "ATreailscon the Combustioa of CooJ ni
of Smoke," By C. W. Williams, A.LC.E. With e
ailditionj on Recent Practice in the Combuitlon aed Ecou.,
Fuel— Cod, Coke, Wood. Peat, Petroleum, && i Inr O. ]
NEAR ClauK, C.E„ M.LCE. Second Edilioo, n"'—' ■<
lus lUustrationi. lamo. 4J. cloth iKuuds.
Jioiild buy lh< book uid vai 11, u cne of ihe intst ronritttndal
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Roads and Streets.

THE CONSTRUCTION OF ROADS AND STREETS. '
Two Parts, L The Art of CoiistniclinE Comi&oD Rooili. '
Henrv Law. C.E. Revised and ConilpTi-fd,
Practice in the Conslniction of Roads v' ~i-^-i
Pavemenls of Stone, Wood, aiid ABphn'i.
C4JIIIK, C.E., M.LC.E. Second EdiL. I.

be at ctuuidenU* lerticc M arefaiieeu, builden, ■«! vi-.

■ PUBLISHED BY CROSBY I.OCKWOOD & CO. 9

Sizuing Machine {The).

SEWING MACHINERV; being a Practical Manual of ihe
hewing ^lacliine, cumpiuing its Hutory uiil UeiailE qE ils Con-
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ing Machines. B)' J. W. UxfjUtiAKT, Autlior of "Eletlro
riaiin^: a tnctical Manual;" "Electric Liglil ; iis Producuon
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Field-Book /or Engineers.

THE ENGINEERS, MINING SURVEYOR'S, and CON-
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^^ CoDsuDng of a Series of Tat>les, with Kules, Explanations of
^M^ Syslenu, and Useof TheodoliterorTraverseMurveyingandPlotdng
^h Ihe Work with minute accuracy by means of Straight Edge and Set
^^B Squaieonly; Levelling with the Theodolite, Casting out and Re-
^^B ducing Levels to Datum, and Plotting Sections in the ordinaiy
^^^L mannei; Setting out Cmrei with the Tbeuilolite by Tangential
^^K Angles 4nd Miniipies with Right and Left-hand Rcadingi of the
^^^B InstnuncDI; Setting out Curves without TlieoUotite on the System
^^V of Tangential Angles by Sets ol Tangents and OtT^ts; and Earth-
^^^ work Tables to So feet deep, calculated for eveiy 6 inches in depth.
With DOmerous Woodcuts. 4th Edition, enlarged. Cr. Svo. izi. cloth.

"ComollAit, from LU puruEMlin AD. _. .

Earthwork, Afeasuremeft/ and Calcu!-a,tioit of.

A MANUAL 00 EARTHWORK. By Alex. J. S. Gkaham,

C. £., Resident Engineer, Forest of Dean Cential liaiiway. With

numerous Diognuns. tSmo, 21, bJ. cloth,

" Aa a nally hsudy tvoii lor rvTercAce, we luow nf n{» work equal 10 It ; and Iha

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work will and a frtat auMmpi uT practioi] infvuwtioii very atinuratily vran^, and

-._L._ * _ ._.. _ . ._ ... -L ._-_..._ m,^ u f^, |]ig mors aaacl caltulatigu*

Rawing for Engineers, &c.

I THE WORKMAN'S MANUAL OK ENGINEERING
I DRAWING. Ely John Maxtun, Insiiuctor in Engineering
I prftwing. Royal Naval College, Greenwich, foimerly of R. S. N. A,,

Ih Kcnsintpon. Fourth Edition, caiefully revised. Withopwardl
of 300 Fifties and Diagrams, llmo, ctoth. sliongty bound, 4;.

■■' iTit idunild be kepi Tor reference ineverydrawina omcia." — Enpujtrini^

liable fur Itfachert of enj^Miecnng drawing."— ^i/ffivDc/ Bi^^umt.

Vealis Dictionary of Terms.

A DICTIONARY of TERMS used tn ARCHITECTURE,
BUILDING, ENGINEERING, MINING, METALLURGY.
ARCll.«OLOGY, the FINE ARTS, 4c. By John Weals.
Fifth Kdilioo. revised by Rubkrt Hiaht. F.R.S., Keeper of Mining
ReeordiV Editor ol " Urc's Dictionary of Aru." iimo, (u. t\. bds.
"^M teat uiall R£hnol(tgi<al diciuiiaTY 10 Ihebn^i^re.'' — -Airhilrcl.

' ' ..... racier cjo only be judged of after
. .^. ._j ^^

MINING, METALLURGY, ETC.
Coal and Iron.

THE COAL AND IRON INDUSTRIES OF THE DNrTED
KINGDOM : inmpcisiiigaDesciiption olthe Coil Fidili, nd

the I'rindpil Seams nfCoa], w[lh return- ur' then' F'rorJuoc anl i
I/iitribiiliun, aiiil Analysesof Spe.'. n AccnuBl

of I lie occurrence of Iron Ores v i-lyieiol

each V'atiety ; and ■ Hislory of il" ' <*ii> IriKl

ManuFnct lire since the year 1740, ■. „,< uiIf>

liuced in the BInil FumacM lot ii.- 1 . .. ;.iuuiei«i«il.

By RiCiiAUD Meaue, Assistam Kecjn;!- ..( Mmi.ij; KctutiU. Wtfli
Map! or the Cob! Fields mid Iraostane DcpusJts of (b« UiriCol
Kint^dom. Svo., £1 &i. doth. [Jml fmt&Jui.

Afetalliferous Minerals and Mining.
. ^ m&e:

Second Edition, revised . '
■od in[cUittU|r."— itrtfltiv jninaL

S/ale and Slale Quarrying.

A TREAT IS K (t.N i^i.\V\: A^!
SdenliGc, I'l .
MininC Er^:
Plates. Si-i . :

.^LATE ,:iL'ABRVII«:.
. F.G,S.,
FdUbv

Metallurgy of lion.

A TREATISE ON THE METAU.URGV OF IRON. _
taining Oullines of the History of Iron Manufactarc, Uetludtrf
Assay, ond AnalyKs of lion Ores, I'loccoet of Msnob
Iron and Steel, &c Ry H. llAUEtiUAK, F.G.S. Y\tA
Revised and giently Enlafj^d, Willi Niuueroo* lllui__.. _. .
I2niu. 5J. &/.. cloth boanlf,. \3mit fmliMtd.

Manual of Mining Tools.

MINING TOOLS. For the ntc of Mbie Uanaeas, AMt%
Mining Students, &c By \\'ii Lt*u Mim<iA\s, VcTimg ofTot,
lamo. y. With an AlUs of PIbIck, cuutainine ^iS llkutnUoU-
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Mining, Sitrvcyifi'^ -■•"'' ' "'""">

THE MINERAL S' COM-

PLETE Gl'IDE. c... ! Mining

Survcyinc, with new ■ ' ' '

proved Iiu.lniD>cnls :
uf Laying uul aud \
Mineiii Properties, 1
EDeineei. With four V
",• The above, hotinil "
Tiicc 7t. 64. doUu

Coal and Coal Mining.

COAL AND COAL MINING; » RnaimenUiy TraiUse on. Bjr
Wahino-mjn W. Smyth, M.A., F.R.S., &c.. Chief Inspe«o(
of the Mines of the Crown. Fifth edition, revised and coirected.
I into, with numennij lUustiatioiis, 4J. cloth boards.
•■ Every pwnpn of iKc vglutne ' . - . . -l _ j

Underground Pumping Machinery.

MINK DRAINAGE ; being a Complete and Practical Treati&e
I so Direct-Acting Undetground Steam Pumping Machinery, with

^^^ ft Oesctiptioo of a large nmnber of the bcsl kauwn Engine^ their
^^ Gcnenl UCilitr and the Special Sphere of (heir Action, the Mode
^M of their Application, and their meiits compared with otlier fomu of
t^ Fnniping Machinery. B^Stephen MiCkell, Joint-Authorof "The

ConHshSystemotMineDrainaEe." 8vo, i5(.clot!i.

NAVAL ARCHITECTURE, NAVIGATION, ETC.
Pocket Book for Naval Architects&S' Shipbuilders.

THE NAVAL ARCHITECT'S AND SHIl'BUILDER'S
POCKET BOOK OF FORMULAE. RULES, AND TABLES
AND MARINE ENGINEER'S AND SURVEYOR'S IIANDV
BOOK OF REFERENCE. By Clement Mackrow, M. Inst.
N. A., Kavnl Draughtsman. Second Edilion, leviseil. With
~ aerous Diagrams. Fcap., izj. bd., strongly bound in leather.
Id bciucd by all wha UA eD£jt£«i in tbe coDSErucuon or dai^ of vcalck.''

Grantham s Iron Ship- Building.

ON IKON SHIPBUILDING; with Practical Example* »nd
Details. Fifth Edition. Imp. 410, boards, enlarged from 24 to 40
^k Plates (li quite new), indoding the latest Examples. Together

^B frith xepaiate Text, also consideizbl; enla^ied, lamo, cloth limp,
■u By John Grantham. M.Inst. C.E., &c a/, w. cnmpleie.
B^'Mr, Cnmham'i mrk .lofgreil inlcnU. Il »iLI, arctrr coafidcoL, cocgnuud in

TtiXT. (he wurk «nll 'aim ijic mi-book on wRicli ih« ciE4min>IuiD tn 'mm ^i|F-buildi^
of tandjcUlB lor pTovotiCfQ is Ibfl dockynrda will ba ivAUll]r b4HiL" — Eigvtttriiv-

Pocket-Book f of Marine Engineers.

A POCKET-BOOK OF USEFUL TABLES AND FOR-
I MUL<E FOR MARINE ENGINEERS. By Fkank Proctor.
VA.1.N.A. Third Edition. RoyaJ jzmo, leather, gill ed^s. 4/.
\f Biiybhiiif Kqaired b| ■ aani eutfuwer appon to hxi9 bc«a tn-

Ligkt-Houses.

EUROPEAN LIGHT-HOUSE SYSTEMS; brine i Report d|
a Tonr of Inapertkm made in 1873. Bjf Majcu GcCKfil HT
Elliot. Corps of Engitieers, U.S.A. lllustntcd bji Jt £■
gniviiigs and 31 Woodcuts in the Tou. Bvo, iu. doth.

Surveying {Land and Marine).

LAND AND MARINE SURVEVIKG. In Refcrenoe to ik
Prepamlioii of Plans (or Roadi »nd Roilwajrs, Csmli, R"*^^^
Towni' Walei Supplies, Docki uid Harboura ; wnb Dctcnp^
uid Use of Survefuig InsmunenU. B; W. Davis Hajsolu C-E
With r4 folding PiMM, uid munerous Woodcuts. Svo. lU.UdiA
" A nuul lucful uid wcU unngrd book fa chc mill bT > «i»leiiL '-~BmUir.
ohii upiri u> btconw clou ud upcn •umr«»."— «m<V ?>»r^M/.

STORMS : their Naluir, Classifieotioii, and Laws, with
Means of Predicting ihem \rf their Enbodimails. the C
By WI1.LIAM Blasius. Crown 8vo, lar. W. cloth boards.

Rudimentary Navigation,

THE SAILOR'S SEA-BOOK : a Rudimentary TreWije (» S«

eslion. By James GkeenWuOd, ii.A. New and ealaiged eiilif
By W. U. RossER. I2mo, 31. cloth boards.

Matliematical and Nautical Tables.

MATHEMATICAL TABLES, fbr Trigonomelrical, Astrawmii
and Nautical Calculations ; to which is prefixed a TioriiM
Lof^rithmi. By Hbnkv Law, C.E. Together with a Sena
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New Edition, i2mo, 4/. doth boards.

Navigation {^Practical'), with Tables.

PRACTICAL NAVIGATION : consiiling of the SaOor'*
Boole, by J.*MEs Grbeswuod and W. H. Russeh ; k
nitii the requisite Mathemilical and Nautical Tallies for the
ing of Ibe Problems. By Henrv Law, C.E., and Piwfc
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WEALE'S RUDIMENTARY SERIES.

The fMcnuing beoks iit Navai Arthitecturt, etc., art fHtliihid i» t

abovt serif!.

MASTING, MAST-MAKING, AND RIGGING OF Sim's.

RoitERT Kipping, N. A. Fourteenth Ed iuou. iiino,u. W,d

SAILS AND SAII^MAKING. Tenth Editi,..i., r.-I:.ri;«l.

RoHEKT KirriNG, N.A. llluslrated. isn. - - ■> - - -<.
NAVAL ARCHITECTURE. By James Ti ■

with P1nic5 and Diaerams. lamo, 4/. clu!
MARINE ENGINES, AND STEAM VI
Mukrav, C.E. Seventh Edition, ixmo, .

PUBLISHED By CROSBY LOCKWOOD & CO.

ARCHITECTURE, BUILDING, ETC.
Constnution.

1 ^*

THE SCIENCE of BUILDING s An ElementoiT Treatise on
the Principles of Consiruction. By E. Wvndham Tabn, M.A.,
Arebitecl. With ;8 Wood Engiavings. Second Kdition, revised nnd
Millrgeil, incladiog an entirely new chapter on Ihe Nature of
'Ughtninj, and the Means of Protect tng Buildings from Lis Violence,
Crovm 8v(i, ii. bd. cloih.

^ . ■ ^ book, which *c t&onflr Tfconm«ad Lo all tbtdaiti.''^£ifilUrr,

fhcuLd be without ihu luuid-boolc" — A rskHtct.

Civil and Ecclesiastical Building.

A BOOK ON BUILDING, CIVIL AND ECCLESIASTICAL,

liicludine CrtuRCK Rkstobation. By Sit Edmund Beckett,
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Watches »nd Bells," hti. iimo, 51. cloth boards.

" We amnrnd ilic Innli to the thuughlful cooiidinUDD ol lU wba an micntted
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Villa Architecture.

A H.ANDY BOOK of VILLA ARCHITECTURE; being.
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IDetiiled SMcihcatiooi and Estimales, By C, Wickes, Architect,
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Useful Text-Book for Architects.

THE ARCHITECT'S GUIDE : Being a Texl-book of Useful

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The Young Architect's Book.

HINTS TO YOUNG ARCHITECTS. By G. Wigmtwick.
" m Edition. By C. II. Ci^tllaiimk. iimu, clolh, 41.

K toiind «n AcquiiiliOD to pupili, uid a cftpy ought to bo considered at
a pBrduAC u 1 boa of iBstrumvttu."'-,^ txktitct,

vingfor Builders and Studetits.

■ practical rules on drawing for the OPERATIVE
BUILDER and YOUNG STUDENT in ARCIIITECTUKE.
y Gbokc.i Pvnb. With 14 Plates, 410, 71. 61/. boaidfc

* and Factory Chimneys.

^OILEK AND FACTORY CHIMNEYS ; their Draught -power
kI Stability, with achapter on Lighining Condactors. By RoBEitt
t, C.E, CrawD Bvo, 31. td. doth.

14 WORKS IN ARCHITECTURE, BUILDING. ETC.,

Taylor and Cresy's Rome.

THE ARCHITECTL"i(AL AN'TIQUITIES OF ROME
the late G. L. Tavi > - -

New Edition, Edit"
o( (heUtcG. L. 1 ■
onaUn!^ Kale, mi i
inisu, IhepiindpklN)

uul JetaiL Laije fi'!ii., i.itli Ijo I'l.ilr.. iL.iK-liijund, >'- 3*
*** Orfginallj puUisheil in iwo volumes, (olio, at l&L iMl

Vitnnnui Architecture.

THE ARCHITECTURE OF MARCUS \1TRDVIII
ruU.IO. Ti«ralnted by JnsKm Gwilt. F.S.A., F.R.A.f

NunienjUK Ptiles. I3DU), duQi lim]), y.

Ancient ArchUuture.

RUDIMENTARY ARCHITECTURE tANCIEST)i a
priiing VTTRUVIUS, tnuuJdted by Josbpm Gwilt. F.S,
itc., wiih 33 fine plales ; and GRECIAN ARCniTECTt'S
By the EutL or Abebdkek ; izma, 6f., hdf-baund.

•,* r/uoiiytdHuna/VITKUVIUSfrantntUataitmltfatifiiim.

Modem Arckitecture.

RUDIMENTARY ARCHITECTURE (VtODERNi
prLsine THE OKDERS OF ARCHITECTURE. b»
LEnns. Esq. ; The STYLES of ARCHITECTUKEofVARIul
COUNTRIES, By T, Talbot Borv ; and The PRINOPL"
of DESIGN in ARCHITECTURE. By E. L. C*K»
NumeroDi illuscrations, ixtno, &i. balf-bouiid.

Civil Architecture.

A TREATISE on THE DECORATIVE PART of CIl
ARCHITECTURE. By Sir William Chambbm, F.II
With Uluilralioiw, Noles. ind an Examination of GrecUa A«
lecture. By JosBPH GwiLT. F.S.A. Revised and edited by
H. LsEDS. 66 PUles, 410, iii. doth.

House Painting.

HOUSE PAINTING, GRAINING, MARBUNO, A

SIGN WRITING ! a Practical Manual oC With

Plates of Woods and Marbles, nnd nearly 150 Wood
By Ellis A. Davidson. Third Edition, Rdrisrd, tim
Plumbing.

PLUMBING ; aText-lxxik to the Pnrtice of the Art or CnA of
Plumber. With chapters upon House- dnina^, crabodyitv;
latest Improvemctll*. By W, P. Buchan, hnnilary Eiicini
Fourth Edition, Revised uul much enlarged, with 300 iIlasifBiit
dmo. +1. cloth. [Jul/ fHitiii

joints used in Building, Enginerring. &£.

THE JOINTS MADE AND USED BY BUIU " '
constiuction of varimii kinds of Engineering and
works, with cspccinl lEfcrence 10 those trroiuht *
erecting and liuiahing KabiuUeSmctum. nrll
Architect, Willi 160 lUiulralions. lamo, y. id..

PUBLISHED BV CROSBY LOCKWOOD & CO. 15

Wa'ia'6o0k of Specifications.

' THE HANDBOOK OF SPECIFICATIONS; or. Practical

Gniite ID the Aichitect, EngincEr, Surveyor, antl Kiiilder, in drawiiig

I no Sprcifiutluiu ukI Contraen for Wurlu >d<I Cfmstnictions.

I iDuxlnlEil by )' raced enU of Buildings actually eiecuted bgrenuaent

Aichitecu and Enj^niwra. By Profcssoi I'uomas L. Dnr4At.o-

' :ilinn, in One large volume, 8vo, wilh

npwudi of 1000 pages of lexl, and 33 riatci, clolb, U. vu. bd.

*!■ Uii* work fartr.fa,ir ApcdAcjationa of eiecuwd vorka uc fiLveit. . . . DwiaU>

wa'< Huabeok ef SpeoAcmoiH muu be bausht b; all aicbilem."— £aiM>r.

Specifications for Practical ArchitecUtre.

SrKClFICATIONS FOR PRACTICAL ARCHITECTURE:
A Guide to the Archllect, Engineer, Surveyor, and Builder ; with
I «n Eteajr cm ibe Slnictnte and Science of Modem Buildings Bj
C FKtnsxKlE RciCiKRS, Architect Srn, l^. cloth.
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*. ImpniUucBl ihmibove.— £i.'nMf /iiunr/'nirtiiA

'gning. Measuring, and Valuing.

'HE STUDENTS GUIDE to Uie PRACTICE of MEA-
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■» for the VaJuation of Labonr and Maieiia]i in the re-
1 Slater, Cirpenlcr and
4c With 43 Plates aod Wood-
ARD DciBsOK, Architect. New
and Construc-

hted I^Edi

OriginaUy editi
Edition, re-wrillen, with Addili
tlon, and lueful Tablet for facilitating Calculations
. ments. By E. Wvnduam Takh, M.A., 8vo, loi. bd. cloth.
■"■ ■■' ■'■ ■ ■proiBBeofiHtitlc-pMe. Mr.Tim'i jAiiliMoaiid revwonihave
E uriAilnen of the vork.'''.-£«f "■'r^''*^-

Uotis Pocket Estimator.

POCKET ESTIMATOR FOR THE BUILDING

DESi bcitig an easy method of estimating the various parti

■ Building coIlecU'rely, more eipeciatly applied to Carpenteis*

' * leis' work. By A. C. Braton. ^cond Edition,

tl-pocket sue. ir. &/.

•n'sBuilder^ and Surveyors' Technical Guide.

IE POCKET TECHNICAL GUIDE AND MEASURER

RBUILDERS AND SURVEYORS: contuninga Complete

^nation o( the Tenns used in Building Cunsinictiat;, Mono-

. .da tot Kelerence, Tedmicol LHredions for Measuring Work in

It tire BuJding Trades, &c By A. C. BKATOIt. U. dd.

: House-Owner's Estimator.

IIOUSE-OWNER'S ESTIMATOR; or, VHiat wfl! il
to Build, Alter, or Repair? A rrice-Book for Unprofes-
I Pcuule, Aichiteelural aurvpyoni, Builder^ && By tile late
UtiM D. SiMOM, Edite.1 by F. T. W. M11.UIR, A.R-LB.A.
Third Edition, Revtnil. Crown Sro, 31. 6^, clulb,
lb Imi TW* U "ill "l>y if cad ■ hnadRd Qmo mc.'—ltfti

i6 WORKS IN CARPENTRY. TIMBER, ETC,

Cement.

PORTLAND CEMENT FOR USERS, By I1«mkt F*iJ

A.M. Insl. C.F-., wilh lUuMialionL Ciown %ia. p. 6J. dolh.

"A uHful csmtieialiuaiof tnuJiifoi Ihetmlldei mill guchiiat'—^tM^Av-'^''"

Builder^s and Contractors Price Book.

LOCKWOOI) A CO.'S BUILDER'S AND CONTRACTOR

CARPENTRY, TIMBER, ETC.
fs Carpentry, new and cheaper EdittM

THE ELEMENTARY PRINCIPLES OF CARPE^■TRlt
a Tica^se on the Pressure and Equilibriuin of Timber Frmung,!
Resistance of Timber, uid ilie CoDstruciion of Flood, Arch
Bridges, Rooh, Uoitinglronuid Stone Willi Timber, Ac TowM
it added an Esay on the Natore and Properties of Timber, <
with Descriptions uf Ihe Kinds of Wood tued in Building ; a
numerous I'ables of the Seantltngi of 'Hinber for difleicnl inuna
the Specific Gravities of MatcriiSs, &e. By Thomas Tkumm
CE. Edited by Pktki Barlow, F.R.S. Fifth Fdilion, d
reeled and enlarged. With 64 Pistes, Portrait of the Author, ■
Woodcois. 4to, published at xi. aj., redoced to U. 51. cIoiIl
^' OugTii IQ 1m in vnrj architect*) and «very builder'i Ubrarr, and ttifitc 1
do nni aLready pokicKf il ougkE la awl UwniKlva of Ui« new ibub*— ^knKdfrr.

" A work whoK mapumaniaJ ciodlenu ibiui conunend ii wh«nrftT akOnil J
pcniry b caocDned. The Auibor't priodpla arc rather c<Mifinitvd tlBa laMNci
time. The additioiul pbtei are DrKreal intriniic valus.'— -AauU^ MhT^

Grandy's Timber Tables.

THE TIMBER IMPORTER'S, TIMBER MERCHAA-T
S; BUILDER'S STANDARD GUIDE. By R, EC GuirV
xnd Edition. Carefully reriicd and corrected, lamo, 31. 6A dM

*" "" be! built upKTaduallr. It lea^ ooo fnun - ' —

JiewdBhi. sbw (if nwitrial cnncerniu bi
- — — a to wlHuB U appeal! ■viilirei.''— JS v>>'*

Timber Freight Book.

THE TIMBER IMPORTERS' AND SmPOWNEB
FREIGHT BOOK 1 Being a Comprehentivc Scries of TaUol

the Use of Timber Imporiets, Captains of Ships, S)iipln>b
Builders, and Dlhcri. By W. RiCMAXUSCUi. Crown Svo, 61,

Tables for Pcuking-Cttse Makers.

PACKING-CASE TABLES j showing the number of Snperlic
Feet in Boxes or Packing-Coses, from six mclies amufv ■
upwards. By W. Richaiibsun. Oblong 410, 31. &/. doth.

*' 1n¥alunbk labnuv4iiviii« tabita. ".— /ni mati^rt.

Carriage Buildtf^, &£.

COACH BUILDING : A Praclical Tk
Descriptive, contnlnlng full infcmialion of 1
Processes invulvrd, with Hints on llie prrij-.. 1
&c. S7 lUuMiTttJwu. l!y Jaiii» W. BVk.i

"Everyttunf it pfcretidiio be: built ui

bx A)
Dnwi

Hartons Measurer.

THE COMPLETE MEASURER; seirmg forth the Meamte.
mcnt of Boanis, Glus. &c. ; Unei]uel-sided, Squaie-sided. Oc-
taf^oiwl-udcd, Rooad Timber and btone, and Standing Timber.
With juit ailowantes for the bark in the respective spcciei at
troo, uwl ptope' <Je<luctiDns for the waste in hewing the lr«s,

I ici atan a Tible "h owing the solidity of hewn or eight-sitted

^^_ timber, or of aojf ocij^onal -tided column. By Richakd Hokton.

^^L Kounh Edition, with conFidcrablc and valuable additions, vaao,

^^H^ Mrongl; bound in leather, 51.

^^Borttnis Underwood and Woodland Tables.

^H TABLES FOR PLANTING AXD VAI-UING UXDER-
^H WOOD AND WOODLANl-i ; also Lineal, Superficial. Cubical.
^^H and Decimal T^iblcs, &c By R. Hokiom. izmo, u. leather.

^^mieholson's Carpenter's Guide.

^^ THE CARPENTER'S NEW OUIDE; or, BOOK of LINES
far CARPENTERS: coniiinsing all the Elemcntar? Principles
«M«nti>l for acquiring a knowleilge of Carpentry. Founded on the
'lie PtiHa Nichoi^ok's siamlard work. A new Edition, revised
f A8TIIi;r AsHPtTKL, F.S.A., together with Ptacticil Rulei ub
•rawing, by GruRGl Pykk. With 74 Plates, ^\a, U. u. doth.

Dowsin^s Timber MercJiant's Companion.

THE TIMBER MERCHANT'S AND BUILDER'S COM-

§PANI0N ; containii^ New and Copious Tables o( the Reduced
Weight and Measuiemenl iif Deals and Uuttens, of all si«s, irom
One la a Thousam] Pieces, aLo the relative Price Uial each siie
bean per Ijneol Foot to any given Price per Petersburgh Standaid
Hondred, &c., &c. Also a variety of other valuable information.
By William Dowsing, Timlier Merchant. Third Edition, Re-
*is«l. Cmwn 8vO, jr. cloth.

Praeiical Timber Merchant

THE PRACTICAL TIMBER MERCHANT, being » Guide
for the use of Building Conlractors, Surveyors, BuiTilirs, &c.,
COmprLsing useliil Tables for all tiurposes cocineclcd with the
Timber Trade. Essay on the Strength of Timber, Remarks on the
I Growth of Timber, Sc. By W, Riciiabdsok. Fcap. 8vo, jr. W. cL

Pbodworkin^ Machinery.

\ WaOUWQRKING MACHINERY; its Rise, Pregnss, anJ
I CooMructioii, With Hints on the Management of Saw Mdb and
I Uw Econarmical Conversion of Timber. lUustiated with Eiaiiipics
I V( Recetit Designs by leading En^liih. French, and Amencim
"igineers. By M. Povus Balb, M.LM.K. Large t
t. 6if. cloth.

iS WORXS IN MECHANICS, ETC,

^ . MECHANICS, ETC.

Turmng. — » —

LATHE-WORK: a Pnctical Trwiise on lb« Tools, ApplUwa,
asdProecsm employed in IheArtof Tumine. By Paul !«'. Hj*
LUCK. Wilh UloUntioni dnwn by the AnnioT. Ctntm Sw>, 5^

" EvideiLly wnne« Gum pBiwimt eipcrieacv. Hud glvct % \sa^ r^ — '■ -' — ■
iTui «pit cf iflfbiniBEidn whica bcfmbeisACibclAther^uuc" — BmM

Mechanic's Workshop Companion.

THE OPERATIVE MECHANIC'S WORKSHOP COM-

PANION. »nd THE SCIENTIFIC GENTLEMAN'S PRA&

TICAL ASSISTANT. Bjr W. Templeton. 131b Edit. wi '

Mechanical T>blei for Openitivc Smiths, Millwrights, Eiwiaee

&c. ; and an Extensive Talile of Powen and Roots, ■ imo, Ji, botiii

*' AdmirAbly jidtpled to the wmnti af k vcfy tant^ ckA- ll hu met wtih c*

1UCCCS ui ih« cDginHTine worluhop, as we on (calilV : ud Ihv? ue ■ pent i&4i

mtn hIw. in 1 (real mcuure, owe ttwir rUg isliTetalbUUUIevott' — BmUit^ MM)

En^neer's and Machinist's Assistant.

THE ENGINEER'S, MILLWRIGHTS, and MACHINISTS
PRACTICAL ASSISTANT ; comprising • CoUc«ion of Uteft
Tables, Rules, and Data. Uy Wm. TuiFLirroit. iSmo, ti. 6J,

Smith's Tables for Afechanics, &'c.

TABLES. MEMORANDA, and CALCULATED RESULT!
FOR MECHANICS, ENGINEERS, ARCHITECH
BUILDERS, kc Selected and Arc^nged by Fkancis Sum
WaJslcoil-pockct siie, 11. W., limp leather. lytiit fwUiii*

Boiler Making.

THE BOILERMAKER'S RE.\DY RECKONER.

Examples of Practical Geometry and TenipUting. for Ibe u
Plateis, Smiths, and Riveleis. By JOHN CoUKTNEV, Edtaad t

D. K. Clark, M. I. C,E. iimo, gj. half-bd. \Jut! f^MslM
Superficial Measurement.

THE TRADESMAN'S GUIDE TO SUPERFICIAI. %
SUREMENT. Tables calculated from I lo 200 iache* ia le
by I to 108 inches in breadth. By J. Hawking^ Fcp. 3/. tiA cL

The High-Pressure Steam Engine.

THE HIGH-PRESSUKE STEAM ENGINE. By Dr. Ew
A1.11AN. Translated from the German, with Notes, by Uc. fOU
F.R.S. PUtes, 8vo, 16/. dd. doth.

Steam Boilers.

A TREATISE ON STEAM BOILERS : iheir Slrei^ Ca
stmction, and Economical Working. By R. Wilson, C.r
Fifth Edition, iimo, 6j. doth.

" The bot work on boilm -which tmcomt imdgr our noiii:e '— gfiawrfiy.

Mechanics.

THE HANDBOOK OF MECHANICS. By Diosfvni
LiiKDNEE, D.C.L. New Ediiitm, Edilfd and conndaraUf S
larged, by BENJAMIN LOKWY, F.K.A.S.,&C, ponSvo, d. (M

MATHEMATICS, TABLES, ETC.
J^irical Units and Systems, &e.

T MODERN METROLOGY: A Manuaf of the Metrical Units

1 Syslemi of the present Century, With on Appendix con-

I taiaing ■ propoacd tti^fli^h Sy&iem. By Lowis D'A. Jackson,

■ A.-M. Inst. C.E., Auihor of "Aid lo Survey Pnciice," &c.

Laree Crown Svo, 121. &/. cloth. [Jiut fuilishtJ.

Gregory's Practical Mathematics.

M.-VTHEMATICS for PRACTICAL MEN; bdng a Common-

ELice Book of Pure am) Mixed Mathemalics. Desitnied chiefly
ir the Uk of Civil Engineers, Architect!, and Surveyors. Part 1.
. pDKS Matuimatics — comprising Arithmetic, Algebra, Geometry,
I Menmration, TriBonomelry, Conic Sections, Propenies of Curves.
Part II. Mixau Mathematics — comprising Mechanics in gencraJ,

icoiiv, LL.D., F.R.A.S. Enlart-edby H, Law, C.E. 4th Edition,
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yithematics as applied to the Constructive Arts.

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MOITK. Small 4M, 91. Elegmliy luiuid, cloth xntu)D&
•' Tire eiainplei oTucieM MSS, recuiii mended w the nudaBI. »!

ORNAMENTAL ALPHABETS, ANCIENT and MEDUETAI
frura the Eighth Cenlury, «rilh Numerals; including C
Church-Text, German, Ibiliui, Aiabuqiie, Iniluls, Mom:).
Crosses, Sk. CoUectiid and engnved by F. DsiAMont, k
piinted in Culoun. New and Cbeiper Edition, ttopl tro,
obloi^ u. 6d. amuncDtiil lioanii.

]ecen,lA over »lu?p-dwo», wh*

Deodocu^ Lhii bock wtU be u

EXAMPLES OF MODERN ALPHABETS, PLAIN uul ORNA-
MENTAL ; iadading GenoAn, Old English, Saxon, ItalK, Po-
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Riband, Gotliicv Rustic, and Arabesque, &c, Uc CoUcctol and
engraved by F. Deiamotte, and printed in Coloim. New isd
Cheaper Edition. Ro^ al Svo, oblong. 21. 6J.
*' Tfaert it o*aipn5ed la it vrery poviUe ihape into whjcti Ibc Lcnen of Ibc al|

■nd fium«»lB can be fonqed,' — SttatdanL

MEDI-«VAL ALPHABETS AND INITIALS FOR UXQll
NATORS. By F. Delamotte. Conuuniiig ai P1»M% ■
Illuminated Title. pKnted in Gold and Colours. With an ' "
dudion by J. Willis Beooes. Small 4:0, 61. doth gtlL

THE EMBROIDERER'S BOOK OF DESIGN ; contamiii. "
Emblems, Cypher^ Monograms, Omaroental Bonlen, E
tical Devices, Medieval and Madera Alphabets, anil Nali.
Emblems. Collected and eiig;TBTed by F. DKUMCm, I
piinted in Cola ur& Oblong rojslSTo, iJ.6£onianteatal<njq>pa

JFood-CarviKg:

INSTRUCTIONS In WOOD-CARVING, fot /

Hints on Design. By A Ladv. In embiemalic vrajifier, t

somely printed, with Ten large Plates, Zr. 6rf.

(rom'ALiV>'p"l>li=an™.--i2nl«*«. "' "" **'

P^mlar Work on Pmntinx-

PAINTING POPl'LARLV EXPLAINED; »UIi FTottatal '

dJarged. WithFrontispieceatidVignclte. InsniaD 8*0, 51. 6^.c1o(k
*,* Thii H'ori hai tten adeflid ai o Prar-buok i» tlu Scittii •!
Art at Simlli KmsinttaH.

"Omuiiua Iuk* BRkOuni of rpri^nwl *uatter, aireeaMr eiinv«re>i"^^«'A^'^

*" MurCt rnvf SxXr^iwA, even by tbove tfUu ftj,! vrbn do iiiU »«tuiW to te n^AL.

<iailKUiiJuI|inn>''ei'tl>'*»>>P«twiliH

PUBLISHED BY CROSBY LOCKWOOD & CO.

AGRICULTURE, GARDENING, ETC.

KlmaU and Sum's Complete Grazier.
THECOMPLETEGRAZIER.MdFARMER'S and CATTLE-
BREEDER'S ASSISTANT. A Compendium of IlosbiUidiy.
I^ W11.LIAM VouATT, Esq., V.S. 12th Edition, »cry con-
■iaenibly enlarged, uid brought np to tbe present tequiremenU of
^kukoml priKticc. By Sdhirt Scott Buhn, One Urge 8vo.
T^nnib K60 pp. with 144 Iltuttrations. 1/. t;. half-bound.
>T)w«nilui1iiid Kil'luiili. wilh Ihr larmosndgisiia.'— >=iir>iwr'( ATatiui'-v,

■gnCullu'B enUbne^"— Jfdri Lant Expnti.

History, Strueture, and Diseases of Sheep.

SHEEP; THE HISTORY, STRUCTURE, ECONOMY,
AND DISEASES OF. By W. C. Spoonhi, M.R.V.C, 4c.
Famth Edition, with fine mgrmvin)^ including specimeni dE New
d Improved Breeds. 366 pp.. qj. dotti,

'duetioH 0/ Meat.

I MEAT PRODUCTION. A Mftnunl for Producers, Distributor*,
I »nd ConsunKTi nf Butchers' Meat, UeliiK a Ireal'iM on meonl of
I' Increasini; its Home Production. Also irenting of the Breeding,
y Rcarine, FaitpninR, and Slanghtering of Me«t-yidding Live Stock ;
IndknUonsofthe Quality, etc. By John Ewaht. Cr, 8vo, 5>.dotli.

—MhI ami /'nv.i/dii TViwVi* Xnira.

'■aldson and Burns Suburban Farming.

L SUBURBAN FARMING. A Treatise on the Lavins Cot and
r Cultintion of Farms adapted lo the pnxluce of Milk. Hulter ami
I Cheese, E^s, Poultry, and V'xai. tty the lale I'rofeswir Jotfn
I Donaldson. With Additional, lunstrBiing the more Modem Prac-
I tice, bjrR. ScoTl' Burn, iimo, 41. ctotb board*.

igiisk Agriculture.

THE FIELDS OF GREAT BRITAIN. A Tent-book of

A^cuiture, adapted lo ibe Syllabiu of the Science and Art
L Sepuimcnt. For Elementary and Advuiced Students. By
T Ruck Cleml.sts (Uotnl of Trade). With an lulrodoctloa by
f H. Kains-Jacu«>n. i8mo, 11. bd cloth.

^^dnttjr wiiUEndEKriiiiion of Iheordiuur rouiliic Hi Eii|rliih ^xnii.\lt7'-Liimd.

PA««rully'»r>lI*nlril-l~iriln>f rtpiculluiB."— .<'&-i™«i. ^ \^Eem.-^ltl.

Modem Farming.

OUTLINES OF MODERN FARMING. By R. Scott BuB.t.
Soils, Manure^ and Cnipi — Farming and Fanning Economy —
Cattle, Sheep, and Hornes^ Management of the Dairy, Pigs, anti
Piiullry^Ulilisationof Town Sewage. I iriijsiion, &c. New Edition.
In 1 vol. ti;ovp., hiirkound. profuicly diuttrated, iir.

30 WORKS IN AGRICULTURE, GARDENING. ETC.

The Management of Estates.

LANDED ESTATES MANAGEMENT: TraHLnc of tie
Varieties of Lstids, Mcihoils of FBrtning, Fann BiiildinK. Irri|,>ttia^
Drainage, &c By R, SCuTT BUKN. Ilmo, 51. doli.

DWIH ef luadtfl tMntn."— 7.ii>r«/ p/finilry,

T/u Management of Farms.

OUTLINES OF FARM MANAGEMENT, »nd the 0 . __
lion of FartD Labour. Treating of (he G«nem] Work of the Fun^,
Field, and Live Stuck, Details ol ConCnct Work, Spcdihtei «f
Labour, EGanomical Maaagement of the Farmhouie oiid ContpV
Domeslic Animals, &c. By Robert Scott UtiRN. tzmo, jj.

Management of Estates and Farms.

LANDED ESTATES AND FARM MANAGEMENT.
R. Scott Burn, (The above Two Works in One Vol.) (a.

Hudson's Todies for Land Valuers.

THE LAND VALUER'S BEST ASSISTANT: beinpT>l^
on ■ very mudi improved Plan, for Calculating the Valae
Estates. With Tables for reducing Scotch, Irish, and I^tm
Customary Acres to Statute Measure, &c By R. HuDSilN, CB
New Edition, royal jzmn, IcaibcTi gilt cdgc^ cltstic lunil, 41.
Ewart's Land Improver's Pocket-Book.

THE LAND IMrROVER'S POCKET-BOOK OF FO
MUL^. TABLES, and MEMORANDA, required in any C«
putBtiou relating to the Permanent Improvement of Landed F.,
perly. By JoHM EWAKT, Land Surveyor. 32010. leather, ^^.

Complete Agricultural Surveyor's Pocket-Book.

THE LAND VALUER'S AND LAND IMPROVER'S COl
PLETE POCKET-BOOK ; consUdng of the above hro «o^^
bound together, leather, gilt edges, wiSi strap, ^1. bd.
"Weconiidcr Hud-on'i biHik wbiliiE hat rady-nckmiB iin lunnitlili^
the valiuijun n\ land uui cnjf4 we bkve ever t«ii. aad itt cunjlMtwiieii wilb .
l^wut'm work iieatly cnhvu^n the taLub and uHfulnev of iht Uncr-mcaliMd
li ii man luefui u a nunuid far ni'ovaet.'-^SirHnj Et^tinit far^n

Grafting and Budding.

THE ART OF GRAFTING AND BUDDING. UyCUAXI
Baltet. Translated [lom the French. With DJiiTBnli of
Illustrations, llmo, 3^, cloth boards yjiut fmttili

Culture of Fruit Trees.

FRUIT TREES, the Scientific and TrofiuWe CDltore ot
eluding Choice itf Trees, Planline, Grafting, Training, Rdtotal
ot Unfruitful Trees, &c. From the French of Dij Jliteuii, TI
Edition, revised, Wiih3nIulrodnctionb]rCer,E(;KGLUKY. ij
"Th<ibtw1iic*ch»ho«ta[niDcaiiiitnBifHiii-nwla|«t<-.ir:ii."- FitU.

Potato Culture.

POTATOES. HOW TO GROW AND SHOW TUEU.
Practical Guide to the Cullivaiion and General TrcarmcMaf
Toiato. By Jauks PiittL With lUiutmiioni. Cr. 8«o,Xivi

PUBUSHED BY CROSBY 'LOCKVVOOD & CO. 31

Good Gardenings.

A PLAIN GUIDE TO GOOD GARDENING; or, How to
Grow Vegeiablea, Fniiw, and Flowers. Wiih Practictt! Note* on
SoiL, Manures, Seeds, Planling, Laying-out of Gotdeiu and
Ground), &c. By S. Wood. Third EJittjn, Cr. Svo, 51. cloth.
"A n>r Eood book, ud oni to be highly RcamuuiDded at 1 pnctiol guide
lit pntoci] direcUDDt are mc^lcat."— A litumm.

rinful Gardening.
MULTUMINPARVO GARDENING; or, ITowto make One
Acre of Land produce j£'6io a year, by the Cultivation of Fruits
wnd Vegctnblei ; also, How to Grow Flowers in Three Glass
IioU!>Ci, soa&tore3ltse;ft76peruinuinclear Profit. BySAUtJBL
Wood, ird Edition, revised. Cr. Svo, ir. cloth.

'* Wear* boiutd lo Tecommend it as ddE only >nited 10 Lhecnacof the imaleiu aad
fenileman't canJcDcr. but to the itukHtet grower."— t^flnA**r'j Mtigtune.

Gardening for Ladies.

THE LADIES' MULTUM-IN-PARVO FLOWER G.\RDEN,
and Amaieur'i Cotnplete Guide. By S. Wood. Cr. Svo, 31. dd.

Bulb Culture.

THE BULB GARDEN, or. How to Cultivate Bulbous and
Tuberous- rooted Flowering Plants to PerfectiorL By SamuBL
Wood. Coloured Plates. Crowti Svo, y. tJ. cloth.

Tree Plaaiing.

THE TREE PLANTER AND PLANT PROPAGATOR!

A Practical Manual on the PropBgalion of FotesI Trees, Kiuit
Trees, Flowering Shrubs, Flowering Pliinls, Pot Herts, Sic.
Numerous Illustrations. By Samuel Wood, laiuu, 2j.6^.dotb.

7'ree Pruning.

THE TREE PRUNER : A Practical Manual on the Pruning of
Fruil Trees, their Training nnd Renovation ; also Ihe Pruning of
Shrubs, cumbers, &c By S. Wood, iimo, 3s. tV/. doth.

T^ree Planting. Pruning, &" Plant Propagation,

THE TREE PLANTER, PROPAGATOR, AND PRUNER,
BySAML-EL W,«.D, Author of "Good Gardening," Ac Consisting

of the above Two Works in One Vol., jr. haif-bound.

rly Fruits, Flowers and Vegetables.

THE FORCING GARDEN: or. How to Grow Early Fruils,

Flowen, and Vegelnliles. With Plans and Estimates for Building

' Ofatuhouses. Pits. Frames, &c. By S. Wood. Crown Svo, 31. dd.

^arket Gardening, Etc.

I THE KITCIIKN AND MARKET GARDEN. By Coo-

[ Uibuiors Id " Tlic Garden." Compiled by C. W. SttAW, Ediloc

'"Ganlening lllustraleil." lamo, JJ. 61/. cl. bds. [jajl^lisM.

'itchen Gardening.

I KITCHEN GARDENING MADE E.\SY. Showing how to
I preptreand lay oul the ground, the best mean^ of cultivating every
I known Vegetable and Herb, etc By G. M. F. Gle.m(v. iiiao, 1/.

33 WORKS PUBLISHED BV CROSBY LOCKWGUD 1 Q

'A Complete EpUmne of lite Laws o/ihis C&untA

EVEKV MANS UWN LAW^'ER; « HaoJy-Book rflft* W
ciplcs of Law and Eigaity. Bf A Barriscm. Nc« f"
CorrcMcd to the end of laat SeaiuD. Embndn opn
3.500 .'ilalemenis on PainU of Lmw, Veiiliet) b^ ibr bUII
Notes anil Kefcrenctl lu ibe AqiIiihiUcs. Cniwn 8*0, IJ

price 6j. &/. (saved at tvcry taK-^H.'lintu,

LAW, GAMK A

'* fio Enffl^itimui aufhi In ,\...

" VfUt il prorata to be- . ■ . "I I

iqlelticible In nDH-pntciaiupi . ' - ij t

Auctioneer's Asium/u.

THE APPRAISER. AUCTIONEER. BROKER. WH
AND ESTATE AOENT, AND VALUER'S POCKETl

SISTANT, for the Vulaation ftir Fan^ax, Sale, t ~
Leases, Annuities, and licveisions, and of propa ^
with Prices tar Iiiv«n<oiies, &C. By Jaiut WHuiusft, VI
Poanh Ediuon, enlarged, by C NimxiK. Royal 3300.
" A concitc book of nfcrctace, conuiiHi a el«Mrl)MHfH|^ tnt dl
iDVCntones, M praclicAl cuidc li> dHoirune ihc tuiuc oi fuinil — ^-^ ** -

A uctioneerin^.

AUCTIONEERS: THEIR DUTIES AND LIABII
By RoBEHT Squidbs, Auctioneer. Demy Sto, |i
" Every aiLL-tioncvr utA tiUuct cugfil 10 funcu a fi*py f/ tfaii

House Property,

HANDBOOK OF HOUSE PROPERTV : a Popnter and IV—
tlcll Guiile to the Purcliase. Mnrlgi^, Tcoant-r, anil Catnpalx *:;
Sole of Houses and Land ; mclaim^ uie Law oiT IXUpiduMit :"i
Fiitures, &c. By E. L. Takuuck. 2nd Edic tijuu, v. M. cUk>
;;We .tc «lad la W .hie w Kwrnmrad U."-*Ki*i-,

Aletropolilan Rating.

METROpni.iTAN RATTNC. ; n Snmmnrr ftf iV Alf(l

'3lW$ ^utiimentarii Setter-

PHILADELPHIA, 1876.
THE PRIZE MEDAL

Wii ^o^Lidrd ta<hi7PuUlih<.'nfor

BdoIu : Badimentary, EoientiSo,
"WEALESSEfllES/'ETC.

A NEW LIST OF

WEALE'S SERIES

IRUDIMENTARY SCIENTIFIC, EDUCATIONAL,
AND CLASSICAL.

1*1 H^ici 0/ Hi

\

I

WEALE'S SERIES includes Texl-Books on almost every bnnch o[

~ Induslry. comprising such subjects as AgriculLure, Architecture

~, CiTil Engineering, Fine Arts, Mecluinics and MBchuiicol

_ Physical sad Cbemicaj Science, and many raiscellancouj

Tbe whole are constuitly uadergoing revision, and new editloni.

3 the latest diacoreries in "•—"<!•'-

which they tie aoli

H LiUraiy CattUi.

. . „st the literature of lechaical education. WEAtK"a Sbriks has over

I obeyed > hiEh repuldtion, and the addition* being made by Messrs. CKUsnv

LOC^WOOD & Co. render Ihs series even more complete, and bring the infor-

malion upon (bo several subjects dowu to the present time." — Mtiiing

testimony lo the value ot

\ impossible to do otherwise
I WKAt.it'ft Series."— Enjiwer.

" Everybody — even that outrageous nuis.-u)ce < Every Schoolboy '—knows
e marils of 'Weale'b RtmiuKHTAHV SBtiiiss/ Any parsoas wisbing lo
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gut all the books they require. The Series is indeed an inexhaustible mine
o! literary wealth." — Tht Mciropalilan.
"WF.ALE'S SERIES hat become n standard as well as an unrivalled
ID et treatises in all brunches of art and Bcienec,"— i'utli* Opiniin.

LONDON. 1862.
\J>THE PRIZE MEDAL^

I aoaidi^d lu l!>e I'ubllilx

"WUlfS SERIES."
"CROSBY LOCKWOOD & CO.,

7, STATTONCR^.' HALL COURT, I.UDCATK IliLL, LONDON, B.C.

I

VTEALE'S RUDLUENTAlir SSKIES.

'WEALE'S BUSIHESTART SCIENTIFIC 6EBIE8,

MInaititnf-

„, ARCHITECTURE, BUILDING, ETC
lb. ARCmn ..

17. arch'it:

The Oiilcts nod Ihcif .SHutis
Alt.]. 11. 6d.
The History and Dp*ri|«inii "I

ij. THE ART OF £L

at CofUtmction. AUlf' '

jj. BRICKS A\-D ra

IHRol: ronUiniBr »< < '
I)a»ON,M.K.t.lCA.\\.

15. MASONRY Am> :- ■

o( UudbIc Pnqrctinn

44. FOUNDA .

FwHinti. I
4*. COTTAGE i>lu.ui.\^,. v.s <■- l-k^"^

Nindi E4ilion, r.-v.>«l uml i-i<iar(vJ. Nuiii>i<....s Hit

45. LIMES, CEMENTS, MORTARS, CONCRETESL

PLASTERiNG. •& Ily G. K, MUMIU, C.R. ■IWelftl. **
57. WARMIXG AXD VEXTILATiOS. -i Rudiir

116. THE ACu^. ...

PlindnlcJpflhT-S.;,'
Builder. BtT.Koc

LOSDON'. CR-J--.

w bale's

Architecture, Building, etc., continued.
i»r. ARCHITECTURAL MODELLING IN PAPER, the Art of.

BrT. A.KicMAiiDsos, Arcbilfct. Uiuiilralcd. i..6d.
■ iS. VITRUVWS—THE ARCHITECTURE OF MARCUS
fiTflt/yiUS POLLO. In Tim Booki. TriuUled from Ihn Litin by
Jonrii GwiLT, F.Sji.. FJt^^. With >j Platu. ii.
b GRECIAN ARCHITECTURE, An Inijuiiy into the Principles

> An frtctdiHt tt'rrtt in 0>u htmbami Vvl., half SounJ, rntUlmd "Axcni'T

AncHitacTU*!." j)n« 6i.

:, DWELLING-HOUSES, a Rudimeotuy Ttealise on the Erection

oC Illuntnlal l>r a l/iin»cIlTe Vine, Plini, Elcviliou, and Scclimu of a

pair ef Scmi-dcnctud Villu. with Ihe SpeciGuIiaii, QuinlUiH, ud E«t-

lUHt, ud eiBrr nqninUi debit, in Hquenn, for iheir ConilmctioB Hud

Flaiibini- Uyls.H. Buixiiii.AictiitKt. NewEditioB.witti PUta. u. M.t

1. QUANTITIES AND MEASUREMENTS, How to CilcuUte uid

"" *" ~^«BiaBricktivcn',MiiiDiu',Ptulemn* PtumbBn*. FaintEn*. Paper-

i. Gildcn', Smitlu'. CaiKnlen', and Joinen- Wock. By A. C.

H, AftUUcIudSurVFyDr, New uidKiitarEKiedi^aD. Illiu. U.«d.

1. LOCKWOOD fs- CO:S BUILDER'S AND CONTRACTOR'S

PRtCB BOOK, fmiSej.cndUminrllKiUteilPHcu of ill kind! ufBuilden'
Maurlal. and Ijbnur. and of all fiadn connfcUd wUh Building, kc., ftc.
KtvlKdand Edilnl bt t'. T. W. Milli*. Aicbilcct and Survcnir. u.U.;

KEATISE O.N JOIXERY by £. WvMiiu

i'.ii.i

. CARPENTRY AND JOINERY. ATLAS of 35 Plates to
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'. HINTS TO YOUNG ARCHITECTS. By GaomE Wioht-
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^V'itb nuDcmiu Woadcuu. ji.bd.t

t HOUSB PAINTING. GRAINING, MARBLING, AND SIGN
WRITING: A Pnwiical Manual of, coDoininc full Ufwniaiioo on the
rwetim of UouM-PalnliaE, Ihe Ponsatloo of LdtHi and PncUce of
SilixWritiD^ IbB Prindplu if Decoraiiv. Art, a Couw of Elemsnlvr
nnwiu ferHonie-PalDlen, Wrilcn, Sc, to. With g Colonred Plata bT
W90lb and MarblH, and nurlv ISO Wood EncnviiiEL Hy Blu> A.
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k Ti/£ RUDIMENTS OF PRACTICAL BRICKLAYING.
laSiKSeclioliit General Piinrlptea; Arcb Drairine, Cutlinc.and SeRinir ;
"—-=—- Pavuic. Tiling. MattiiaU; Slating and Piutenog: PtacU.al
Uaiunlion. Sc. Hy Adam HAxiiovn. niuiUaicd. u.6d.

t, PLUMBING. A Text-Book to ihe Pnctice of Ibe Art ax Craft nf
lb* Plambn. With Chaplrn upon Hduo DTainage. embodvioE A" lalnt
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UliHWaiioBL By W. P. lluuuM. ^iamtaty Cngionr. i%.6A.%

L yaS TIMBER IMPORTER'S. TIMBER MERCHANT'S.

Old RUILDEK'S STANUAHI) GUIOli: ceDpriiine cupiaui and nil. -
■Ua HntiDianda for the Kiuilvr and builda. by Richahu ff. Uaaim..

, !l<K(nd Edition. Rcvi«J;i..i

1 THE ART OF LBTfER PAINTING MADE EASY. By

■ T.O- tiADiHOni. lliustntedwilhiafull-paar UngngliigiulEuinplci. t*.

y. A BOOK ON BUILDING, Civil and EaUnasUtat. indudine
Cmkkh RUTOiUTiDH, With Van Thootv o( Don" and tbo Gitat VjnmA,
&[. BySiiBDHui>DElB[KiTT.Itan..Lt_I).,Q,C.,F.R.A,.S. tincond Kdiiioa,

- Tkt t tmiitmfll Hiitl tkrtt %iib. wnr it kaJ ,1-VHcly ^nnil al U. itltw.
, STATIOXBRS' HALL COURT, LUDCATK HILL, E.C

4 WHALES RUDIMENTARY SERIES.

Archltvclure, Building, etc^ continued.
»j6. TffE yOrNTS MADE Al^D USED BY BUILDERS is ttt
Canimcliofl ul tviaui kindi of EnEiDerrin; and ArcliitKign] Wsiti i >
Prscllral Tmti« CD). Wiib cfpecial rcfereon ta thoia wn)ii(lil t; Am-
iCFfi id braciint uid FiBiihiof Hibicibla Smcisni. B7 Wiviu J.
Chuhiy. ArchltKi. WIIlinpwatiliofrtaKiiertviiirion Wend. JU
J18. TUS CONSTRUCTION OF ROOFS OF WOOD AND !R^
— ■ , Dfducfd ctuFflj Innn Ihs Wocki at RiMiK

d liiiinba. Br E. Wrmius Tj,>

, U^u AicbilBI. '

»i9. ELEMENTARY DECORATION: A Guide t
Fmnii of Evnvilu An. u apolM 10 Ibe loUrioi >nd Eu
of Owetliiig-HiHMi. *c. By J*mi W, Facet, Jm.
Sulv-tfivbl enUiuEan Bqtfr«viDei- n.

3J0. UANDRAlLlNG (A Praclicsl Tnaliss on). Showios KevM
Simpli Utihodf foe Cndiiul the PiDrli of ths Planl:. Unwing ihn U«"'
Boetting, JninHnc-iip, lad Sqiuring the Wmtli. By tiional Ceua

CIVIL ENGINEERING, ETC.
J 19. CnnL ENGINEERING. By Hbnby Law. M-lnst C
Indading a Trciliia on HiDiiAuijc EnoummvO by Oio. R. B"" '
M.lnil.C.B. Siilli Bdltim, moed, with LAMn Adiiiiiiwi <hi
PucTict IN Civu. Bhoii>iiiuhg, by D. Kinkub Cuik. M.Iul, -
Aulhornf '' Tranwiin : TbeirCoiiltniciiDii/'kf. At.U..ClolbbauIt,lV'
ji, WELLS AND WELL-SINKING. By JOBN Geo. SWWDO
A.R.I.B.A.. and 6. R. BuRtnu, C.K. Kc>i>H] Edition. WiA > H
AnpeBdiiiiBtlu'QBiUtici of Water. II1iutrnti>a. ai. [Jtut *HUHii*

3S. ?ȣ BLASTING AND QUASSVING OF S'/dNB, I

Bulldlne and atbn PDipom. Witli Renatlu on Ibe Blowuis op o( Bi '
By Gm. Sir John BPawmr*. Bart., K-C.U. IllostnitKi. ».6d.
61. RAILWAY CONSTRUCTION, Elemetitiuy >nd Pnt&eA I
ittoctiooi on Iho Scleim dC By Sir M. SnrTKmsow, C.E. "— "*"

UEDtrAiD KuniNT, C.E. Witli SutMia ol Ibe Capital, l>
otkiae orRoilnya in ibe United Kingdom. Br E. U. Cm

8o», EMBANKING LANDS FROM THE SRA, the I

Tnalad u a VUxa of FcoBtable Einplr>)inctit lor 1

and Particnlan of actual EnbanirnTi'
Bl. WATER WORKS, for the Sl;

a DcKiiption of Ibe Principal G.

aaencin«SuBpliei of Water; udD.'i

for railing Water. Br Sa>mLH['<^<> '
117. SUBTERRANEOUS SURVLl...^.,.. .

lical TrealiH on. By Thdmai Fbk»-il;k. Ai^r. t!

SubleFTaneoni Samy* witbout tbe U>e o( tbe Ha

Modem ImpravemenU. By Tkouai Bakui, C.B.' Illu«i
I rS. CIVIL ENGINEERING IN NORfH AME»i

of. By David iywaacm, F.R.S.E.. kc. Plalai ud t>h,
197. ROADS AND STREETS [THE CONSTRQ.

in tH'o Pats; I. Tm Am or ConsiaucTiiio CnntOM IT

Ljiw. C.E., TCTiwd by D. K. ClAiiK, C-K. ; U. RlUKT P«,

p.-i»cinent. of Stone, Wood, aed Araballe, by D, K, CitM-

203. SANITARY w6RK iN TBE ShiALLER TOW

VltXAGF.S. CoBiptiiiDi :— I. Seme of tb« mnn Coa
Nuiiaoi^e and Ibeir Remnllei ; >. Dnuage i y W«IaT St

aij. PlONtii 1

is- 7-*.t.w.

WEALES RUDIMENTARY SERIES.

MECHANICAL ENGINEERING, ETC.
. CRANES, the Construction of, and other Macliiiieiy for Raising

" iRoHh. Brjosir" "'.r-

M ENGL

, THE STEAM E

kGINE. ByDr. Labijnkr. Illustraled. is.M.
S, STEAM BOILERS : Uieir Construction aud Management. BT

R.AMtniioiie.C.S. Illiutraicd. ii. M.
1. CLOCKS, i^AlVHES, AND BELLS, a Rudiraentiry Treatise

on. ltrSiiEo«i.'TOB.ci«it,Ll..D.,Q.C. Scrraih Ediiion,™vi«dMde<i-

lufd. ja. U. limp: ti-6<l.<:l>iEhl»ardi. \Jml fuUhkid.

. THE POWER OF WATER, aa appKed to drive Ilour Milll,

iDaioeivemoiioBtoTafbm«,»c. BtJob.™ Glyhh. F.R.S. aj
L PRACTICAL MECHANISM, the Elements of; and Machine

Tooli. %T.Bak.i., C.e. WilhAddiii<,n»bTj-f<A»«"ii, C.E. u.M.I
I. TUB STEAM ENGINE, a Treatise on the Mathematical Theoiy

(•CwilhKu[»>iidRnnipl«<orPnelia1Mni. RvT. »*kiiii, C.K. ii.M.
. TBS BRASS FOUNDER'S MANUAL; Instructions for

" ■ "■ " IKm-Makinc, MouMinc. Turning, FQing, BimiitaiBt,

„—. A'ilh Conian/ltBCeipl., Kc. H. WaLIEK GlUHlH. H.t

|. MODEIrN WORI^HOP practice, a* applied to Marine,
Lud, and LocDmotiTR EneiDci, Floaling Uoclti, \JitAjnT.f: llicbinu,
»ridnt,Cnn(!i,Ship-biiildinc.k^tr. ByJ-G. Wimiom. ll!uilr»leil. j».«
IRON AND HEA T, exhibiting the Principlea concerned in the
CgosltDCIieB of Iron nnuni, Pillan, and Bridge Girden, uid the Action of
Hou ID Ibe SmeltiniFumace. Br J. Auioub, C.E. ii. M t
i. POWER IN MOTION^ Horae-Power. Toothed-Wheel Gearing.
LoDEud Short Drinngllanda, and AnniUiForr«. By T. Aauoua, a.M.t
i6j. IRON BRWGES, GIRDERS, POOPS, AND OTHER

WORKS. HyFii*:'CnCA«M»,C.E, z.. 6d4
171. THE WORKMAN'S MANUAL OF ENGINEERING
DRAH1NG. Ky Johh Maxtoh, EngluHr. Faucth EdiUoD. lUiuUiUd
^_:.t _ *.!_- a .. --'y i^^WoodcuU. «. 6d.t

HE STEAM ENGINE, Slalionary and
_,. vrtLLaodD. K-Ci-AHK, W.I.C.E. i>.«il.l

t FUEL, It* Conibostion and Economy. By C. W, Williams,
Vnik Kccrnt Piacllce in IhcComNutlion and Bcnnmnr of Fuel— Coal, Coke,

,■ Wood, Peat. tBtrolciun. ac-by D. K. CULBK, JI.I.C.E. J..M.1

I, LOCOMOTIVE ENGINES. By G. D. Dimpsey. C.E. ; with

'' larnadditioni hr D. KnniRAii Cuik. M.r.C.B, ji.t

I TBB BOILERMAKER'S ASSISTANT in Drawlnn, Tem-
" ~ " Tm BoilM and Tank Woik. By Johh CoiiatNtT,

, ,._ .-. Edited by D.K.Cuan. C.E. looIlluitraliDni. u.

b MATERIALS AND CONSTRUCTION ; A Theoretical and

■ - KticslTreali.oon the Strains, Daignine, and Krtclioo o[ Work) of Con-

Iv-"".

ClHI'

, C.K. J

r, SEWING MACHlNER-i: Itii Conitruction, History-, &c.. wilh

- - ~ - — U.QUBAai " " --

. __. . _. .. ^risiDC M

„ __ », F(™or.'''<»l»,'W'orfciliop Macbinrrr. Maa

m EncinE. »c. Br FaAiru Clvpln, C.E. aj. 6d-l

L COACH BUILDING, A I^raciical TrcntiiC, Historical and
Doaipllte. nyJ.W. Huioiis. ». ed.t

!, PRACTICAL ORGAN BUILDING. By W. E. Dickson.

MJ(..Fre«nIorofElvCalbcdnL lllttttraled-M.&l.I ij—l f-HiiktJ.
k DETAILS OF MACHINERY. Comprising Insiruclions for
UW EiecnliDB of rariona Work, in Inm in Iha JLlliog-StifT.. I'ouudrr. ,«i
Bml«-Yafd. By FaAsat Camph.-C.E. i..t \y„,i fHl-UiliKi.

i THE SMITHY AND KJJC^,- including the Farrier's Art and
CoacbSnilihlne- ByW.J.E.CiiAiis. lUuitratrd. u.U.I \J%tt fuihikiJ.
THE SHEET-METAL WORKER'SGUIDE;aVt»cwi\hMi-
.. Coppe™

iM> A. had ttrrtrlr tntnit

\inTvtt. ll)r

W. i7e. CaJ

7, ETATIDNSRS' HALL COUKT, LUDOATS, tt\U., I.-^.

6 1AEALES RUDIMENT ARV SCtUES.

SHIPBUILDING, NAVIGATION, MARINE I
ENGINEERING, ETC.

SI. NAVAL ARCHiriH-IfRE. \\:^ Ru-liiDtii!. of- c in TijK

cation lo Nival Cii-i.
UnM Piiu, Sclwl
Founh Ediilm, com. ;
II*. SHIPS FOR Oct .

Ind Piactical Priniip:.

rm»t, Sb(«™ of It* Koval NorT'i^i.n N,.>T. W n!i jn A.iprr

St"". AN ATLAS OFBNUiiA t-/NiiS to lllu«trite ihe aiiDTi

Urec fDtdinc plalei. Ronl 4te. .brth. i^aa. _,

54. MASTING, MAST-MAKING, AND RIGGING OF SBOt

Rodimi!BUn-lir-.tiw on. Ale. T.,U.-. ..i Sj. ,r., K.;i--™, W«bj_OJl

i Ol- iORlY 1-LAlliS

" Hclloroplimi :" H.M. Tn»p Sbr -!

5tom» ; and a Briel 1 1 -
»nd Colauicd Plain, ul I .

edition. llyW.H.Ko"! .,

Bo. MARINE ENGINES. AND STEAM VESSELS. ■
on. TantlinwitliPtaetiuI Remaib on IhsScrn
a> uinl m the Royal imd UHchinl Niry. Bv .

T«in>. and Ibeu EqnliiOeDli \"v:. '''■'^"'-
Kdjtion. Tcriicd BDdcfilAmd. liln i
StJ/j. r^£ FORMS OF SHIPS .■!:■
■lljDem-cd, on lonieaf Ihe Pri...
Hu HD. Scrrnth Edition, revi>ed,w>i:.
99. NAVIGATION AND NAU!i<
Md Pnctirt. By Prn' ' "' "

cat f,

Jf!

■ DO*. Tyi/rZ^y intended to facilitale Uie Opcniioi
Nautical AiImDomT, u u AccompwiinKnl to Uui

106, SHIPS' ANCHORS, liTreataeoa. ByG.CoTStU
Hg. SAILS AND SAJL-MAKJNG. »a ™

■With Dranghting. and (ho Ccmtm of Effort

und Sk. of Rop« ! Moitine, Rigpnr. wd SJIi of fM
ElewBth Bdilion. <-nU<«d. with an Amwwdia. "- ■-
Sailmakci, Q^aytidc. r^KCune. II]D>tnit«].

15s. THE ENGINEER'S GUIDE TO THE .

UERCANllLB NAVIES. B; ■ pRACiirAI. E-biioMjI

i PRACTICAL

'■ Pmblm"-"'
Ma(h«.M < '

NAVIGATION.

UOSVOM \ CUQ&Wl UyLVHOQIl Mn» c

WEALES RUDIMCMTARV SERIES. 7

PHYSICAL SCIENCE, NATURAL PHILO-
SOPHY, ETC.
. CffSiflSTRy, fot the Use of BegiDners. By Professor Georgb

t^rXru

le Applic.

TVRAL PHILOSOPHY, Introduclion to the Study of; for
I U4a of Hcpnncn. Hy C. Twiii.'kik. LecKm^r an Natuiil Sdnce in
KiaB'»Co1lc([DSclioi.l, LonJon, WooJcuU, i..M.

MINERALOGY, KudiTncnIs of; a coadse View of tlie PropErtics

irfWBorali. ByA. R«1UAV. Jan. WodiIcuci jud Slml flnld. ^.1
MSCHANICS, RudimcnCacy Treslise on ; being » Eoncise £l<

BCMltion of llie GcdriI Principlot of Mechanical Scicncr, and Ihdi Appliia-

tuna. Hy Ciuaui Tduunhin. lUuitratcd. i>.£d.
ELECTRICITY ; showing the General Principles of Electrical

SehaM, nd Iha puip«« to which it hu Xxea anplitj. Br Sit W. Show

B<itin, ¥.K.S^ &c. Wilb Addilinoi br K. SuiflB. C.E., F.SJl. u. M.
GALVANISM, Kudimentur Treatise on, and the General Piin-

^-" Voltaic Electricity. B. Sir W. S»ow Harkii. New

ib1«AddiiionibyR0B»»rSABis»,C.E., F.S.A. i.,M.

MAGNETISM; being a concise Exposition of the General Prin-

ctplea oF ManHlcal Sciebce, aad the Purpcuet to nvhEdi it haj, heea applied.

By Sir W. Snow UkBBia. New Ediiioc, rcviied and enlaned by H. M.

nou), Ph.D., Vice-Praident at the Chemical SodolT, Aulhar of "A

lfailwlorBI«lridlv,"I.r.,b<:. With i6j Woodcuta. it.6d.t
rffS ELECTRIC TELEGRAPH: its History and ProBrcss;

witkDeHripllinitafiDmeaflbnAiipjuatut. Bv R. Suuxa, C.E., F.S.A. ji.
PNEVMATICS, for the U:c of Beginneis. By CHA&LU

ToaumoH. IllmlraWd. u. 6d.
MANUAL OF THE MOLLUSCA ; a Trwliie on Recent and

FbhU Shelli. By Dr. S. P. WooDnAnn, AX.S. FoHrth Bdilloa. With
" ~ "airn Taii, A.L.S„F.G.5. With enmermu Plata ani! joa
6d. CiDlh hoardi, ^t. M.

PHOJOGRAPHY, Popohu- Treatise on; with a Desciiption of
' '* ~ "' ' .ted 6«ni the Fienrh t^O. V'jkM UoNCKiiovaH.

J5raSVai/J'.""ByliieiWRev. RoBENrMAiif.M.A., F.R.S..

'-— ' KaJclino Obactrcr .it Oxford. Third E^liDn, reviled ts the

iDie. HrWlLUAUTiiTHHaLTSii, H.A.,F.R.A.S. ».

t STATICS AND DYNAMICS, Ihe Prindplcs and Practice ofj

t MgbnciPff atia a dear dev«lopipflni of Hrdroftatici, UTdrodynaDuci, and

I Central Fore.-,. Ur r, Hn«i.«, C.E. ...fiU.

I: of Ihe; > Klanual of Telegraphy,
. -T. .ind Guilts to CandidatH for Emplar.
11V K. HoND. fuurtli Edition, renKdud
I niTELSTIONS on MAGNETISM, ELEC-

, l^LEGKAPHV. for Ibe Uie or Stad«nn.

brW.M I ■-■■, ^ .:.i:.:Supnt. Indian G(«,Ttlp»raph». JU

L PHYSICAL UEOLOGV, patt]v based on Major-General Po»T-
t l*a('»"RiidiincnUofG™lugy." ByH*UTiT*Ta, A.L.S.,l.c. Woodeuu. «.
VBtSTORICAL GEOLOGY, parUy based on Major-Gener«l
i Pwrnooc"! ■' Rudimonu." By RAini Tati, A.L.S..ac. WooJcnti. u.6d.
I RUDIMENTARY TREATISE ON GEOLOGY, Physical and
* *IUorici>1. Partly bawd on Majci-Omotal Poarnjot'l " RuiUnnot. of
_ ^^len-" Rt Ralph Tatb. A.I,. S.. F,U..S.. >c. in One Volume. 4>- «d.t
I ANIMAL PHYSICS, HandlMjob of. By Dr. Lasdneh, D.C.L.,
I Natural Pliilotopbr and Aitmoony in Dnlrentty
-a On. Vol. 7>. M., dof- •-— '-
■ SaldalaiH Tvn Parli. at Mlraa :-
KyDr. LAaoiui. ■■ - • ■- ■ -

CoUe(«. Land. With jao Hlulra

Aana

es. Brl»r

La

RDXII. Paltll

Chap

I.nVIl

-xt

■

rn.

■Wuii

Utlhallki^

»»

b.mmyt*l>^,t

■^nxh

t^inJa

bj.^

■

7, STATIOUERS' HALL

COURT, LUDCATK

HILL,

E.C

J

^^H

^^^1

■

^^1

8 WEALK S RUDIMKNTARV SERIES.

MINING, METALLURGY, ETC.
117. SUBTERRANEOUS SURrEYJNG. EleraenUry and
IrcallK on. iriih ui sriihoui iho MieiMi' N'relJe. Br Tdqhi

ijj. METALLURGY OF COPPMR ; on IntroJuction ia Ibelldl
nf S«*klnt. Hinjnfi and Aawrin^ Captvr» aad MAnu&cturiaf iu /'

131. ilhTATluROY'oF' SILVER AND LEAD. By Dr.I

I. IfETAi^dRGYOFWoN. "contniniHg ^a\
liflaic. MMboda of Anar, and AnslnEi of Inm On*. Pl
facMn of Inn ud Stwl. Ilc. llr:H. flAUiMUH. I'"

. COAL'Mm"^'At*M/mXG. A Rudiroenti^ 1

Br WakikctO!. W. SurcH, M.A., F.8.S. Fi""- •'^--~~

iTffto:

;. T//E MINERAL SURVEYOR AND VALUSfPS COtH

PLETEGCIDE.wlth iiewTa«n*T.iW.r -nl T'-iriii.(,^, "

InilniniHil*! »l»llwCarTW[prinriri- ■ ' - ' '

Propcrtio. By WnxiAii LtTtTinx. ,^l '

. SLATE AND SLATE QUAKh

Comneicial. Bt D. C. Davib. 1
i.un.<.reu< Illiirt«ri™. .nd PoldinL- I'l
,. THE GOLDSMITH'S HAKIj
tioni roc tliii AllorrDC iBd Wnrkiae <ii i .
and SilnnmiUi' S«cflDdBditioii,cf^n< .'
;. TjKe SILVERSMITH'S h.-!.\

•tmctioni for LhD Alloring »nd -Wo.Vi :■

1. MAGNETIC SURmviNG, -/.>

ING, mthRKoniinf IhePcculiaciliMW .Mr. <iir- ii;.1u,i.,t,.

FINE ARTS.
t. PBRSPBCTIVB FOR BEGINNERS. Adopted

andenti uid AaUeun in AichiI«Iiin-. Punlisi. ftc. BvGitnii.

) e£^55 STAINING, AND THE ART OF PAINTING 0
I. CLASS. Prom ilio GinBan nf I>r. (lasaiit *nd Kumun. Otto 1^

iin.n. Wtlb >n Aiinrndli u'l Tim Aar nr BBlMiLliiia. u. 6d
). MUSIC, A Ruiilmentary tn<l PrirtiMl Treatise o

nunmniui Kumplri. By Ciuaiu Child Sputcn. ». tA.
. PIANOFORTE, The An of Playing tile. Wilh niimefoni I

(iin & Lmoni from thn !<«» MuCen. By Cujiius Chilh .Snonc
I. MUSIC AND THE PIANOFORTE. I» ^.nr voluniB.

bouadjl.

PAINTI2

Si. painting POPULARLY E. \

JOHN TiHU, F.S.A. FoaRta EdillDn.
GRASiMAR OF COLOVU
Pnintine and Itio ArU. By Gconr.r
adiplrd^ to lbs Uk of tbe Oimnmr.: :
DiviosoM. Wiib WD BF* Cnltigml J ■

Ijombow 1 CB.OSW \iw:it.-«a;i\i t

weale's rudimentary series. 9

AGRICULTURE, GARDENING, ETC
131. SflLLER-S. MERCHANTS, AND FARAfERS READY

KECKON'EK- UhbuppcDilinale v>lu«i>fUillitan<.i, MiUwork. Ac. 11.
lie SOILS, MANURES, AND CROyS. (Vol. t. UUTLlNts OP

MoDiiix FAMHixa,) Bv R. Scott Bimn. Wbndcuti. u.
141. FARMING &■ FARMING ECONOMY. Notes, Hisloricil «nd

FnuMkal.Do. (Val.>.Oviuii>9orMoDtiu>FARHiHn,) HrK. ScoiilliriiH.ji.
MS- STOCK: CATTLE. SHEEP. AND HORSES, (Vol. 3.

OUTLIKU 01 MODtlB Fahkinq.] Bt K. ScijTT Buitx. WwdcuU. >•. 6d,

Ui. DAIRY, PIGS, AND FOULTRY. Mmiflgemenl of Ihe. By

1 d( &I(K

(Vol.

SEWAGE. IRRIGATION, AND
F WASTE LAND. (Vol. }. Ouil»u o» Mod»«h
>ttBuilk. WoodcuU. ilM.

■be FKnch dI Dit Buuiu KcvUcd by Gbd. Guhhy. 1R7 Woodcuu. it. «d.l
I. SHEEP: THE HISTORY, S7RUCTURE, ECONOMY. AND

DISEASES OF. Br W. C. Spodkih, MJt.V.C, ftc. Faunb Edidon,

rslnr^, indaduiE f-peciioeai of New and Impioved Uieedi. ji. bl.t
. KITCHEN GARDENING MADE EASY. Showing how to

pnpare xnd lay dji the |rrDUDd, the bat u«ld* of fullivatine ftrpry kjiown

'. OUTLINES OF FARil MANAGEMENT,' 2^ She Organi.
ulum^/Fanm M«»r' T™'i"« "f ">" Gcnoral Worf. of tliB Fjno ; Field

^^■t Plowsrinr Shrulu, Flemrine Planti. Ice. Bt SAHCtr. Wood. ».]
^^B 7ZK ?»££ PRUNER. A Practical Manual on the Pruning or
^^V Fnlt Tim, includios alio Iheir Tnlnlne »ai Rniontlan ; alia tbs Frnaiu
^^P a(5hnibt,Cliiiiben,aiidFlDvnriaif]k[iti, Hr.-SUIUIL Wood. u.I
^H. S* Nk. »9 ^ ITD t<i 0<H C</., handi^mrlf /u/f-hunj, rmlilUi" Till Tmi
Plastih, PiOPAOAiaii AKn l-Ki'Knn.-' By Ra»d>l Wood. PhUu.
Sf8. 7y/£ HAY AND STRA IV MEASURER .- Baog New Ta.hle»

TntllnsDf ttu Varistia of Lindi, Uelfaadi nf Parr....^, __..

iRitltion, Dnipagc. Sc. B; R. Scoir Bukk. u.td.I
,* Ahi. K7 &• KB r'n Out Ifal-./miJismtly ha/j-lmiHj.tHtitltJ" Ovnvmw
Lahmd EsTATu AKO Farm MtKAOtHUiT. Br K- bcniT Bit*ii. /Vif<te.
Z/fJ 7M£:£ PLANTER AND PLANT PROPAGATOR.
A Fnctical MuuaI on ibg piDpagatiDn of Fomt Tnoi, Kniit Ti«,
~ ■ "" ibi, FlowBriuB Plant!. Ice. Bj SAiif*- "■— -- -

fortl

lUw

■■"?'"

__ , ,._uCilciiLLli>randKEady-RKkonc.. . . .^ __,.

penDfii comiicled nitli Aericultim. Fourth Edition. Br JohnSihu. u.
I. SUBURBAN FARMING. The Laying-out and Cultivation of
Faiai, adapted lo the Produes oF Ulth. RultEt. and ChocH, E(ei, Ponltiy,
and Piin, Hy Prot lomi DovAtiMoTi and K. l^ean Bi-nn. u. 6d.t

. THE ART OF GRAFTING AND BUDDING. ByCHAU-BS

KALriT. With IlliutnluHii. n. 6d.t O'liitMUiiU.

. COTTAGE GARDENING; or, Flowen, FniiU, wid VcEeuble*

for Smalltiaidm.. BvE.Hosdav. ...W. IJuil fKihilud.

,. GARDEN RECEIPTS. Editedby Charles W.QtCN. Ig.6d.

i

B, Editor of-Gardm-

ine l<l<"»aled.-' 4)0PP- Ji-! [y~./ fHlittluJ.

DRA/NINNG AND EMBANfCI.VG. By Pmnresson Jonst

7, stationers' hall court, LUDGXTE. \SIVA., «„t.

lO WEALE5 HUDIMKNTARV SEJIIES.

ARITHMETIC, GEOMETRY, MATHEMATICS,
ETC.

31, MATIiEMjnr-ir. JX.-<7A'r:,UFXT.';. .1 Ti,'.u;.^

60, LAND AXn LXIilXhhKjyG SUIil'IiY/Xi;. a TrMtbc M
nrllh all (lie Modern liDprovrnirnti. Amnnd inr tht Um of ScWablri

T. BlKE>, C.E. New Katlioii. roued by Edwaiu
Irilcd with FUMI ind DmETam,. ».t

b\*. READY RECKONER FOR THE ADAfEASURSUBNTfA
LAND. BvAbuhah AiiiiA!>.Sebii(.lni3>tn,'n>iulri|Fh,Badt T«aW
i> added aTihl^>ba«rin(Ibe Price of Wolk.lnimif.od, In iCipKiocli
Tab]« for the ValnadOD ai Land, froni ». u £i,Da>|>« an*. «ad fenM

•,b. DESCRIPTIVE GEOMETRY, "a.n Elemeiitary TifMhe If
wiLb a Theorv of Sbadom and at Penprclivr, citriflrd fiofB lb« Vi*~^
G. Moxaa. To irtiicli ii added, a ducrpiioa of ibc Priocipln aad tt

AppTicaliaD ctf Dncripiivfl Gfometry t4 Tariouq braniihei of (ha Ai
J. P. HuiHH.U.A. I]liutral«l<nlbi4platn. u.

irS. PRACTICAL PLANE GEOMETRY: gime ihe !
MadnorConilmctingFlEumcanlaincdEnoiiFplani-aodGtMr^
■traninnirftbeGnDiid. l!f J. F. Huther, M.A. WiHnlsV

179. PROJECTION : Orthograpliic. Topoerapliic. "nJ '
Kivinc Ihc varioDi Uodu of UernflatiDe Solid Fonni by C«b
SiagU Prane Surfai*. By J. V. UcAiRU.MJl. [/■

•.• Tliiaii-vi/JintvtlHmamllfyrmaCaKrLtTK BLtnIKTAKT CcUan ■
UaiHaiiaTtrAt, JliitwiKQ,

83. COMMERCIAL BOOK-KEEPING. With Commnriil P

and Forma in EflgUih. Ftencb, lUliaa, and OennaD. Bj' I **

M.A., AHtlineiicalMuuirof KJDf'iCollaceSdnal. Umd^

84. ARITHMETIC, a RwlimentBty Treatise on : with fall I

tioni of it! ThoontiMl FrlnciplEi, and nnmnroiu Eiin,pl««ftit Pi —
IheUxofScbooIiaDdfotlMf-Inttniclion. RyJ.K. Yovi-c,la
of MalbetsalK:! in BeL(aM CnWt^. -|Wlt> Rdtf>ar<, i-^itkiM.

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