57TH CoNGREss, } HOUSE OF REPRESENTATIVES. { DocuMENT 

1st Session. No. 56. 

DEPARTMENT OF THE INTERIOR 

'VATER-SUPPLY 

AND 

-IRRIGATION PAPERS 

OF THE 

UNITED STATES GEOLOGICAL SURVEY 

No. 56 

METHODS OF STREAM MEASUREMENT 

WASHINGTON 

GOVERNMENT PRINTING OFFICE 

1901 

UNITED STATES GEOLOGICAL SURVEY 

CHARLES D. WALCOTT, DIRECTOR 

METHODS 

OF 

STREAM MEASUREMENT 

WASHINGTON 

GOVERNMENT PRINTING OFFICE 

1901 

CONTENTS. 

Letter of transmittal_ . ______________ . ___________ . ___ . __ .. __ . __ ... . _ .... 

Introduction ____ .. ____ . ___ . ___ . ______ .. ____ . . _. _ .. ___ - __ . _.-- ... -... -.----

Weir measurements ... __ . . ____ .. __ . _ .. _ ... __ · __ . _______________ . __ .. ______ _ 

Milldams as weirs ____________ . ___________ . _______ . __ .. ______ .. ___ .. __ _ 

Velocity measurements ___________ . _______ . ________ .... __ . _. ____ . _ ... ___ . _ 

Floats _______________ . _ .. _ .. _ ~ ______ . _ _ _ _ _ .. _____ . _ _ _ _ _ . ___ . _ ... _ . _ ... . 

Current meters _ . ___ . ___ . ___ . _ . __ ._. ____ .. ____ .. ___ . __ .. _ .. -. _ .. _. ___ ... _ 

Unit measurements ____ . __ . _. __ . _______________ ... __ .. _. _. ___ .. _ . _ 

Multiple measurements ___ .. ______ . _____ . ___ . ~. _ _ .... _. ___ .. _ .. _ 

Integration method __ . _. __ .. ________ .. _ .. __ . ___ .. _____ .. ________ . __ 

Gaging stations ___ .. _ ......... _ . _. __ . _ . _. _. __ .. _ ... __ . _ . _____ . ___ ..... _ .. Bridge stations _ . _________ . ___________ . ________________ . _____ . ____ .. _. 

Cable stations ___ .. __ . ________________ . _____ . ____ . _. ___ .. _ .. __ .. __ . ____ _ 

Rod gages . _ .. __ .. ________ .. _. . . ___ . _ ... _ .... _ .. _-- __ ... - . ---- -- ---- --

Wire gages ____ .. _ _ _ _ _ _ _ _ _ _ _ _____ . ________ . _. __ .. ~ ... ____ . _. _ .. __ . _ .... • 

Bench marks ______ . _. ____ . __ . __ . ___ .. ____ . ____ . ______ . _______________ . 

Stay lines and trolley equipment ___ .. ____ .. _ .. ___ . __ . _______ .. ___ • _ .. __ _ 

0 bservers . __ . . __ . ___ . ___ . _ . . _____ . ___________ .. __ . ______ . ____ . . ... _ . __ 

Care of instruments . ___ .. _ . __________ ..... _____ .- ___ . _ ... __ . __ . -... -... - .. 

Methods of rating meters ___ - ___ .. __ . __ .. _ .. ____ -. _ .· _____ .. __ . -.. - - . -- --. -

Notesandcomputations ·-------------------------------- _ --------·----- Reports of discharge measurements ___ . _____________ . __ . _ .. ____ . _____ _ 

Flood estimates ________________ . ____ . _ . _ .. ___________ .. __ . _______ . ___ . 

Rating tables ____ .. __ . _ ... _ _ _ . __ .. ___ .. ___ . _____ . _____ . _. _ . -- _ ---.-- .. 

Tables for computing results for publication ________ .. _ . _______ . __ .. __ . 

nstructions to computers .. ___ . _ ... _ .. ___ ... __ . _____ .. _ .. _ _ _ _ _ _ ___ ..... 

Gage heights ____ . ___ . ___ . _____ . ___ . __ . _____ . ______ . _ _ . _________ _ 

Rating tables ____ ... __ . _____ . _ .. _______ ..... _ ... _ ....... ---- -----. 

Averages, run-offs, etc . ____ . __________ . _____ •.. ____ .. __ .- - . 

5 

Page. 

9 

11 

13 

14 

16 

16 

18 

18 

19 

20 

21 

22 

22 

23 

24 

25 

25 

28 

30 

34 

35" 

40 

43 

43 

44 

49 

49 

50 

50 

ILLUSTRATIONS. 

Pag, 

PLATE I. A and B, Cars used in measuring velocity of streams _ _ _ _ _ _ _ 12 

II. A and B, Measuring weirs _ _ _ _ . _ _ _ ... ___ .. __ .. _______ . ___ . _. _ . . . 14 

III~ A, Measuring weir; B, Gaging station . ____ .. ______ . ________ .--.- 16 

IV. A and B, Dams suitable for use in measuring flow of streams _ _ _ 18 

V. A and B, Dams not suitable for use in measuring flow of streams. 20 

VI. A, Measuring velocity of water from ferryboat; B, Suspension 

bridge fur making stream: measurements. ______ . _. _ . _ 22 

VII. A, Measuring velocity of water from bridge; B, Measuring velocity of water by means of boat and cable __ ... __ . _____________ .__ 24 

VIII. A and B, Measuring velocity of water by means of boat and cable. 

IX. Measuring velocity of water from suspended platform __ ... _ _ _ _ _ 26 

X. Gaging apparatus in position ________ .. ______ ._ . _ -- ____ . ------ 28 

XI. Price electri0 cur:r:ent meters, with buzzers __ ._ . __ . _____ .. _. _____ . 30 

XII. Apparatus for rating meters . _. _. _ _ _ _ _ _ _ _ _ _ _ . ____ . _____ .. _ .. _. 34 

FIG. 1. Diagram showing method of manipulating stay line from small 

cable .. _ .. ______ .. ___ . ______ .. ___ .. _ _ __ _. ______ . __ .. __ . _ ... __ . __ . _ 26 

2. Diagram showing method of attaching stay line to meter by use of 

small pole __ .. ___ .. _ _ _ _ _ _ _ _ _ _ _ _ . _______________ ... _ . _____ ... ___ . 27 

3. Cross section of small Price electric current meter, showing details __ ' 30 

4. Weights and weight vane of small Price e:ectric current meter_ . . . . 31 

7 

LETTER OF TRANSMITTAL. 

DEPARTMENT OF THE INTERIOR, 

UNITED STATES GEOLOGICAL SURVEY, 

DIVISION OF HYDROGRAPHY, 

Washington, D. C., July 10, 1901. 

SIR: I have the honor to transmit herewith a manuscript describing 

the methods of stream measurement in use by the Division of 

Hydrography, and request, that it be published in the series of WaterSupply and Irrigation Papers. This material has been compiled from 

various reports and letters of instruction, and is intended to embody 

not only a description of the operations but in some cases minute 

directions which may assist the hydrographers and serve to increase 

the accuracy of results. It is designed not only to assist and guide the 

hydrographers employed by the Survey; or working in cooperation 

with it, but also to exhibit as nearly as possible the degree of accuracy 

of the operations and of the computations of results. It is hoped that 

hydraulic engineers and others who may be engaged in similar lin~s 

of investigation will adopt these methods or so modify t,heir ~own 

operations that the results will be comparable with those obtained by 

this Survey. 

Very respectfully, F. H. NEWELL, 

Hydrographer in Charge. 

Hon. CHARLES D. "\V ALCOTT, 

Director United States Geolog1'cal Survey. 

9 

METHODS OF STREAM MEASUREMENT. 

INTRODUCTION. 

The object of the work herein described is to obtain data bearing 

upon the water resources of the United States. In undertaking with 

limited funds an investigation of this charact.er, it is obvious that a 

plan must be adopted which will yield useful results with moderate 

outlay. The United States is so vast and offers such diversity of 

topographic and climatic conditions that measurements of rivers in 

one section give data of little vrtlue concerning those of another section. It is therefore necessary to consider carefully the distribution 

of field work so as to obtain typical res.ults, and at the same time not 

to diffuse it so widely as to destroy its effectiveness. The chief object 

has been to lay out the operations so that there would be obtained 

results of practical value and of a reasonable degree of accuracy, 

broadly representative of conditions prevailing throughout the United 

States, without expending money for the attainment of an unnecessary degree of precision. There is of course room for wide difference of opinion regarding the best way to attain this object. In the 

pract.ice of the Survey localities have been selected where the results 

will have a local application to problems of development and at the 

same time will yie]u data which can be applied to adjacent areas 

under similar topographic conditions. 

The operations o.f the branch of the Geological Survey which has to 

do with hydrography can be divided into three distinct classes: (1) The 

measurement of surface streams; (2) the survey of sites for and the 

estimation of capacity and cost of reservoirs; and (3) the study of 

the quantity and movement of underground waters. The greater 

part of the funds available, however, is devoted to the measu;ement 

of surface streams, for those are of first importance, regarding both 

the quantity of water obtainable and its industrial application. 

The work of ascertaining the flow of a stream, as developeu by 

the experience of the Division of Hydrography, extending through 

about thirteen years, consists of (1) observing and recording the daily 

height of the water, (2) measuring the quantity of flow at different 

heights, and (3) computing the probable flow at each height or stage 

of the stream. 

The first step is to select a suitable locality for a gaging station. 

Although apparently simple, this is really a difficult task. Not only 

must the actual conditions be favorable-the water moving in nearly 

11 
12 METHODS OF STREAM MEASUREMENT. 

straight lines over a solid bed and between well-defined banks-but 

the place must be accessible at moderate cost, and there must be living near a competent person who can be engaged to serve as observer. 

Usually it is impracticable to hire a man to reinain at a locality to 

observe daily the height of the water and make occasional measurements of the volume. It, therefore becomes necessary to locate the 

station where a person of ordinary intelligence can be employed, at 

from $2 to $5 a month, to observe and note the height of the stream 

once or twice a day, and each week send to the Survey a postal card 

containing a record of these fact::;. So that in perhaps the majority 

of cases the station is located not at the most desirable place for 

obtaining the information desired, but at the best locality where a 

competent observer can be procured. 

When a suitable location has been found a gage is established, on 

which the height of the water can easily be read to tenths of a foot. 

The gage may be either a vertical or an inclined scale, fastened to a 

pier or attached to supports firmly bedded in the bank. If inclined, 

it is graduated, after setting, to vertical tenths of a foot, thus affording a magnified reading which is always at the shore line. Sometimes a wire gage is used, a weight being lowered from a bridg·e or 

overhanging support, and the distance noted along the horizontal 

scale. Whatever the device the gage should be referred to permanent bench marks and maintained without alteration. 

From time to time the engineers-or hydrographers, as they are 

termed-visit and inspect the stations and make measurements of 

the volume of flow by means of a current meter or otherwise. Many 

forms of current meter are in use. Those preierred have an electric 

appliance so arranged that· every revolution of th~ wheel causes a 

click or buzz in a .small sounder in the hand or pocket of the hydrographer. Many automatic devices have been tried, but in the long 

run this form bas proved the most satisfactory. In using it, the 

hydrographer eount,s and records in a notebook the number of repetitions of the sound during, usually, 50 seconds. The meter is placed 

in various parts of the cross section by suspending it from a boat or 

bridge,.or, more commonly, from a car in which the hydrographer 

sits, which is supported by a stout steel cable extending across the 

stream. (See Pl. I.) 

·From the occasional measurements of discharge there is constructed, 

usually by graphic means, a table showing the volume of flow for 

each tenth of a foot height of the water. From this table the discharge is placed opposite the corresponding gage height for each day, 

thus giving the fluctuations of the stream, which may be stated in 

terms of maximum, minimum, and mean for the month, or be shown 

graphically by diagrams. If the area drained be known, these results 

can be expres~ed in units of area and volume, or in depth over the 

entire catchment basin. The details regarding these measurements 

and computations are given on the following pages. 
U. S. GE.OLOGICAL SURVEY WA rER -SUPPL Y PAPER NO. 56 Pl. I 

A. 

II. 

CARS US E D IN MEASURING VELOCITY OF STREAMS. 

A. , Shenandoah River near Millvi lle, W.Va.; B, Arkansas River at Canyon, Colo. 
MEASUREMENTS OVER WEIRS. 13 

WEIR MEASUREMENTS. 

The flow of water in open channels is controlled by a variety of 

conditions due to artifieial as well as natural features, and no definite 

rule for gaging can be prescribed which will be applicable to all cases. 

The methods of operation must therefore be governed largely by 

local conditions, and should be varied as circumstances require. The 

accuracy of the results obtained is consequently dependent in no 

small degree upon the judgment exercised by the hydrographer· in 

dealing with individual cases. 

In general, measurements of the volume of flowing water in open 

channels may be classed under two heads: (1) By means of weirs or 

dams used as weirs, and (2) by determining the mean velocity and 

the sectional area for a given cross section. Using the first method, 

the discharge of the stream is computed by means of an empirical 

formula, which varies for different types of dams or weirs. On creeks 

or small rivers it is sometimes practicable to build a timber weir 

across the ehannel, causing the total flow of the stream to pass over 

the sharp edge of the weir crest. Various forms of these weirs are 

shown in Pls. II and III. By observing the head on the weir computations of the flow can be made. This is probably the most accur~te method applicable to small streams. On large rivers,- however, 

the cost of a weir is usually so great as to be prohibitive, so that if 

there is not a weir or dam already in the stream it is necessary to 

resort to measurements by floats or current meters, as described 

further on. 

On many rivers of moderate size the conditions are unfavorable for 

successfully applying either of these methods. For inst.ance, on 

streams used for manufacturing purposes dams occur at frequent 

intervals, interrupting the regular flow and in many cases holding 

back the night flow for use during the following day, so that the discharge during the night may be either nothing or a very small percentage of the day flow. Then, too, the shutting down of the mill 

wheels for an hour at noon may have a pronounced effect upon 

the results of float or meter measurements made below the mill. 

Unfortunately these variations are not always apparent to the hydrographer, and surpr~se and annoyance are caused by finding that 

the river height differs by several tenths from the gage as read by the 

regular observer possibly an hour. or two before the hydrographer 

arrived at the station. 

Frequently it is almost impossible to find a section upon a stream 

used for industrial purposes where the flow \s not interrupted by ~he 

backwater from dams below. If a station is selecte-G. at the time of 

high water this backing up of the river may not be apparent to the 

hydrographer, but at the low-water season he may find that the river 

at the station is merely a placid pond, apparently without current, 

making measurements impracticable. Examples are Blackstone 
14 METHODS OF STREAM MEASUREMENT. 

River in Massachusetts and Rhode Island and the Sandusky in Ohio . 

. If the fall of a stream is sufficiently rapid a section for meter meas.:. 

urements may be found just below one of the milldams, measurements at such points not being affected by the backwater. They 

are, however, ~ubject to all of the changes due to gate openings at 

the mills above. · 

MILLDAMS AS WEIRS. 

·Under the conditions described better results can undoubtedly be 

obtained if there exists upon t,he stream a good dam which can be 

used as a weir. It should have a level, even crest and a constant 

cross section, with sufficient pondage to reduce the velocity of 

approach, and it should be free from leakage. Masonry dams are 

better for this purpose, for they are more likely to be tight and to 

have an even crest. Timber dams although level when firRt constructed are likely to settle at various points across the st.ream, thus 

producing an uneven crest elevation. There are, however, many good 

timber dams practically free from leakage and with crests sufficient-ly 

uniform for accurate work. Pl. IV shows two dams suitable for use, 

and Pl. V shows two not suitable. for·use. 

Having selected a dam as the proper site for a station, a careful survey must be made of the crest line and of the upper and lower slopes, 

so that it can be compared with other dams or with experimental sections for which the coefficients of flow are known. The experiments of 

James B. Francis, of Fteley and Stearns, and of John R. Freeman, 

George W. Rafter, and others at Cornell University have given 

coefficients upon many sections of various forms. It is probable that 

the dam selected for the station will not be exactly like any of the 

experimental forms, but it will resemble some ·of them so closely that 

coefficients can be selected for the computations. 

When the mill gates are open a part of the flow of the stream is 

diverted from the river through the millrace, the gates, and the tailrace. Tlie amount of the diversion must of course be measured and 

added to the quantity flowing over the dam in order to determine the 

total discharge of the stream. In many factories the quantity flowing 

through the wheels varies from day to day, and also during different 

hours of the day, so that careful records must. be kept of the gate 

openings in order that proper allowance may be made for these variations. The size and the make of the water wheels must be ascertained .and the wheels be used as water meters for the determinat.ion 

of the flow through them. Many of the modern wheels have been 

carefully rated. Where such ratings have not been made, usually 

records of· wheels of the same type, though possibly of different, 

makes, can be found and the records be compared. Water wheels as 

meters give fairly accurate records of the discharge. 

It will be seen that this method of measuring the flow of streams. 

over dams and t.hrough the wheels is somewhat complicated by the 
U. S. GEOLOGICA~ SURVEY WATER-SUPPLY PAPER NO. 56 PL. II 

A. 

R. 

MEASURING WEIRS. 

A . Los Angeles Rive r, CaL; B , Cippoietti we ir on Little Cottonwood Creek, Utah. 
Sample of record blank used by United States Geological Survey for recording the flow of ~dreams ove1· dams and 

through water wheels. 

U. S. GEOLOGICAL SURVEY. 

Gaging 1·ecord kept on Schoharie Creek at the Schohm·ie Falls Dam of Ernpire State. Power Co., Mill Point, N. Y. 

For the month--, 190-. ----,Recorder. 

TWO PAIR 40-inch LEFFEL, SAMSON TURBINES. Canal Overflow 

DAY RUN. 

Crest Gage NIGHT RUN. Above Dam, Gage and Head 

feet. Waste Gates, Race TailDAY. Pair No.1. Pair No.2. Pair No.1. Pair No.2. 

feet. ~age race Ill Gage, --------- -------------

--;;:;,;:· -1·-p_·;,;.--

--------~------ Fore bay, feet. 

Number \Average ~umber Average Number Average Number Average t'eet. 

hours Gate hours Gate hours Gate hours Gate ~ -.. ~ ~. --.. -.. -.-... -- run. Opening. run. Opening. run. Opening. . a.m. p.m. 

: 

~~Opening. --

--;- (2) ___ 1· (3) 

-------- -------

(W)I(ll) ---------

(1) (4) (5) (6) (7) (8) (9) (12) (l:J) (14) (15) 1 

---~--- --- --- -=I= 1 

---- ·------- -------- --------

2 

--------- ----------------------------------

3 

-------------- --------

_ _j 4 

:- I ---------------- ----

5 I 

All gage readings are in feet and decimals. Write each reading plainly in pt·oper column. Put notes as to leakage, ice on dam, waste gate openings, etc., on back of sheet. 

[The blank bas spaces for 31 days; the above is simply a sample.] 

I 

I 

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16 METHODS OF STREAM MEASUREMENT. 

When flashboards are used records must be kept of their height and 

of the time of placing them, so that a different formula can be used 

for flow over the flash boards than for that over the broad-crested weir. 

It is customary to use Francis's formula for sharp-crested weir for eomputing the flow over the flash boards. Some of the difficulties encountered in measuring the flow of streams by using a dam as a weir are 

described in the Twenty-first Annual Report, Part IV, page 31. 

VELOCITY MEASUREl\IEN~.rs. 

The second method, and the one commonly used for determining the 

flow of streams, is that in which the area of cross section is multiplied 

by the velocity per second of the water passing through the section. 

The units commonly employed are those expressing the area of the 

cross section in square feet and the mean velocity in that cross section 

in feet per second. The velocity can be measured. by either of the 

following met,hods: (1} By means of floats; (2} by means of current 

meter or other mechanical device. 

FLOATS. 

This method is employed only when circumstances do not permit 

the hydrographer to use a cnrrent meter. If possible the site should 

be-on a straight reach having a fairly uniform cross section. The 

flow of the water should be regular, without sudden rapids or stretches 

of still water, and should exhibit no tendencies to form eddies or cross 

currents caused by irregularities in the channel or resulting from the 

effect of a, sharp bend above the reach. ~l'he course of the floats 

should have a length of from 100 to 300 feet, and the areas of the 

cross sections at the upper and lower ends of this course should be 

carefully determined by soundings. In the case of courses more than 

100 feet in length it is desirable that additional cross sections, spaced 

at equal intervals apart, should be sounded. As a preliminary step 

a base line should be laid off, by tape, on the bank, as nearly as possible parallel with the stream, and points :;hould be marked opposite 

the m·oss sections to be measured. If the stream is not too wide the 

soundings in a cross section can be taken most conveniently along a 

tagged rope stretched across the channel at right angles to the base. 

If the depth does not exceed 4 feet this can be done by wading, the 

depth being read on a rod graduat,ed to feet and tenths. Should the 

depth of the channel or the temperature of the water make wading 

impossible, a boat should be used. On large rivers, where a tag rope 

can not be employed, the boat from which· the soundings are to be 

made should be located by simple triangulation or stadia. Soundings 

should be read to tenths of a foot and be taken, preferably, at equal 

distances apart. In deep rivers a tagged rope or chain with lead 

weight can be substituted for the rod. 
U. S. GEOlOGICAL SUR '/fY WATER~SV PP LY PAPER NO. 56 PL. til 

A MEASUR ING WEIR I N GENES EE RIVER NEAR PORTAGE, N. Y. 

B . GAGING STATION ON CLEAR CREEK, WYO. 
FLOATS. 17 

• In reconnaisance work, in which the equipment is as a rule limited 

by transportat,ion facilities, surface floats consisting of chips will be 

found most convenient. The use of rod floats, though giving more 

directly the mean velocity, has many disadvantages and should not 

be attempted unless time and opportunity permit of obtaining floats of 

the required lengths. In the simplest case but one man is needed to 

make the observations. The surface floats should be thrown into the 

stream a considm·able distance above the first cross section. The 

hydrographer should att.empt to start the floats, successively, at different distances from the shore, in order to determine the velocity in 

different parts of the channel. The time of the passage of each float 

between the upper and lower cross section should be noted, preferably by a stop watch, and also the position of each float with respect 

to the tags on the ropes. This will enable the hydrographer to 

determine whether or not he succeeds in covering the different parts 

of the stream, and it will serve as an aid in the eomputation. The 

observations should be continued until all parts of the stream have 

been covered. 

On wide rivers range poles should be established on opposite shores 

to mark the upper and lower cross sections. The location of each float 

as it crosses these imaginary lines can readily be recorded by triangulation. .A light traverse plane table will be found especially useful 

in obtaining a graphic record. 

In case rod or tube floats are employed care should be taken to select 

their lengths to suit the depths of the channel. They should be 

weighted and adjusted as to depth of immersion so as to move in a 

vertical position, the bottom clearing the bed of the stream sufficiently 

to avoid contact with irregularities and the top projecting far enough 

above the water to be plainly visible. The velocity indicated by a 

rod or tube float is slightly in excess of the mean velocity of the path 

traversed, the error being mainly traceable to the distance between 

the bottom of the float and the bed of the river, the slowest velocities 

not being taken into aecount. .As a rule the error is small enough to 

be negligible in this class of work, and the velocities so obtained may 

he regarded as representing mean velocities. 

The method of gaging streams by the aid of floats can be simplified 

or elaborated according to the nature of the case and the time and 

facilities at the command of the hydrographer. 

In making the computation the area of the cross section is obtained 

by averaging the areas of all the cross sections measured, provided 

they are taken at equal distances apart. Care should be exercised 

to exclude from the computation all areas of still water along the 

shores. The float measurements should be grouped and reduced to 

form a set of velocities about equally distributed across the channel, 

and the mean of this set be taken to represent the mean surface 

IRR 56-01--2 
18 METHODS OF STREAM MEASUREMENT. 

velocity of the stream. The mean velocity for the entire stream may 

then be assumed to be 0. 8 of the former. For the average stream this 

relation is close enough for all practical purposes, provided the motion 

of the floats is not affected by wind. For that reason floats should be 

selected which while being easily discernible do not project unnecessarily above the water. 

While this method of gaging does not yield accurate results, it is 

useful in reconnaissance work. Aside from the uncertainties entering into the observations, the assumptions on which the methods of 

observation and computation are based introduce additional sources 

of error, and the method should not be used at regular gaging stations. 

CURRENT METERS. 

The mean velocity in a vertical can be determined with the current 

meter in three ways: (1) By making point measurements at a depth 

corresponding to the approximate position of the thread of mean 

velocity; (2) by deducing the mean velocity from observations made 

at other points in the same vertical; and (3) by the integration 

method. 

UNIT MEASUREMENTS. 

Studies of the vertical velocity curve made on the Mississippi by 

Humphreys and Abbot, on the Connecticut by T. G. Ellis, on the 

Merrimac flume by Wheeler and Lynch, on the Potomac by C. C. 

Babb, and recent experiments by others, notably those at Cornell 

University by E. C. Murphy, indicate that the position of the thread 

of mean veloeity in a given vertical section oceurs at a depth varying 

from six-tenths to two-thirds of the total depth of the section, 

measured from the surface down. The values found in the experiments mentioned ·were as follows: 

Depth. 

C. C. Babb -----------------------·- -------------------------- 0.58 

H urn phreys and Abbot .. ___ . ____ . __ . _ . _. _ . ___ .. _ .. ~. ______ . __ . . 63 

T. G. Ellis _____ . _____ .. _____ ... __ . . ... ________ .. _____________ .. _ . 64 

Wheeler and Lynch ______________ ~ _. ________ .. __ . _____ . _ . _ . _. . 67 

The Cornell experiments indicate that measurements made at 0. 60 

of the depth yield results 4. 7 per cent too large, the depth of mean 

velocity eorresponding more nearly with the values obtained by 

vVheeler and Lynch. In this connection it, should be noted that the 

Cornell experiments, as well as those of Wheeler and Lynch, were 

made in canals ~nd flumes, the cross sections of which have a geeater 

ratio of depth to width than those of the Mississippi, Connecticut, 

and Potomac rivers. That this difference in the ratio of depth to 1 

width is a factor likely to affect the position of mean velocity will be 

seen from the followir:g considerations: 
U. 8. GEOLOGICAL SURVEY WATER - SUPPLY PAPER NO. 56 PL. IV 

A. 

DAMS SUITAB LE FOR US E IN MEASURING FLOW OF ST RE AMS 

A, S:one dam at Holyoke , Mass. , with 2 feet of water on crest; B , dam on Hudson R1ver at 

Mechanicsvil le, N. Y. 
CURRENT METERS. 19 

It is a well-established fact that owing to the roughness of the lining of a channel, be the projections ever so minute, particles of water 

are continually deflected from the sides of the channel, the deflection 

naturally taking place in the direction of least resistance, i. e., toward 

the surface and center of the stream. This causes a constant upward 

flow along the sides of the channel, and a surface flow toward the 

center, with a tendency to lower the position of the thread of maxi..: 

mum velocity in any given vertical and in the entire stream. This 

depression of the maximum velocity is known to become more pronounced as the roughness of the lining increases. It also increases 

with the steepness of the banks and as t,he ratio of depth to width 

increases. 

In the ~:xtreme case of a wide, shallow stream, where the bottom 

merges imperceptibly into the banks, maximum velocity occurs under 

normal conditions at or very near the surface of the center of the 

stream. On the other hand, in a· deep, narrow channel, as, for 

instance, in a flume with vertical sides, maximum velocity occurs a 

considerable distance below the surface, and, as the Cornell experi-

. ments indicate, this depression may amount to as much as one-third, 

and even two-fifths, of the total depth. 

Evidently, in such cases depression of maximum velocity must 

result in a lowering of the thread of mean velocity, and hydrographers 

in making unit measurements for mean velocity should therefore 

bear in mind t)lat while observations at 0.60 depth give fair values 

for mean velocity in wide, shallow rivers, this ratio should be 

increased to 0.67 depth in the case of canals and flumes or narrow 

and deep natural channels. 

MULTIPLE MEASUREMENTS. 

The following ILethods are in use: (1) Observations at top and 

bottom; (2) observations at mid depth; (3) observations of surface 

velocity; and (4) observations at a series of points in a vertical. 

{1) By the first method measurements are made in each vertical as 

near the bottom as the construction of the meter will permit, also 

just below the surface. The mean of the results so obtained is taken 

as the mean velocity. This method should never be used except in 

streams shallow in comparison with their width. The method assumes 

that the vertical velocity curve is a straight line, a condition. which 

exists in very few streams. In all streams where the depression of 

maximum velocity is material the mean velocities obtained by this 

method are invariably too small. 

(2) The second method consists of making measurements at mid 

depth, and taking about 95 per cent of the result to obtain the mean 

velocity. This method at best is\unsatisfactory, as the velocity at mid 

depth can not be said to bear a constant relation to the mean velocity. 
20 METHODS OF STREAM MEASUREMENT. 

(3) Measurements of surface velocity are frequently the only measurements obtainable, as, for instance, in streams of great velocity 

during a flood stage, when it becomes impossible to lower the current 

meter or to maintain its position at a desired depth. In such cases 

the only course left is to measure surface velocity and deduce the 

mean velocity from it by multiplying the former by a factor. The 

error in this method is the assumption that surface velocity, or the 

velocity indicated by thA current meter just below the surface, bears 

some direct relation to the mean velocity. From the foregoing discussion it will be apparent that the assumption is not correct, and 

considerable judgment should be exercised in computing the mean 

velocity. Where from the nature of the conditions it appears that 

the surface velocity practically represents the maximum _velocity, a 

factor of 0.8 should be taken; while in case the maximum velocity 

occurs lower down, a factor of 0. 9, and even of 1.0, should be used 

to obtain the mean velocity. 

( 4) The fourth and most accurate method is to make measurements 

at regular intervals in a vertical, plotting the velocities so obtained 

on cross-secti9n paper, and determining the value of the mean velocity by dividing the area inclosed by t.he curve by the total depth. 

INTEGRATION METHOD. 

By moving the current meter uniformly in a vertical from the surface downward until the bottom is reached, then moving it upward, 

repeating the operation as often as desired, the velocit,ies in the vertical are integrated mechanically, and the mean velocity can be computed by noting the time and the number of up and down movements 

made. Care should be taken that the motion is uniform and sufficiently slow to prevent the introduction of large errors into the 

resultant velocities, due to the up or down motion of the meter. 

:;tearns's experiments indicate that in moving the Fteley meter at a 

velocity not to exceed 5 per Jent of the velocity of the current no 

material errors are introduced. The construction of the meter should 

always be taken into account in' considering or allowing for errors of 

this kind. Thus in the use of the Fteley meter a too rapid up or 

down motion causes a decrease in the velocity indicated, while with 

the Price meter, or, indeed, with any form of meter adjusted to head 

in the direction of the resultant velocity, the results will be too large. 

For both kinds of meter, however, the errors, whether negative or 

positive, will be largest in integrating low velocities. 

Aside from the method just described, integration of the entire 

cross section of a stream can be made by moving the meter obliquely 

up and down, s·tarting at one bank and proceeding across the stream. 

This method has a limited application, for in the first place the 

measurement must be made from a bridge or by wading, and in the 

second place the time of the up and down motions must be varied pro-
U. S. GEOLOGICAL SURVE) WATER -SUPPLY PAPER NO. 56 PL. V 

A 

B 

DAMS NOT SUITABLE FOR MEASURING FLOW OF STREAMS . 

.A. , Rome waterworks dam on Mohawk Rive r at Ridge Mill s, N. Y.; B , dam on Ninemile Creek at 

Stittville, N.Y. 
GAGING STATIONS. 21 

portionately to the depth, which in an irregular channel requires considerable computation. The method is employed to best advantage 

on flumes, where the depth is uniform and where a plank can be 

thrown across at any suitable point to permit the hydrographer to 

proceed gradually across the channel. 

GAGING STATIONS. 

In the selection of sites for permanent gaging stations much depends 

upon the judgment and discretion of the hydrographer. If possible 

the section selected should be in a straight portion of the channel, 

where the flow is regular and free from natural or artificial obstruction. Sections near bridges which contain accumulations of brush 

and snags in which current meters are likely to become entangled 

should be avoided, also proximity to dams, either above or below the 

station. It is important that the banks be fairly high and not likely 

to overflow except at unusually high stages of the river, and that the 

bed should exhibit no tendencies to shift or be subject to other 

changes produced by scouring out or filli~g in of sediment. 

A river channel is often obstructed by piers and cofferdams, which 

set up cross currents and render it impossible to obtain accurate 

measurements in their vicinity. In such cases other points of measurement must be selected and other means of making them be 

employed. Where the streams are deep boats are used (Pis. VI, A, 

VII, and VIII) or cables are suspended out of reach of flood water. In 

some localities boats possess a certain advantage, but where they can 

not be hired at moderate outlay it has been deemed impracticable to 

purchase and keep them, for they are likely to be injured or stolen 

during the intervals between measurements. 

It is desirable that the gage be set so that no minus readings will 

occur-the zero being placed say 1 foot below the lowest known 

stage; but information on this point obtained from the oldest inhabitants will often be found erroneous ·or unreliable, and a safe margin 

should be allowed. 

'Vhere possible two or more gages should be established at each station, 

being connected by level lines, so that the slope of the water surface 

can be read at various elevations. 

It should be borne in mind by the hydrographer in the field that 

the object is to obtain data of the most value to the public. Work 

that has only local application or is limited in scope should not be 

undertaken. In entering upon an investigation, or in preparing a 

report of the results of. the work, full information should be given 

regarding its purpose, and mention should be made of all facts which 

in any way affect its value. The simple statement that a certain 

st,ream was carrying at a specified ti!he a stated amount of water is 

in itself important, but its value can be greatly increased by the ' 

statement of additional facts, such as, for instance, the reason for 
22 METHODS OF STREAM MEASUREMENT. 

making the measurements, the character of the drainage basin above. 

and below the station, and the changes in the behavior of the stream 

which may have been produced by annual fluctuations in the run-off, 

by excessive temperatures, by artificial obstructions or diversions of 

the water, or otherwise. Facts of this character usually are well 

known to the hydrographer at the time he makes his report, and n• ay 

appear to him too trivial to mention; but it should be remembered 

that the figures which he submits will be used again and again by 

persons who do not understand the local conditions, and for that 

reason may be misapplied. 

The object of. daily observations is to procure material for the 

computation of discharge. If the conditions at a station are such that 

the readings can not be made with a reasonable degree of accuracy, 

the observations should not be continued. The difficulties may arise 

from several causes-from the irregular, shifting character of the 

channel, from the impossibility to obtain reliable gage heights and 

soundings, or from the inability of the resident hydrographer to visit 

the place at proper times and seasons. It is necessary, therefore, to 

carefully consider from time to time the advisability of maintaining 

stations already established, in order that efforts may not b.e wasted 

in continuing readings of dubious value. 

BRIDGE STATIONS. 

Because of the permanency· of their character, the small expense 

involved, and the great freedom of movement which they permit the 

hydrographer., bridges are preferred for gaging stations and for the 

making of discharge measurements. (See Pls. VI, B, and VII, A.) 

High trestles and railroad deck bridges should, however, be avoided, 

for they unnecessarily expose the hydrographer to danger. Covered 

bridges, unless provided with numerous windows, are not desirable, 

for they limit the operations. Bridges that are to be used as permanent gaging stations should .. be marked once for all, either on the 

guard timber or in some other conspicuous place, with stenciled 

figures, say 5 or 10 feet apart, indicating sections and points for 

measurement. In case a stencil is not available nails or tacks can 

be used to advantage. 

·CABLE 'STATIONS. 

Frequently it is impossible to establish a permanent gaging station 

at a bridge. In that case the wire cable of a ferry can be utilized, 

or, if that is not available, a permanent wire cable can be swung 

across the river. ·For spans of average length a galvanized wire 

cable three-fourths of an inch in diameter is safe. It should be supported on each bank by means of high struts or by passing it through 

the crotch of a tree. The cable should be run into the ground and 

anchored securely to a "dead man" buried at least 3 feet below the 
U. S. GEOLOGICAL SURVEY WATER·SUPPLY PAPER NO. 56 PL. VI 

.A. M EASURING VELOCI T Y OF WAT ER FROM FERRY BOAT, TUGALOO RIVER, NEAR 

FORT MADISON, S.C. 

B . SUSPENSION SRI DGE FOR MAKING STREAM MEASUREMENTS, N ESHAM I NY 

CREEK, RUSH VALLEY, PA. 
BRIDGE AND CABLE STATIONS. 23 

"ltrface. In the portion of the cable between the strut and the ''dead 

.1.n" a turn-buckle should be inserted so as to permit tightening the 

cable when it begins to sag. 

A few feet above the cable a wire, provided with tags 5 or 10 feet 

apart, should be stretched across the stream to serve the same purpose as the stenciled distances on the bridge already referred to. 

For this purpose the ordinary twisted barbed fence wire has been 

found yery useful, as the tags can be fastened firmly so that they will 

not slip from side to side, and barbed wire is less likely to be stolen 

than the ordinary smooth wire. · The best tags are made of metal 3 to 

4 inches wide, deeply notched so as to indicate at a glance the distance 

from the initial point. (See Pls. VII, B, and VIII.) 

A box large enough to hold two men should be constructed and 

suspended from the cable, by means of cast-iron pulley wheels, in 

such a manner that it can be run freely in either directi9n. (See Pls. I, 

IX, and X, A.) An iron or wooden bar lying horizontal and parallel 

with the cable should connect these pulleys so as to hold them apart. 

The cable should be high enough above the river so that there will be 

no danger of the box striking the water during floods. 

ROD GAGES. 

Well-seasoned timber should be selected for the construction of rod 

gages, t,he usual size being 5-inch by l-inch or 6-inch by l-inch boards, 

with at least one face planed. The rods should be graduated to feet 

and tenths, the graduations being painted in black on white ground, 

the even-foot. marks being conspicuously indicated by painted or brass 

figures. The datum used is immaterial, provided the zero of the rod 

is covered by water at even the lowest stages, so as to obviate the 

use of minus readings. Care should be taken to set the rod vertically. In case the gage is at a bridge station it will generally be 

found possible to spike it securely to an abutment or pier, where it· 

can easily be read from the shore and not be carried away by ice or 

floating debris. At cable stations the rod should be spiked to a tree 

standing in the water, "'r, if a tree is not available, it can be bolted to 

a ledge in the stream. 

Frequently it will be found best to incline the rod, if it can not 

he secured in a vertical position without danger of being swept away. 

An inclined gage should be held in place by long stakes driven into 

the ground, and no graduations should be marked on it untH it has 

been properly fastened. The slope of the rod should then be accurately determined by the aid of a surveyor's level, and the length of 

the graduations be computed on the' basis that one division on the 

rod corresponrling to 1 foot vertical is equal to the cosecant of the 

angle of inclination of the rod, in feet. It may be found more convenient to secure the .gage rod in position and then graduate it by the 

use of an engineer's level. To put the graduations on an inclined 
24 METHODS OF STREAM MEASUREMENT. 

gage, particularly on that portion extending under water, ~etal strips 

will be found most convenient. They can be nailed on without difficulty, and are more permanent than paint. 

WIRE GAGES. 

Wire gages will be found useful, especially on high bridges where 

it is difficult to read with accuracy the water level on a vertical rod 

gage or where the abutments or banks are not favorable for the erection of any other form of gage. A rod gage graduated to feet and 

tenths in the manner already described can be utilized for this pur~ 

pose, being nailed in a horizontal position along the bridge rail or 

guard timber. The fluctuations of the water leyel are noted on this 

gage by lowering a weight at,tached to a wire or chain provided with 

a pointer or marker which is made to run along the graduations of 

the rod. The position of the pointer is read on the rod when the 

bottom of the weight just touches the surface of the water. The 

movement of the weight and wire is facilitated by means of a small 

cast-iron pulley fastened to the side of the bridge. Wire gages can 

also be used in other places, as illustrated in Pl. :X:, B. 

Experience has shown the necessity of frequently testing the wire 

gages and correcting them to the original length. Great confusion is 

introduced in computations unless the gages are kept within a tenth 

of a foot or less of the correct length. When installed the gage 

should be so arranged and permanent marks be so made that the 

length of the gage can readily be tested. The description of the 

method used to accomplish this result should be written plainly, so 

that it will be understood by all concerned, and sent to the Survey, 

where copies can afterwards be obtained. 

The wire gages should be tested under as nearly as possible the 

same conditions as those under which the height of the water is 

measured, that is, with the weight hanging vertically. A substantial 

mark or stop should be so placed that the upper or lower end of the 

weight will he brought against it, and a moderate pull given to the 

wire will remove all kinks or bends. The best weights for these gages 

are the ordinary ones used for window sashes, weighing from 7 to 10 

pounds each. The weight should be attached to a flexible wire or 

chain. The most satisfactory is probably one of the composition or 

brass chains used for heavy windows, as that stretches less than a 

twisted wire. Objection to the chains, however, is found in the fact 

that in exposed positions they are more likely to be stolen than is the 

wire. E is preferable to box in the chain or wire by long narrow 

strips placed horizontally on the bridge. One of these strips can be i,'.1~ 

arranged as a cover, so that access to the wire ean be had. This ~ 

cover ean be hinged and held in place by a padloek. With such an 

arrangement the chain is usually not disturbed. 
U. $, GEOLOGICAL SURVEY WATER-SUPPLY PAPER NO. 56 PL. VII 

A MEASURING VELOCITY OF WATER FROM BRIDGE MISSISSIPP I RIVER AT ANOKA, 

MINN. ( ELLIS METER ). 

B. MEASURING VELOCITY OF WATER BY MEANS OF BOAT AND CABLE, MISSISSIPPI 

RIVER ABOVE MOUTH OF CROW WING RIVER , MINNESOTA 
BENCH MARKS. 25 

Great care should be given to joining the cord or chain and the 

weight to the handle at the other end so that there can be no slipping. The wire cord should be placed through the eye of the weight, 

bent back, and carefully wound and tied. In the same way the 

handle, if used as the index, should be fastened firmly. It is preferable, however, to place the index beyond the handle, and in such a 

way that, although perfectly firm, it can, if the wire stretches, be 

moved for the purpose of adjust,ing. Any adjustment that is made 

should be reported at once, so .that the records can be corrected. 

BENCH MARKS. 

Wherever it is intended that permanent records shall be kept it 

is of the greatest importance that the relation between the datum 

of the gage and one or more fixed points be determined. Such reference marks, generally known as bench marks and indicated by the 

symbol B.M., may consist of a United States Geological Survey standard bronze or aluminum tablet, or a. copper plug set in a drill hole in 

a rock; or, in case neither of these can be had, across cut in a ledge, 

or the head of a wire nail driven into the root or stem of a tree, will 

serve the purpose. In every instance it is desirable to have more 

than one reference mark, in order to insure against removal or accident. A surveyor's level and leveling rod should be used in determining the difference in elevation between some stated foot mark on 

the rod and the bench marks. In the case of wire gages, aside from the 

precautions just mentioned the difference of elevation between the 

water surface and the bench mark should be obtained by leveling and 

the gage reading for that particular stage be noted, frmn which data 

a permanent relation can be deduced, and a gage, if found disturbed, 

can at any time be verified and reestablished in its former position. 

Full descriptions of bench marks should be made and forwarded to 

the Survey, where they will be kept on file for future reference. 

Hydrographers are required to test, with the aid of a level, the correctness of each gage at least once a year; oftener if necessary. 

STAY LINES AND TROLLEY EQUIPMENT. 

When the velocity of the water is conAiderable-as, for example, 

more than 5 or 6 feet a second-the sounding line and meter are likely 

to be swept backward down the stream, so that it is often necessary 

to provide an additional stay line. This consists of a cable or smooth 

wire stretched across the stream from 50 to 100 feet above the bridge 

or cable from which measurements are made. A small twisted wire 

clothesline or sash cord can be used for the purpose. It should be 

anchored at both ends and supported in a manner similar to the 

main cable. On this smooth wire a small pulley is placed, which 

travels freely from side to side of the river, and from the pulley a 

small flexible cord leads diagonally downstream. This can be attached 
26 METHODS OF STREAM MEASUREMENT. 

to the end of the sounding rod, thus holding it in place; or a :ti.111:3 :r~re 

can be similarly fastened near the head of the meter, so that WHdn 

the instrument is lowered it will be prevented from being carried 

backward or tilted by the force of the current. Usually the guy line 

adjusts itself as the hydrographer moves from one side of the stream: 

to the other. 

A method of manipulating this stay line from a bridge is sho·wn 

FIG. 1.-Method of man,ipulating stay line from small cable. 

in fig. 1, in which case a small cable or stay wire is stretched across 

the river above the bridge, and a trolley or double pulley (a, b) is 

placed on it. The stay line (c) runs from the bridge to the small 

trolley (b) and back {c) to the meter (e). As the instrument is moved 

along the bridge the trolley on the cable follows the movement. The 

meter is raised and lowered by the cord d. When the ·meter is 

iwmersed in the swift water it is swept downstream and the cords are 
U. S. GEOLOGICAL .SURVEY WATI:R-SUPPLY PAPER NO. 5G Pl. VIII 

A 

B. 

MEASURING VELOCITY OF WATER BY MEANS OF BOAT AND CABL E, MISSISSIP PI 

RIVER AT ST. PAUL, MINN . 

.A , Preparing to make meter measurement; B , reeling in wire . 
U. S. GEOLOGICAL SURVEY WATER -SUPPLY PAPER NO. 56 PL. IX 

MEASURING VEl.OCITY OF WATER FROM SUSPENDED PLATF ORM , RUM RIVER 

ABOVE MILL POND AT ANOKA, MINN. 
STAY LINES AND • TROLLEY EQUIPMENT. 27 

stretched to the position a.', e', d', but by a slight adjustment the meter 

can be drawn to the desired spot. Another device is shown in fig. 2. 

A further use of stay lines has been successfully tried and adopted 

on a few streams where the conditions we1·e favorable. It is known as 

the cable and traveler method, and is described in the Eleventh Annual 

Report, Part II, page Hi. By means of a suitable number of wires and 

cords it has been found possible to hold the meter at different places 

FIG. 2.-Method of attaching stay line to meter by use of pole. 

in the stream while the hydrographer remains on the shore. 11he meter 

is run out on the main cable by means of halyards, and is lowered and 

raised by a double incandescent-light cord, or insulated wire, which · 

serves the purpose of conveying the electric current from the battery 

and instrument on shore to the meter and of acting as a suspending 

and sounding cord. The stay line just mentioned is fastened to a 

pulley which travels across the river on a .second smaller cable placed 

above the main cable. The lower end of this stay line holds the meter 
28 METHODS OF STREAM M:lASUREMENT. 

and prevents it from being swept downstream. By manipulating the 

various ropes the meter can be held in any position ln the cross sect,ion, the revolutionR being reported by an electric sounder near the 

observer. 

In the same manner soundings can be made quickly and accurately, 

the rod being held in a vertical position by the stay line, and the 

·depth, if necessary, being read from the amount of movement of the 

cords on shore, the sounding and insulated circuit cord being graduated to correspond with the marks on the sounding rod. 

With careful training and experience one man can do all of the 

work of gaging more easily, it is probable, by this method than by any 

other. As stations are at present located, however, in most of the 

basins it is necessary for the hydrographer to have an assistant, and 

even at stations which can easily be reached by rail it is found economical to employ the resident gage observer, for the few hours 

consumed in making the measurements, as helper or recorder of notes. 

At time of high water it may be difficult to count the revolutions 

of the meter, owing to the velocity of the current. It may even be 

impossible ~o keep the meter in the water, the tendency of the current being to throw it downst.ream and toward the surface. It is sometimes possible, however, to obtain a count of the revolutions of the 

rueter by means of an electric counter when the speed is several times 

greater than can be counted by the hydrographer from observation. 

OBSERVERS. 

The work of reading gages requires no special educational attainments, the main requisite being faithfulness and regularity in the discharge of the duties assigned. It is generally advantageous to employ 

persons who from long residence in the locality are familiar with the 

river and evidence an interest in the matter. The hydrographer should 

satisfy himself that the observer fully understands his duties, and he 

should spare no pains to make clear the manner of reading the rod, 

~ailing attention particularly to. the fact that the graduations are feet 

subdivided into tenths and not into inches. Instructions should be 

left with the observer, telling him how to proceed in case of accident 

to the gage, and to telegraph the fact to the hydrographer in charge 

of the station. A book (form 9-175) is furnished the observer in 

which to record each day the stage of the river and the time of the 

observation. At the end of each week he is required to fill in a mailing card (form 9-176) containing the record for the week, and send it 

to the hydrographer in charge of the station. 

'rhe blanks provided for the use of the observer have space for 

remarks. This space is iptended, as is noted at the bottom of the 

blank, for the insertion of facts concerning rain, snow, change of 

weather, and other conditions 'likely to affect the height of the stream. 

It is expected that during floods notes will be made of the rate at 

which the water rises, of the extreme height reached, and of the hour 

at which the maximum stage occurs. Observers are likely to care-
U. S. GEOLOGICAL SURVEY WATER - SUPPLY PAPER NO. 56 PL. X 

.A. 

]I. 

GAGING APPARATUS IN POSITION , BLACK FOR K OF GR EEN RIV ER NEAR 

GRANGER, WYO. 

A, Cable and car; B , wire gage. 
OBSERVERS. 29 

lessly omit memorandums of this character, and their attention should 

be ealled to the matter from time to time, for it is essential that these 

mi!lor details be noted, in order that the changes in the height of t,he 

stream. inay be interpreted correctly. 

In case of a sudden rise of the stream frequent readings should be 

made, and at the time the observer is hired he should. be instructed when 

and how often to make extra readings; otherwise in "flashy" streams 

a flood may pass between two observations without being noted. 

When practicable the resident hydrographer should arrange for the 

observer to telegraph him when an unusually high stage seems imminent, so that high-water measurements can be made. . 

rrhe remuneration paid to observers varies from $2 to $5 a month, 

according to the distance t,hey live from the place of observation and 

the ext,ent of their duties. 

The principal work of the hydrographer is the measurement of the 

streams at the stations in the district assigned to him, but his supervision of the stations should be such that he will know that the local 

observers are .careful and accurate in their readings and reports. At 

the time a station is established the reasons controlling the selection of that particular locality should be carefully recorded, and after 

the work is begun vigilance should be exercised to see that the 

records of the gage heights and the discharge measurements made 

can by proper interpretation be converted into quantities of discharge. The observer should be required to fill in th~ blanks fully 

and carefully, for these original records are preserved in the files of 

the Survey. Carelessness in forming the figures or in omitting the 

dates or other details should be promptly checked, and reports of 

that character should be copied at once and returned to the observm· 

with the request that the details lacking be supplied. 

One Qf the greatest difficulties in the work as now conducted is to 

obtain accurate and reliable reports from the observers, who are not 

at all times alive to the importance of accuracy. For this reason the 

readings of the observers should be verified occasionally, and if there 

is a well-founded suspicion that at any time heights are reported 

which are not actually observed, the observer should be reprimanded 

and if necessary the station be discontinued. It is better to discontinue a station than to have records that are open to suspicion. 

In a case where it is impracticable for the observer to make regular 

readings the fact should be noted in the report, in the "Remarks" 

column, and he should have impressed upon him the fact that it is 

· better to report that observation was not made than to attempt to fill 

in the blank by guessing at the gage height. The observer should 

also be carefully instructed regarding the best method of maki~ the 

readings, and he should. be cautioned against reading at too great a 

distance a vertical gage on a pier from a position on the bridge at 

which estimates can not be made nearer than two or three tenths. 
30 METHODS OF STREAM MEASUREMENT. 

CARE OF INSTRUMENTS. 

Hydrographers are responsible for the care of current meters and 

other instruments of the public property intrusted to them, and are 

required· to account at stated times for all such property in their 

keeping. Since the accuracy of stream gagings depends largely upon 

the correct working of the current meter, great care should be exercised in handling t.hese instrtiments and iq keeping them properly 

adjusted. Inaccurate work and poor results can be traced directly to 

neglect in caring for instruments. 

The following description aud suggestions regarding the use and 

care of the small Price electric m~rrent meter (see Pl. XI) are intended 

for the guidance of hydrographers in the field. 

Section A-A 

~': 

~-

f 

I •• ,. 1 e 

FIG. 3.-Cross section of small Price electric current meter, showing detaHs. 

When in use the meter is suspended by a double conductor cable 

of No.14 or No. 16 flexible copper wire, heavily insulated. Wire of 

that size is of sufficient strength to hold the meter and weights, 

and it obviates the necessity of additional rope for suspending the 

equipment. The cable is attached to the meter with a spring snap 

hooked into the circular end of the trunnion p, fig. 3. The heavy 

copper wires are connected with the meter binding posts hand d, fig. 

3, ~ith smaller and more flexible wires. The wire connected with 

the b,nding post , d should be threaded through the metal loops on 

the yoke o, within the trunnion frame and at g. It is desirable that 

these wires should he flexible and loose to allow the meter to swing 

free in the vertical plane when it is in use. 
U. S. GEOLOGICAL SURVEY WATER·SUPPLY PAPER NO. 56 PL. XI 

PRICE ELECTRIC CURRENT METERS, WITH BUZZERS 
CARE OF INSTRUMENTS. 31 

Lead weights (a, fig. 4} are attached to the lower end of the trunnion by means of a detachable weight stem (b, fig. 4), to hold the 

meter steady in moving water-the higher the velocity of the stream 

the greater the weight. 

The weight vane (c, fig. 4) should be attached to the weights at all 

times when the meter is used suspended from a cable. When gaging 

small or shallow streams it may be necessary to make the observations by wading. Under such circumstances it will be more convenient to dispense with the lead weights and attach the meter to a light 

rod or pole. If desired a brass standard can be supplied for attaching 

the meter to the pole. 

The meter is supported in a trunnion or hanger (p, fig. 3), and is 

free to swing in a vertical plane. One revolution of the wheel or cups 

is indicated by a buzz of the electric buzzer-the observer being 

required to count the number for a certain interval of time, preferably 50 seconds, as the computations can more easily be made from 

that number. A second obs~rvation of the same length of time should 

immediately follow the first observation, in order to verify the count. 

l 

FIG. 4.-Weights and weight vane of small Price electric current meter. 

The vertical axis (n, fig. 3) bearing the cups of the current meter, 

and hereinafter referred to as the cup shaft, terminates at the lower 

end in an invert,ed cone, which bears or turns on the cone-shaped 

point of e, fig. 3. The part marked Z, fig. 3, will be referred to as the 

point bearing. This is the most delicate part of the meter, and should 

be given the greatest care, as it is made of highly tempered steel and 

is liable to be fractured or broken. To protect this sharp point bearing during shipping or carrying the meter, a milled sleeve (k, fig. 3) 

is provided. This sleeve is threaded on the inside, and screws up or 

down on the screw thread on the extension of the lower end of the 

cup shaft shown in fig. 3. When the meter is not actually in use, and 

bef<?re putting it into the wooden case after using, see that_ the milled 

sleeve k is screwed down until it bears on the top of q and raises 

the cups and cup shaft off of the point bearing, thus protecting it 

from possible injury. It is not necessary to screw this sl(':eve down 

very tight, and if it is screwed down tight the shoulder of the journal 

on the upper end of the cup shaft will be thrust hard against the end 

of its bearing and perhaps be injured. 
. 32 METHODS OF STREAM MEASUREMENT. 

When preparing to make a measurement with the meter the milled 

sleeve should be screwed up on the cup shaft as far as it will go, so as to 

be absolutely certain that the cups are turning on the point bearing 

and are working with the least possible friction. This sleeve is milled 

for adjustment with the fingers and not· with a wrench or ~liers. 

If it becomes necessary, on account of injury, to replace the point 

bearing, an extra one will be found in the meter case. To replace the 

bearing slacken the screw i, fig. 3; with the small spanner wrench provided with the meter remove the large nut q, with the point bearing 

locked in it. After its removal hold the head of nut q firmly with a 

small wrench or pair of pliers, slip the small spanner wrench over the 

flat sides of the nutj, and loosen it. Remove the nutfwith the fingers, 

and with a small screw-driver take out the damaged point bearing from 

the large nut q. Replace the large nut q, and with the spanner wrench 

screw it firmly into the yoke o. Remove the lock nut from the new 

point bearing to be inserted, and with a screw-driver send the latter 

through the large nut q. Great care should be exercised in making this 

most important adjustment of the current meter. A slight amount of 

play or movement of the cups up and clown must be allowed, so that 

they will revolve freely and without friction. When the point is almost 

up turn it a part of a revolution at a time, with the screw-driver, 

until the proper adjustment is obtained. After the adjustment has 

been made a full turn of the point bearing in the nut q would crush 

the sharp point of the bearing e into the inverted cone of the cup 

shaft and break the point. After the point has been satisfactorily 

adjusted remove the nut q, with the point in it, put the lock nut on 

the point, and draw it down on the face of the large nut, taking care 

while turning it not to allow the point to turn in the large nut and 

thus dist.urb the ,adjustment. Should the adjustment of the meter 

be too tight the results obtained from its use will be erroneous. 

An examination of the meter when received from the Survey will 

give an idea of the proper adjustment. Do not disturb the adjustment of the meter unless it is necessary to put in a new point 

bearing. 

Section A-A, fig. 3, shows the construction of the binding post 

and coi1tact spring of the meter. A flexible, well-insulated copper wire 

(No. 20, or smaller) is drawn through the metal loop g of the yoke o _; 

the end of the wire free from the insulation is thrust into the metal 

binding post d and secured by the small set screw. This metal binding post terminates in a slender platinum spring (a), which extends 

through the hard rubber nipple c into the contact chamber, to rn. 

The 'top or upper end of the cup shaft terminates in the contact 

chamber with an oval-shaped eccentric (m.), which makes a contact with the spring a at each revolnti9n of the meter cups. This 

contact can be prolonged or shortened by bending the point of the 

contact spring in the contact chan;t.ber in the desired direction. The 

oval-shaped eccentric end of the cup shaft is detachable, and can be 
CARE OF INSTRUMENTS. 33 

removed by taking off the cap R, holding the cups firmly, and 

applying a screw-driver to the small slotted head. 

The insulating nipple c is made of hard rubber, and is likely to 

break if the binding post d receives a sharp blow. An extra insulating nipple will be found in a small tin case in the meter box. Before 

removing o{· replacing t,he binding post d, take out the eccentricshaped top of the cup shaft. If this is neglected the contact spring 

will be destroyed by the turning of the binding post. • 

In charging the battery cell used with the electric buzzer furnished 

with the current meter, one-half teaspoonful of bisulphate of mercury 

is sufficient. Fill the cell with water and insert the zinc pole with 

the rubber stopper attached. When putting the battery cell in the 

leather case be sure that the small platinum point on the lower end 

of the cell and the screw head of the rubber stopper make perfect 

contact with the copper plates. If the buzzer makes but a faint 

clicking sound instead of R buzz, remove the metal cap covering the 

buzzer, and with a knife blade adjust the small upright brass point, 

by bending until the armature produces the desired sound; Never 

allow the liquid to remain in the battery cell over night, as it will 

generate gas and produce pressure sufficient to cause the cell to leak 

at the rubber stopper, and the solution escaping will destroy the 

leather of the case and the brass parts of the buzzer. 

Care should be exercised in the use and handling of the meter that 

it does not get a fall or hard knock, thus injuring the cups or cup 

shaft. An injury to either will change the rating of the meter, and it 

should be immediately returned to the Survey for repairs. When 

using the meter in streams containing grass or moss, examine the 

instrument frequently to see that nothing has lodged or wrapped 

around the cup shaft n. 

When preparing to make a discharge measurement charge the battery cell of the buzzer; remove the meter from the case; take out the 

weights, weight stem, and vane, combine them as in fig. 4, and attach 

them to the meter with the spring pin provided; turn up the milled 

sleeve k_; and turn the cups to see that they revolve freely and that 

the buzzer responds to each revolution. ' 

After making a discharge measurement, or at the close of a day's 

work with the meter, unscrew the large nut q, with the point bearing 

in it, and examine the point caref'ully to detect injury. 'Vith a piece 

of soft cloth remove the water in the opening at the lower end of the 

cup shaft, oil generously, and replace the bearing. Then remove the 

screw cap R, turn the meter over to allow the water to run out of the 

contact chamber, put in a plentiful supply of oil, and replace the cap; 

this protects the top or journal bearing of the cup shaft from rusting. 

After this has been done turn down the milled sleeve k, to protect the 

point bearing while carrying the meter, remove the battery cell, empty 

out the liquid, wash the cell with water, and pack the meter carefully 

in the case, when it will be ready for future use.' 

IRR 56-01--3 
34 METHODS OF STREAM MEASUREMENT. 

METHODS OF RATING METERS. 

li:ach current meter when received from the factory, and subsequently when repaired, is rated by running it through still water, the 

assumption being that the same relation will hold between the turns 

of the instrument when running through still water as when held in 

one position in flowing water. This relatJ_on is obtained by fastening 

the ·metet• in a position comparable to that in which it will be held 

when in use in the stream. Thi!t is to say, if t~he meter is to be used 

fastened rigi?-ly to a rod, it is rated in that manner; if, on the other 

hand, it is to be used on the end of a flexible cord the rating is accomplished under those conditions. 

Two devices for rating meters are shown in Pl. XII. The upper 

illustration is of the equipment used by the Survey at its rating 

station at Chevy Chase, a suburb of vVashington, D. C., the lower 

picture is of the device employed at Lo~ Angeles, Cal. The apparatus used at Chevy Chase consists of a platform, about 200 feet in 

length, built along the edge of a small, dt>ep pond the waters of which 

are practically stagnant. On the outer edge of this platform are small 

iron rails, on which is placed an ordinary mine car or truck, with 

outrigger so that the meter can be held vertically over the water and 

immersed to the desired depth. On the platform a measured course 

of 100 feet is laid off, and the car is pushed by hand, care being 

taken t,o pass over every 10 or 20 feet in a uniform number of seconds, 

so that the same velocity can he maintained from start to finish. In 

the view a meter is shown suspended from the car on the right-hand 

side, and another meter is shown in the background against the door 

of the house in which the car and smaller tools are stored. 

The device used at J_.os Angeles, Cal., consists of a cement-lined 

trough along the edge of the reservoir. Above this is stretched an 

iron cable, suitably supported, on which is a trolley with two wheels, 

by means of which the meter is supported beneath the surface of 

the water. The meter is propelled through the water over a measured course, usually 100 feet, for 20 or more times in succession, the 

speed varying from less thttn 0.5 foot per second to 6 or 8 feet per 

second, or even more, the number of revolutions per hundred feet 

and t~he number of seconds being noted. Thus there is obtained the 

feet per second and the revolutions per second at different speeds. 

When these data are plotted upon m;oss-section paper it will be found 

that for higher velocities the points lie in a nearly straight line, but for 

lower velocities there is a tendency for the revolutions per second to 

deorease, owing to the slight friction in the instrument. A broken or 

somew}1at curved line is therefore sketched for the lower velocities, 

and from this curve values are taken to make the arbitrary table of 

the relation between the revolutions of the meter per second and the 

speed of the water. This table is found to be fairly constant until the 

meter becomes injured or the friction notably increases by the wearing 

away of the more delicate points of the bearings. 
U. S. GEOLOGICAL SURVEY WATER·SUPPLY PAPER NO. 56 PL. XII 

A. 

B. 

APPARATUS FOR RATING METERS. 

A , At Ch evy h~:tse, Md ~ B , at Los Ange les, Cal 
METHODS OF RATING METERS. 35 

In using current meters, especially those suspended from a cord or 

line, it frequently happens that in swift water the instrument is swept 

backward and tipped at an angle from the horizontal, either momentarily or for a considerable period of time. In order to obtain data 

concerning the reliability of results under such conditions a series of 

tests was made at the Chevy Chase rating station. A small Price 

current meter was used, being held rigidly at various angles as measured from a horizontal line. The results are given in the Nineteenth 

Annual Report, Part IV, page 27. 

At an angle of 5 degrees, with a velocity below 4 feet per second, 

the meter apparently revolves a trifle faster than when ·it is horizontal. In other words, at moderate speeds and at low inclination the 

meter· may indicate a slightly higher velocity than actually exists. 

At high speedR, however, and at a high inclination, the reverse is true, 

as the meter turns more slowly than when held perfectly parallel to 

the current,. When depressed beyond 25 degrees the resistance to the 

current approaches that offered by the tail, and the meter swings about 

in a position nearly at _right angles to the current, causing the head to 

approach the normal or zero angle. 

NOTES AND COMPUTATIONS. 

·The ordinary method of computing discharge from the observations 

is indicated by a small field notebook (form 9-198) ruled for the purpose. ':rhe velocity at each element of the section of the stream is 

ascertained by observations at yarious depths, as previously described. 

The area of each element or fraction of the section is obtained by 

multiplying the width by the'mean depth. The discharge is the product of the velocity by the area, and the discharge of the whole section 

is the sum of these products. This has been found to be, under usual 

eircumstances, the most convenient method of computation. It is 

desirable that soundings in the cross sections be made at regular 

intervals and at the sam.e points in the stream. In this way changes 

in the river bed will be noted, and if the gage is broken or displaced 

the soundings will often furnish data for an approximate computation of the mean depth for resetting the gage. 

Referring to the notebook (form 9-198), at the top of the page are 

spaces for recording the date, the name of the hydrographer, the 

.number of the meter, the locality, the height of t,he water at the 

time of beginning and ending the measurements, also the average 

height, and whether the river was rising, falling, or stationary. On 

the opposite page is space for inserting the results, i. e., the total 

.area, the mean velocity, and the total discharge in cubic feet per 

second. On the extreme left are double columns for recording the 

soundings, the first colmhn being !or the distance from the initial 

point and the second column for the depth at that particular place. 

"The following table shows the method of recording and computing 

discharge measurements in the notebook (form 9-198): 
36 ME'l'HODS OF STREAM MEASUREMENT. 

Sample page from notebook, showing method of 

Gaging made (January 26, 1898), by (E. G. Paul and G. H. Matthes). Meter 

No. (95). Gage height: beginning (7.5) ft., ending (7.6) ft.; mean (7.55} 

ft. River rising, falling, stationary. 

Soundings. Observations. 

Distance 

from 

initial 

point. 

D th Register reading. R£i6~~u- Velocity 

Depth. ~ T~me, 1-----;----,.-----1 per se~~~d. observa- secionnd"' B . E d DI'ff.l seeond. 

60 4.8 

Be~ . 5.3 

'j'Q 5.2 

75 5.3 

80 5.2 

85 5. 

90 5.4 

95 5.3 

100 5.3 

105 5.2 

110 5.4 

115 5.5 

120 5.8 

125 5. 7 

130 6.3 

135 6. 7 

140 6.4 

173 1. 7 

185 2.4 

190 3.9 

195 4.7 

200 4.8 

205 5.3 

210 5.1 

215 5.0 

220 4.9 

225 4.5 

230 4.3 

235 4.0 

240 4.0 

245 4.1 

250 3.8 

255 3.3 

260 3.0 

270 1.2 

tion. -· €'gm. n . 

50 ---------- ---------- " 33 

33 

48 

49 

64 

64 

77 

77 

36 

36 

0.66 1.60 

0.97 2.35 

1.28 3.09 

1.54 3. 72 

0. 72 1. 75 

---------- ------ ---- . -·--- ---- ------- ___ [- --------- ---------- ----------

:::::::::: :::::::::: :::::::::: ::::::::::1:::::::::: :::::::::: :::::::::: ~ ... - w- .. • --.. ------ • --- ~--- -----. - ..... - -- ----!---------- --.... -.. ---- -... ---- ---- " . " I _________ • _________ -I 88 1. 77 4. 27 

---------- -------~~-1:::::::::: ::::::::] ___ ·---~~- -------------------- 85 

85 

80 

79 

1. 70 

1.59 

. 4.10 

3.84 

--------------------- 68 1.35 3.26 

---------- -------~~- ~::::::~:: :::::::::: -------~~-~---·------ ---------- 62 

62 

50 

50 

23 

23 

1.24 3.00 

1.00 2.42 

0.46 1.12 

--------.-:- ------ -~:-1:::::: ~::: :::::::::: --------~~ -----~.-~;- -----~:~~-

" ---------- ---------- 3;\ 

------ ----·------ ---- ____ · __ ---- -----. ___ : ---------- ----------1----------

Total ____ ------ __________________ ------ ____________ .-----·------ ____________________ _ 

1 The figures in this column are the number of re,•olutions of the meter in 50 

seconds, a recorder not being used. 
NOTES AND COMPUTATIONS. 

recording and computing discharge rneasurements. 

At station (Frederick, Md.), on (Monocacy) River. Total area (808) sq. feet. 

, Mean velocity (2.90 feet). Discharge (2,342) second-feet. 

Width. 

15 

10 

10 

10 

10 

10 

15 

Section. 

Mean 

depth. 

5.15 

5.20 

5.30 

5.27 

5.37 

5. 70 

6.35 

Discharge ofArea. section. 

77.3 123.7 

52.0 122.2 

53.0 163.7 

52.7 196.0 

53.7 210.0 

57.0 266.7 

95.2 166.6 

~~~~~~~~~:'I~~~:~~~~~: ~~~~~~ :~:: :~~~ ~~~~ ~::: 22 2. 81 61. 8 263. 8 

--··------1------ ..... -··-· ----j--··-----.... . 10 4. 90 49. 0 200. 9 

10 4. 82 48. 2 157. 1 

----···--- ----------1----------------------

10 4. 27 1 42. 7 128.1 

10 4.03 40.3 97.5 

10 3.75 37.5 42.0 

15 2.45 36.7 7.0 

177 -----· ·--· 808.4 2,342.3 

Remarks. 

Edge of still water. 

Edge of still water. 

Edge of second channei. 

Edge of still water. 

37 
38 METHODS OF STREAM MEASUREMENT. 

· At all r1ver stations~ besides the bench marks for the zero of the 

gage rod, there should be chosen an initial point at which to begin all 

soundings. This initial point may be some permanent object on the 

bank, the end of a bridge, or the edge of a pier. A bench mark should 

be permanent, easily identified, and in such position that it will 

always be a short distance beyond the high-water mark. Starting 

from this initial point the soundings are usually made every 10 or 20 

feet, or, in the case of very small streams, at intervals of 5 feet. 

The first sounding should be at the edge of the water, and it·s distance from the initial point should be recorded in the notebook, the. 

sounding being registered as zero. The last sounding should be at. 

the fai·ther edge of the water, and should be noted as so many feet. 

from the initial point and as zero in depth. IE intermediate islands or· 

bars project above water the fact should be recorded in the notebook, 

also the distance of both margins from the initial point. This greatly 

simplifies the comparison of subsequent changes of depth. 

To the. right of the columns for soundings are spaces for the observations, including depth of observation, or number of feet and tenths 

below the surface of the water at which the meter is read, and the 

number of seconds, usually 50 or 100, during which the revolutions 

of the meter are noted. To the right of these are three columns for 

use in case a recording register is ·used with the meter. The first of 

these is for the register reading at the beginning of the observation, 

the second is for the reading at the end of the number of seconds 

{50, 100, or more) during which the revolutions are counted, and the 

third is for the difference between these two re.adings. In cases where. 

the revolutions of an electric meter are counted by listening to the· 

sounder, as in the sample coinputation on pages 36 and 37, the third 

column only is used. It is customary to make two observations of 50· 

seconds each at a point, and if these do not agree to make a third, 

and a fourth if necessary, continuing until it is ascertained 'vhether 

there may have been any accidental irregularity ih the behavior of 

the instrument. If these observations appear to have equal value 

the average of all is taken; if one or more are of doubtful value the 

doubtful ones are rejected. · 

The number of revolutions of the meter as recorded in the column 

of differences divided by the number of seconds gives the revolutions 

per second to be inserted in the column headed thus. Where two 

observations of 50 seconds each have been made it is necessary merely 

to add the revolutions and point off two places. • 

The observations for velocity per se.cond are usually taken not only 

at intervals across the stream but also at the top and near the bottom 

at each locality and at intermediate points. Where the stream is 

shallow it has been found that the average of the observations taken 

slightly below the surface and above the bottom at a distance where 

the meter runs freely, represents very closely the mean velocity of the 
NOTES AND COMPUTATIONS. 39 

section. In deeper streams the mean velocity of the vertical section 

can be obtained by observations at a large number of points, or by 

assuming that the measurement obtained at a distance below the surface of three-fifths of the.depth is the mean velocity, as more fully 

described on pages 18.~nd 19. Taking, therefore, the average of the 

velocities in the vertical plane as obtained in either way, it is 

assumed to represent the average velocity for a portion of the river on 

botl;l sides of t.he plane, which is taken parallel to the course of the 

stream and as extending halfway to the points of observation on each 

side. If these voints of observation are 10 feet apart t.he width of the 

section is taken as 10 feet and is entered in the proper column. 

In the case of a broad, 'smooth channel the mean depth of t.he section is taken as the d~pth of water at the place where the meter is 

run, or as an average obtained by adding the depth of water on each 

side halfway to the next point of observation, adding to this twice the 

depth where the meter is run, and diviqing the whole by four. This 

mean depth, in feet, multiplied by the width, in feet, gives the area 

of the section, in square feet. This area multiplied by the velocity per 

second, as given in the column headed thus, gives the discharge, in 

cubic feet per second, or second-feet, to be inserted in the column 

thus designated. The sum of the discharges of the various sections 

is the total discharge of the river. This is inserted at the top of the 

page. The sum of the individual areas is the total area, in square feet, 

to be inserted also at the top of the page. The mean velocity of the 

whole stream is the discharge, in cubic feet per second, divided by the 

total area thus obtained, but. it is not the average of the velocities 

per second as measured by the current meter. 

In the sections of the river adjacent to the shore special care must be 

taken in the computations, as the current is often so sluggish that the 

meter will barely revolve, and at times reverse currents creep up 

along the bank. Allowance must be made for all of these factors, 

also for still or dead water. In computing the average depth of the 

triangular sections at each end the depth at the shore is taken as 

zero, this being added to the other depths and the total divided by 

four, as in the case just described. Where the current is running. 

diagonally to the channel of the stream, allowance for that must be 

made in the width of each section. The notebook is provided with 

space, under t.he head of ''Remarks," for these details and for comments upon the accuracy of the measurement. 

In making the computations in the notebook it is undesirable to 

carry them out to a degre~ of refinement not warranted by the original 

observations; that is to say, if the meter reading is only to whole 

numbers it is a waste of time to make computations to more than one 

point of decimals, or, in fact, to employ decimals at all except as a 

safeguard against errors creeping into the last figure of the results. 

The hydrographer should occasionally look over the measurements 
40 METHODS OF STREAM MEASUREMENT. 

made during the year and determine whether or not a sufficient number have been made for the construction of a rating curve for each 

station. If either high-water or low-water measurements are lacking a special e~ort should be made to reach the station during that 

stage of the stream, so that doubtful parts o~ .the rating curve can 

be accurately constructed. One of the chief difficulties encountered 

in working up the field notes is that a number of measurements will 

be made at the ordinary flow of the stream and none during highwater and low-water stages. 

It is very important that hydrographers carefully check and revise 

all records before they are sent to the Su~vey; but if mistakes are 

found after the records have been sent to Washington a detailed 

description of them should 'at once be prepared and forwarded, so 

that the records on the books of the. Survey will be accurate and 

complete. Occasionally annoyance is caused by carelessness in this 

matter, and after computations of the discharge of a stream are 

worked up at the Survey notification is received of ei·rors in the gage 

readings, or of the displacement of the gage, which vitiates the 

records on file. 

REPORTS OF DISCHARGE MEASUREMENTS. 

The field notebooks (form ·9-198) referred to are to be retained by 

the hydrographer as long as required and ultimately forwarded to 

the Survey for preservation with other original records. In order 

to report the results as soon as possible, however, a blank (form 

9-197) has been provided which gives space for the date, the locality, 

t.he name of the hydrographer and his assistant, and for a memorandum concerning the number and page of the notebook on which the 

computations are made. Under the head "Description of river stations" is'space for a description of the location of the station, the date 

when originally established, the name and address of the observer 

and his pay, occupation, and the distance which he is required to 

travel in order to make readings, also the time of day at which the 

readings usually are made. A line is also add~d on which to record 

.the fact whether the observer is reliable and js taking a proper interest in the results of his work, and space is provided for memoranda 

concerning the equipment and the condition of any Survey property 

at the station. Attention is also called to the condition of the gage, 

and descriptive words are inserted in order that by striking out those 

not applicable the words remaining will indicate whether the gage is 

in good order or needs attention. Space is also left for comments on 

the bench ·marks, whether the initial point for sounding is on the 

1·ight or left bank, whether the channel both above and below the station is straight or curved, the water swift or sluggish; also for the 

height of the banks, whether high or low, the character of the bed of 

the stream, and similar details. Any changes in the channel shown 

by soundings should also be noted. 
NOTES AND COMPUTATIONS. 41 

Where possible two or more gages are established at each station, 

being connected by level lines, so that the slope of the water surface 

can be read at various elevations. Assuming a value of n for Kutter's 

formula of discharge, it is possible to estimate the discharge by CO!fiputation based upon the slope. This should be done and the product 

be compared with the measured result, in order that the hydrographer 

may obtain data regarding the application of such formulre and the 

value of the constant (n) to be applied in each case. 

The results of the measurement itself are to be given on the lower 

part of the blank, the first item being the height of water and its condition, whether rising, falling, or stationary, the inapplicable words 

being stricken out for the latter purpose. The total width of the channels and their number s1Iould also be given; Space is provided for an 

abstract of the field notes, giving, for important points, the distance 

from the initial point, the depth, and the mean velocity. This is for 

the purpose of showing concisely the character of the stream. It is 

not intended to insert fully all of the observations, but simply selected 

ones which will bring out essential facts most clearly. The make and 

number of the current meter used should also be given, or if measurements are made by means of floats or over a weir the fact should 

be stated. The velocHy and direction of th~ wind should also be 

recorded, as they have considerable influence upon the behavior of the 

stream. In some cases, especially in extremely hot or cold climates, 

it is alE~o desirable to have the temperature of the water and the air. 

A line is also provided on which the hydrographer should note any 

possible cause of error; and, finally, space is provided for a statement 

of the mean, minimum, and maximum velocities, the total area of the 

section in square feet, and the total discharge in s~cond-feet. On 

the back of the sheet a sketch should be made showing the position 

of the gage, the bridge, or cable from which measurements are made, 

the bench marks, the initial point of sounding, etc. Where a number 

of measurements are made in succession at one point, it is of course 

unnecessary to fill in all of the details each time; but in cases where 

the hydrographer visits a station at long intervals, and after changes . . due to floods have taken place, all of the facts should be carefully 

noted, in order to show the extent of the changes and to indicate clearly 

that certain details are unchanged. 

In reporting measurements of discharge it is not desirable, except 

in cases of exceedingly small amounts of water, to give the results to 

decimals of a second-foot, for a false idea might be given regarding 

the accuracy of the measurements. Velocities should be given in feet 

and hundredths of a foot per second, and, for uniforJTiity, the height 

of water on the gage in feet and hundredths of a foot. In state- · 

ments of this kind attention should be paid to the accuracy of the 

data. The field work should be conducted with the greatest care, 

but, on the other hand, the computations made in the office should 
42 METHODS OF STREAM MEASUREMENT. 

. not be carried out to a degree of refinement inconsistent with the 

original work. 

In work of this character aceuracy has been and always will be a 

subjeet for debate. At the outset it should be recognized that in the 

measurement of flowing water either above or under ground the preeision of ordinary engineering operations is not attainable, because 

the quantities to be measured are not fixed, but fluetuate to a notable 

extent even during the proeess of measurement. We can ascertain 

the width of a river by fixing arbitrarily two points whieh shall represent the sides, but, here an assumption comes in as to what shall be 

considered the sides, and usually there is a latitude of several feet. 

We can measure the depth if we assume some fixed object as representing the bottom. But for the top surface, even when artificially 

stilled, there is usually a pulsation ranging from 30 to 50 seconds or 

more and giving a vertical oscillation through several hundredths of 

an inch, so that judgment must be exercised in that also. When we 

come to the velocity, we have the widest. possible range, not only in 

different parts of the cross section but at the same point during successive moments, and in determining that also judgment must be 

exercised. In other words, at every step of the operation of measuring a stream certain assumptions, which may affect the total by 

from 2 to 5 per cent, must be made. 

Engineers, and especially office men, who spend most of their lives 

compiling and digesting figures, are likely to lose sight of these· primary assumptions, and in their desire for accuracy of computation to 

express results in decimal figu1·es, which, if we pause to consider 

the primary assumptions, is generally, except in the case of very 

small streams, not only ludicrous but misleading. In all questions of 

original investigation, like that of the water resources of the country, 

this element of primary assumption must eonstantly be borne in mind 

in considering the plan of work and the results ~ttained. In the practical application of the figures of flow of water above or under ground 

the taeit assumption is that the results obtained at one time will again 

prevail. If, for example, the midsummer measurements gave a 

streaJ! discharge of 100 cubic feet per seeond, engineers and others 

concerned will quote this figure and use it in their estimates, although, 

if they stop to think, they will admit that the stream may never again 

discharge an equal volume, but that the low water in other years or 

for an average of years may be greater ·or less than this one meastuement indieates. Yet there are those who will reeompute the data 

and take great satisfaction in expressing the measurement as 99.63 

cubic feet per second, when they should know not only that there is 

an error of plus or minus 2 per cent in the result, but that the stream 

may next year discharge half or twice as much at the same season. 
NOTES AND COMPUTATIONS. 43 

FLOOD ESTIMATES. 

At the highest floods, when it is impossible to use a cu~·rent meter,. 

it is desirable to make an approximate estimate of the flow. This 

can be done by noting the speed of floating driftwood and other debris 

on the water surface-by placing a certain base line' on the shore parallel to the current, and noting the time that it t,akes the drift to pass 

over a certain distance. It will generally be found that the velocity 

at the center of the stream is greater than toward the edges, and it is 

well to make estimates of the surface velocity at various points across 

the stream. From these velocities and a rough estimate of the areas 

controlled by the various velocities an approximate estimate of discharge can be made. Notes should accompany such estimations 

describing just how they were obtained, so that a false idea of the 

accuracy of the measurement will not be conveyed. Records of this 

kind are often of the greatest value to engineers and investors, in 

cases where it is not important to know within 10 or even 20 per cent 

the maximum discharge of a stream, but where it is important to 

know its discharge within 30 or 40 per cent. Many cases are on record where, without any data upon which to base an estimate, assuril.pt,ions of the maximum discharge of streams have been made which 

afterwards were found to be in err'Jr by 200 or 300 per cent. 

If it is impracticable to make even a rough estimate of the flow of 

a stream at its maximum discharge, the hydrographer should at least 

note on the bank, bridge pier, or other permanent landmark the 

greatest height to which the water rises. It is also desirable to note 

the rapidity with which it rises and falls, and other natural phenomena. 

RATING TABLES. 

The i~nmediate object of measurements made at a river station is 

the construction of a rating table, or series of tables, which shall 

show the relation for· a given length of time between the height of 

water and the quantity flowing in the stream. In order to prepare 

such a table it is of course necessary to obtain the discharge at various stages of the stream, covering the ordinary range of fluctuation. 

This is a comparatively easy task if the channel does not change. 

The simplest method of procedure in constructing a rating table is t<> 

plot upon rectangularly ruled paper each point representing the gage 

height and the discharge for a given measurement, the vertical distance 

from the bottom line being taken to represent the height of water at 

the given measurement and the distance from left to right the quantity of discharge in cubic feet per second. For convenience, the 

measurements of discharge should be numbered consecutively from 

I, the earliest, the numbers being placed opposite the points upon t,he 

rectangularly ruled paper. If there are a half dozen or more of these 

points well distributed according ~o height of water, it will usually be 
44 :METHODS OF STREAM :MEASUREMENT. 

found that they lie approximately in the path of a parabolic curve. 

This curve can be sketched through or near the points, the hydrographer, from his intimate knowledge, giving greater weight to some 

points than to others. This curve shows the relation of gage height 

to discharge for the particular times under consideration. The rating 

table is the numerical expression for the curve described. The next 

step is to read off the figures from th~ drawing, starting with the 

lowest value in the lower left-hand corner. The lowest horizontal 

line representing a tenth of a foot is followed from left to right until 

it intersects the curve, and the value represented by this distance is 

set opposite the tenth of foot taken. The line representing the next 

higher tenth of a foot is then followed out, and its length from the 

·margin at the left to the curve at the right is also obtained, and so on, 

setting opposite each tenth of a foot the corresponding value of discharge. When the table has been prepared in this way it will be 

found that there is an increasing value for the discharge, and that 

the difference between the values is also constantly increasing. 

Owing, however, to the small scale upon which such a sketch necessarily is made, the figures read off from the drawing do not always 

have this constantly increasing value, some being proportionally too 

large and others too small. In order, therefore, to smooth out the 

curve, it is convenient to set off between the lines of the rating table 

the differences in quantity of discharge, making a third column. 

Upon running the eye down this column several points are quickly 

detected where the differences are not regular. Considering these, 

it will be seen that a slight adjustment of the differences and the 

addition or subtraction of a small amount from the figures of discharge will smooth out these irregularities. This adjustment .should 

be made, and as a check upon the accuracy of the work the resulting 

figures, after the rating table has been smoothed out, sh0uld be 

plotted upon the original drawing to determine, by inspection, that 

the rating table as finally adjusted is accordant with the observations. 

This method of graphic construction avoids difficulties and liability 

to error in the use of the higher mathematics, and its accuracy is well 

within that of the original data. 

The length of time during which a rating table can safely be applied 

to the observations should be determined by the hydrographer and 

noted upon it, in order that it may not be used beyond proper limitations. Whe~e the channel is constantly shifting a table can not be 

used for many weeks or months unless it be referred to the readings 

of heights as interpreted by the occasional soundings. 

TABLES FOR COMPUTING RESULTS FOR PUBLICATION. 

The unit employed in the measurement of streams is the cubic foot 

per second. This is described in the Eleventh Annual Report, Part 

II, Irrigation, pages 2 to 5; also in the Fourteenth Annual Report, Part 
NOTES AND COMPUTATIONS. 45 

II~ pages 100 and 101. From this fundamental unit others have been 

derived, and the results of the investigation are shown in these for 

convenience of comparison. r.rhe tables formerly published give the 

maximum, minimum, and mean discharge, in second-feet, for each 

month. They also usually give the total discharge for the month, in 

acre-feet, and the run-off in two t,erms, viz, the depth in inches and 

the rate of flow in second-feet per square mile. The acre-foot of 

water is a quantity equivalent to an area of 1 acre covered 1 foot in 

depth, or 43,560 cubic feet. 

Table for converting second-feet into acre-feet pe·r day. 

Second-feet. 

Days. I 1 2 3 4 0 6 I 7 8 9 

---------------~---

I ------

Acre-ft. Acre-ft. Acre-ft. Acre-ft. Acre-ft. Acl·e-ft. ! Acre-ft. AC1·e-ft. Ac1·e-jt. 1 _____ ---- 1. 98 3.97 5.95 7.93 9.92 11. 9() I 13.88 15.R7 17.85 

2---··----- 3.97 7. 93 11.90 15.87 19.83 23. EO I 27.77 31.74 35.70 

3. ·------- 5. 95 11.90 17.85 23.80 29.75 35.70 4L65 47.60 53.55 4 _________ 7.93 15.87 23.80 31.74 39.67 47.60 55.5! 63.47 71.40 5 _________ 9.92 19.83 29.75 39.67 4i.J.59 59.50 69.42 79.3! 89.26 6 _________ 11.90 23.80 35.70 47.60 59.50 71.40 83.31 95.21 107.11 7 _____ ---- 13.88 27.77 41.65 55.54 69.42 83.31 97.19 111.07 124.96 8 .•.••...•. 15.87 31.74 47.60 63.47 7[).34 95.21 111.07 126.94 142.81 !) _________ 17.55 3.'>. 70 53.55 71.40 89.26 107.11 124.96 142.81 160.66 10 _______ ·- 19.83 39.67 59.50 79.3! 99.17 119.01 138.84 158.68 178.51 11. ________ 21.82 43.64 6.5. 45 87.27 109.09 130.91 152.73 174.55 196.36 

12 .. ------ 23.80 47.60 71.40 95.21 119.01 142.81 166.61 190.41 214.21 13 _________ 25.79 51.57 77.35 103.141 128.93 154.71 180.50 200.28 232.07 14 _________ 27.77 55.54 83.31 111.07 138.84 166.61 194.38 222.15 249.92 15 _________ 29.75 59.50 89.26 119.01 148.76 178.51 208.26 238.02 267.77 16 _________ 31.74 63.47 95.21 126.94 158.68 190.41 22'.3.15 2.53.88 285.62 17 _________ 33.72 67.44 101.16 134.88 168.59 202.31 236.03 269.75 303.47 18 _____ ---- 35.70 71.40 107.11 142.81 178.51 214.21 249.92 285.62 321. 3'.3 19 ..••...••• 37.69 75.37 113.06 150.74 188.43 226.12 263.80 301.49 339.17 

20.-------- 39.67 79.34 119.01 158.68 198.35 238.02 277.69 317.36 357.02 21 _________ 41.65 83.31 124.96 166.61 208.26 249.92 291.57 333.22 374.88 

22.-------- 23 _________ 43.64 87.27 130.91 174.55 218.18 261.82 305.45 3!9.09 392.73 45.62 91.24 136.86 182.48 228.10 273.72 319.3! 364.96 410.58 24 _________ 25 _________ 47.60 95.21 142.81 190.41 238.02 285.62 333.22 380.82 4~.43 

49.59 99.17 148.76 198.35 247.93 297.52 3!7.11 396.69 446.28 

26.-------- 51.57 103.14 154.71 200.28 257.85 309.42 360.99 412.56 46!.13 27 _________ 53.55 107.11 160.66 214.21 267.77 321.32 374.88 428.43 481.98 28 ...••.... 55.5± 111.07 166.61 222.15 . 277.69 333.22 388.76 444.30 499.83 

~--------- 57.52 11il.04 172.56 230.08 287.60 345.12 402.64 460.17 517.68 30 _________ 59.50 119.01 178.51 238.02 297.52 357.02 416.53 476.03 535.54 31. ________ 61.49 122.98 184.46 245.95 307.44 368.93 430.41 491.90 553.39 

' 

As the months are of varying length it is necessary to use three or 

four .factors to convert the average discharge for the month in secondfeet into the total in acre-feet. One second-foot flowing for twentyfour hours is equivalent to 86,400 cubic feet. Since there are 43,560 

square feet in an acre there will be the same number of cubic feet in 

an acre-foot. Dividing, it is found that 1 second-foot for twenty-four 

hours very nearly equals 2 acre-feet, or, in exact figures, 1. 9834 71 acrefeet. This multiplied by the number of days in the month will give 

the total monthly discharge in acre-feet. This quantity, therefore, 

must be multiplied by 28 for the month of February, or 29 for that 

month in leap year, arid by 30 or 31 for the other months. 

For the month of February when it has 28 days the factor to be 

used is 55.537188. For convenience in computation this fact,or multiplied from 1 to 9 is given on the following page.: 
46 METHODS OF STREAM MEASUREMENT. 

1 .. --- -- -- - - - - -- - --- - - - --- -- - -- - -- -- -- - -- -- -- -- - --- - - - - - - - - 55. 53719 

2 - . - -- - - -- -- - - -- - - - - - - - ' - - • - - - - - -- - - - - - - -- - .. -- - - - - - - - - - - - 111. 07 436 

3 - . - - - - -:. --- -- -- - - -- ---- -- -- - --- -- - - -- -- - -- - - - - - - - -.... - - - - - 166. 61154 

4 - - - - - -- -- -- - - - - ---- - . - - - - - - - -- - -. - - - - - - -- - -- . - -- - - - -- - -- - 222. 14872 

5 - - - - - - - - - -- - - -- - - - -- - - - -- - - -- - .. -- - . -- -- . -- - - - - - - - - - -- -- - - 277. 68590 

6 ------- --- --- -----:------ --- .... - ------ ------ -- ---- ---- ---- 333. 22308 

7 - -- - - -- -. -- - - - ------- -- -- -- - - -- - - - --- - . - --- - -- - -.. - - - -- - - - - 388. 76026 

8 -.--------- --- -- .. --- --- ----- --- --- ------ -----. -- . --- ---- 444. 297 44 

9 - - - - - - . - - -- - - - - - . -- .. - . - -- - - " - - - - - -- . - - - - -- - - - - - -. - - - - - - - 499. 83462 

When February has 29 days the factor to be used is 57.520659. This 

when multiplied fr<;>m 1 to 9 is as follows: 

1 - ---- ---- . - -- -- -·- -- -- ---- ------------ ------ -----. -- -. J - -- 57. 52066 

2-----------------------· --------------------------------- 115.04132 

3 ------- - .. -- -- . -- -- ------ . --- .. - ---- ---- ---- -----. -- -- -.. -- 172. 56198 

4 - - --- - .. - -- - - - - - -- -- -.. - . - - .. - . - -- - - - - - - - - . - - - -- - - - - - - - -- - 230. 08264 

5 - - - -- - - - - - - -- - - - - . - - -- - . -- --- -- - -- - - -- - . - - - - J - - - - - - - - - - - - 287. 60330 

6 ----- ---. 7--- • ----- -------- --- --------------- _._ --------- 345. 12396 

7 - --- ----- -.. --- ------ -------- - ---- . -- - ------- --- -- ... --- -- - 402. 64462 

8-- ---- -- . --- .. -- .. ------- ------ ----------- ---- ---------- 460. 16528 

9 - -- - - - - - - ---. -- -- ---- -.. - - - - - . -- . -- - -- -- - ----- -- -- - - - - - - - - 517. 68594 

Table foJ• conve1·ting second-feet into acre-feet pe1· month. 

Second-feet. 

1. ••...• ···--· ----· ·------ .2. ------------------------ .3 _____________ ------------

4 _______ ------ ·-----------

.5. ------------------ ------ 6. ·------- ---------------- 7----------- -------------- 8 ..... -------------------- 9 .••••.. ------------------ 10.------------------------ 11.-------------- ---·-· ---- 1.2.------------·----------- 13. ---------- ·----- -------- 14.------. ----· -~---- ------ 15. ---· ·--- ·----- ---------- 16.------------------------

17. -------------- ---------- 18.---------- -------------- 19 .•• ---- ·----- ------ ----·· 20.---- ------.----- -------- 21. __________ ---·---· ------

22.------------------------

.23.---------------- -------- 24 ......... ---------------- .25.-------------------- ---~ 26.-------.----------------

.27--------- ------ . --- ---·-- 28.------------------------

29.-------------- ·----- ---- 30.------.. -- --------------- 31 ....... ------------------ 32.-----... ---------- ------ 33.--------.... -------- ---- 34.-------- ·--- ------------ 35 ........... ------ ----·--· 36.------ .... -------------- 37 .•.•.•• -- -- ...... --------

38.------------------------

39 ..... ---.---------------- 40.------.. ------------.... 41. ------------------------ 42 ... ---------------------- 43.--------.---------------

44 ....... ------------------ 45. -····· --- ... ------ ·----- 46 ..... ---------- -----· ---- 47- ·----- -- .... ---- .. -----· 48 ..... -------------------- 49.-------- ---·------------ .50.------------------------

Acre-feet [Acre-feet 

per30days.,per31days. 

59.504 

119.008 

178.512 

2a8. 017 

297.521 

357.025 

416.529 

476.033 

535.537 

595.041 

654.545 

714.050 

773.554 

833.058 

892.562 

952.066 

1,011.570 

1,071.074 

1,130.578 

1,190.083 

1,249.587 

1,309.091 

1,368.595 

1,428.099 

1,487.603 

1,547.107 

1,606.612 

1,666.116 

1, 725.620 

1, 785.124 

1,844.628 

1, 904.132 

1,963.636 

2,023.140 

2,082.645 

2,142.149 

2,201.653 

2,261.157 

2,320.661 

2,380.165 

2,439.669 

2,499.173 

2,558.678 

2,618.182 

2,677.686 

2, 737.190 

2, 796.694 

2,856.198 

2,915. 702 

2,97'5.207' 

61.488 

1.2-Z. 975 

184.463 

245.950 

307.438 

368.926 

430.413 

491.901 

553.388 

614.876 

676.364 

737.851 

799.339 

860.826 

922.314 

983.802 

1,045.289 

1, 106.777 

1,168.264 

1,229. 752 

1,21H.240 

1,352. 727 

1,414.215 

1,475. 702 

1,537.190 

1,598.678 

1,660.165 

1, 721.653 

1, 783.140 

1,844.628 

1,906.116 

1, 967.603 

2,029.091 

2,090.578 

2,152.066 

2,213.554 

2,275.041 

2,336.529 

2,398.016 

2,459.504 

2,520.992 

2,582.479 

2,643.967 

2, 705.454 

2, 766.942 

2,828.430 

2,889.917 

2,951.405 

3,012.892 

3,074.380 

Second-feet. Acre-feet I Acre-feet per30days.per31day~ 

51.---------------------- 3, 034.711 

52----------------------· 3,094.215 

53----------------------- 3, 153.719 

54----------------------- 3,213. 223 

55----------------------- 3,272. 727 56--------~-------------- 3,332.231 

57----------------------· 3,391. 735 

58----------------------- 3,451. 240 

59----------·--.--------- 3, 510.744 

60- ·----- ---------------- 3,570.248 

61 ..... --------------; ~-- 3, 629.752 62----------------------- 3, 689.256 

63----------------------. 3, 748.760 

64 ----------------------- 3, 808.264: 65.---------------------- 3,867. 768 66----------------------- 3, 927.273 67----------------------- 3, 986.777 

68----------------------- 4,046.281 69 _______________________ 4,105.785 

70.---------------- ------ 4, 165.289 71_______________________ 4,224.793 

72 ----------------------- 4,284. 297 73 ----- ---·- --- ---------- 4,343. 801 

74.---------------------- 4,403. 306 

75--.-- ---.------ -------- 4, 462. 810 76----------------------- 4,522.314 77----------------------- 4, 581.818 

78----------------------- 4,641.322 

79 ------------------- --.. 4, 700.826 

80.---------------------- 4, 760.330 

81 ••••• ------------------ 4, 819.835 

82.---------------------- 4,879. 339 

83----- ------------------ 4, 938.843 

84:.-----------..... ------ 4, 998.347 

85----------------------- 5,057.851 

86----------------------. 5, 117.355 

87------- ---------------- 5, 176.859 

88----------------------- 5, 236.363 

!:!9- -------- ---· ---------- 5,295. 868 90------------------.---- 5, 355.372 

91------------------- ---- 5, 414.876 

9"Z ....... ---- ...... -----· 5,474.380 

93--------- ·- ------------ 5, 533.884 

94:.---- -~-- -------------- 5, 593.388 

95------- ------ ---- --~--- 5, 652. !:!92 

96 ------· ---------------- 5, 712.396 

97------- ---------------- 5, 771.901 

98--------- ..... --------- 5, 831.405 

9!l ....... ---------------- 5,890.909 lOU --·- .................. 5,950.413 

3,135.868 

3,197.355 

3,258.84:-3 

3,320.330 

3,381.818 

3,443.306 

3,504. 793 

3,566.281 

3,627. 768 

3,689.256 

3, 750.744 

3,812.231 

3,873. 719 

3,935.206 

3,996.694: 

4,058.182 

4,119.669 

4,181.157 

4,242.644 

4,304.132 

4,365.620 

4,427.107 

4,488.595 

4,550.082 

4,611.570 

4,ft73.058 

4, 734.545 

4, 796.033 

4,857.520 

4,919.008 

4,980.496 

5,041.983 

5,103.471 

5,164.958 

5,22£.446 

5,287.934 

5,349.421 

5,410. 909 

5,472.396 

5,533.884 

5,595.372 

5,656.859 

5, 718.347 

5, 779.834, 

5,841.322 

5,902.810 

5,964.297 

6,025. 785 

6,087.272 

6, 148.760 
NOTES AND COMPUTATIONS. 47 

:For the months containing 30 days, viz, April, June, September, 

and November, the factor to be used is 59.5041300. This when multiplied by the unit figures is as follows: 

1 ---- ----- -- ~- ---- --- -- ---- ------------ ------ ------ -- - - ---- 59. 50413 

2 - -- - --- -- - ~ ----- - - - --- - -- ---- ------ - -- - -- -- ---- --- . -- -- - - 119. 00826 

3 - -----.. --- -- --- .. -- ---- . ----- ------ -- . -- -- .. -. -- -------- 178. 51239 

4 - ... -- ---.. -- . --------- --. --- . -. --- . --- .. ------------. ---- -- 238. 01652 

5 - -- -- - - -- ~- - - - - - - - --- - - - - - --. - - - - -- -- - - -- - - -- . - - -- - - - - - -- 297.-52065 . 

6 - ---.· --- - -- -- -. -. -- -- ---- -- -- . - . - ---- --- --.. - - - -- - --- -- --- 357. 02478 

7 ----· -------- ----------- -----------·--------- ·----------- 416.52891 

8 --- ---- ----- -~ ---- .. - ---- - . -- .. - - -- -. ---- --. --- . ----. -- ---. 476. 03?04 

9 - -----. -- - . ---- -- - --- ---- -- -. - - -- -- - --- - - -- - - .. - - - - --.. - - 535. 53717 

For the months containing 31 days, viz, ~Tanuary, March, May, 

July, August, October, and December, the factor to be used is 

61.4876010. This when multiplied by the unit figures is as follows: 

1 - ---. -- .. - - --- -- -- --- - - -- ---. ---.. ------- -- -- - --- ---- - --- 61. 48760 

2 --- - ------------ ------- --- . ------.- . -- . -- -----. -- ----.. 122. 97520 

3 _._- --- ---- . -- ~----' . --- -- . - . - -. ---- -- ... ---- ---- . ----- -- - - 184. 46280 

4 - -. - - . ----- . - ---. --- --- . ---- - . --- - -- . -- -- -- . - -. -- ---- -- 245. 95040 

~ 5 - --- . - . - ... -- ----- - -- -- -- -- - - - - - - - - ---- --- - -- --- -- - -- -- - - 307. 43800 

6 - --- --.. --- . ---- - - -- -- -. - - - - - --. ---- -- ---- -- - - - - ----- - . - - 368. 92560 

7 ·_ ---. ---- -- ------ ------ ------ .. ---- ------ ... ---- ---- -- .. -. 430. 41320 

8 - . --. -. -- -.. --- - . - - . ---- -- - - ---. -- - - - - -- - --- - - - -- -- -- .. -- 491. 90080 

9--------------------------- -- ... ---------- -- ---- --.-- -. --- 553. 38841 

The run-off per square mile is obtained by simply dividing the 

average for the month by the total number of square miles in the 

drainage basin, which is us-ually ascertained by planimeter measurements from the best map available. Being a rate of flow it is independent of time, and therefore the number of days in each month 

does not enter into the ratio. 

r-rhe depth of run-off over the drainage basin is usually computed 

in inches for convenience of comparison with the dept,h of rainfaJl~ 

which is almost invariably given in that unit. This depth can most 

.conveniently be computed from the run-off per square mile by computation based upon the number of days in each month and the 

relation between the rate of flow and the depth in inches for this quantity were it held during the given number of days. One second-foot 

for twenty-four hours is equivalent to 86,400 cubic feet in one day. 

In other words, 1 cubic foot per second run-off from 1 square mile 

would, if held upon this area, cover it to a depth represented by 

dividing 86,400 by the number of square feet in a mile, 27,878,400, or 

5,280 squared. Completing this division, it is found that 1 secondfoot for one day is equivalent to a body of water covering 1 square 

mile 0.003099173 feet, or 0.037190076 inch. :Multiplying this by the 

number of days in a month gives the following factors: 

28 days ___ .. ___________________ . _ _ _ __ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ 1. OH322128 

29 days ______________ . __ .. _______ • _________ . _. ___ .. __ . __ .. 1. 078512204 

30 days ______ . _. _____ . __________ .. ________________ . ____ . 1. 115702280 

31 days ____ . ___ . _. ___ .... ·- . ________ . _______ . _ _ _ _ _ _ _ _ _ _ _ _ 1. 152892356 
48 METHODS OF STREAM MEASUREMENT. 

Table Jor converting second-feet per square mile into depth in inches per month. 

Second-feet per 28 day, s. 29 days. 30 days_·l31 days. square mile. 

L ................ . 2.----------------· 3 ................. .. 4 ......... --- ..... . 5 ................. . 

6 ...... ------------

8 7 .... _________________ --------------_ 

9 .................. . 

10 •••.•• ------------

Inches. 

1.041 

2.033 

3.12! 

4.165 

5.207 

6.248 

7.289 

8.331 

9.372 

10.413 

Inches. 

1.079 

2.157 

3.236 

4.314 

5.393 

6.471 

7.550 

8.628 

9. 707 

10.785 

Inches. 

1.116 

2.231 

3.347 

4.463 

5.579 

6.694 

7.810 

8.926 

10.041 

11.157 

Inches. 

1.153 

2.306 

3.459 

4.612 

5. 764 

6.917 

8.070 

9.223 

10.376 

11.529 

Table for converting run-off in second-feet per square mile into depth in inches per month of 30 and 31 days. 

Second- Second- Second- I 

Second1 30 

I 

feet per 30 31 feet per 30 31 feet per 30 31 I feet per 31 

square days. days. square days. ·days. square days. days. square days. days. 

mile. mile. mile. mile. 

-- Inch. Inch. Inch. Inch. Tnch. Inch. Inch. Inch. 

0.01. ...... 0.01 0.01 .60.------ .67 .69 1.19.------ 1.33 1.37 1. 78.------ 1. 99 2.05 

.02 ....... . 02 .02 . 61. ...... .68 . 70 1.20 ....... 1.34 1.38 1. 79 ....... 2.00 2.06 

.03 ....... .03 .03 .62 ....... .69 .71 1.21. ...... 1. 35 1.39 1.80 ....... 2.01 2.08 

.04 ....... .04 .04 .63 ....... . 70 .72 1.22_,. _____ 1. 36 1.41 1.81. ...... 2.02 • 2.09 

.05 ....... .06 .06 . 64.------ .71 . 74 1.2iL ...... 1. 37 1.42 1.82 ....... 2.03 2.10 

. 06.------ .07 .07 . 65 ........ . 72 . 75 1.24. -----· 1.38 1.43 1.83 ....... 2.04 2.11 

.07 ....... 1 . 08 .08 .6tL ..... . 73 .76 1.25 ....... 1. 39 1.44 1.84 ....... 2.05 2.12 

-~-------1 .09 .09 .67 ....... . 74 . 77 1.26 ....... 1.41 1.45 l, 85 ....... 1 2.06 2.13 

.09 ....... .10 .10 .68 ....... .75 .78 1.27 ....... 1.42 1.46 1.86 ....... 1 2.08 2.14 

.10 ....... .11 .12 .69 ....... . 77 . 79 1.28.------ 1.43 148 1.87 ........ 2.09 2.16 

.11 ....... .12 .13 .70 ....... . 78 .81 1.29 ....... 1.44 1. 49 1.88 ....... 1 2.10 2.17 

.12 ....... .13 .14 . 7L ...... . 79 .82 1.30 •...•.. 1.45 1.50 1.89 ....... 2.11 2.18 

.13 ....... .14 .15 II . 72.------ .80 .83 1.31. ...... 1.46 1.51 1.90 ....... 1 2.12 2.19 

.14 ....... .16 .16 . 73 ....... .81 .84 1.32 ....... 1. 47 1.52 1. 91. ....... 2.13 2.20 

.15 ....... .17 .17 .74 ....... .82 .85 1.33 ....... 1.48 1.53 1.92 ....... 2.14 2.21 

. 16 ....... .18 .18 . 75 ....... .H3 .86 1.3.4 ........ 1. 50 1.54 1.93 ....... 2.15 2.22 

.17. ----·- .19 .20 . 76 .••...• . 84 .87 1.35 ....... 1.51 1.56 1. 94. ·--·-· 2.16 2.24. 

.18 ....... .20 .21 .77 ....... .85 .89 1.36 ....... 1. 52 1.57 1. 95.------ 2.18 2.25 

. 19 .. -- --- .21 .22 . 78 ....... .87 .90 1.37 ....... 1.53 1. 58 1. 96 ....... 2.19 2.26 

.20 ....... . 22 .23 . 79.------ .88 .91 1.38 ....... 1.54 1.59 1.97 ....... 2.20 2.27 

.21. ...... . 23 .24 .80 ....... .89 .92 1.39 ....... 1.55 1.60 1.98 ....... 2.21 2.28 

.2'Z ....... .24 .25 .81. ....... .90 .93 1.40 ....... 1.56 1. 61 1.99 ....... 2.22 2.29 

.23 ....... . 26 .26 .82 ....... .91 .94 1.41. ...... 1.57 1.63 2.00 ....... 2.23 2.31 

.24 ....... .27 .28 .83 ....... .92 .95 1.42 ....... 1.58 1.64 ~.01. ...... 2.24 2.32 

.25 ....... .28 .29 .84 ....... . 93 .97 1.43 ....... 1.60 1. 65 2. 02 .• ----- 2.25 2.33 

.26 ....... . 29 .30 .85 ....... .94 .98 1.44 ....... 1. 61 1.66 • 2.03 ....... 2.26 2.34 

.27 ....... . 30 .31 .86 ....... .95 .99 1.4-5.------ 1.62 1. 67 2.04 ....... 2.28 2.35 

.28 ....... .31 .32 . 87------- .97 1.00 J :/L ............ 1.63 1. 68 2.05 ....... 2.29 2.36 

.29 ....... .32 .33 .88 ....... .98 1.01 1.'4-;" _______ 1.64 1.69 2.06 ....... 2.30 2.37 

.30 ....... .33 .35 .89 ....... .99 1.02 1.48 ....... 1.65 1.71 2.07 ....... 2.31 2.39 

J~:::::j .35 .36 .!10 ....... 1.00 1. 0! I 1.49 ....... 1.66 1. 72 2.08 ....... 2.32 2.40 

.36 .37 .91. ...... 1.01 1.05 1.50 ....... 1. 67 1. 73 2.09 ....... 2.33 2.41 

:s:::::::l .37 .38 .92 ....... 1.02 1.06 1.51.------ 1.68 1. 74 2.10 ....... 2.34 2.42 

.38 .39 . 93 ....... 1.03 1. 07 1.5:L ..... 1. 70 1. 75 2.11. ----·· 2.35 2.43 

. 39 .40 .94 ....... 1.04 1.08 1.53 ....... 1.71 1. 76 2.12 ....... 2.37 2.44 

.36 ....... . 40 .41 .95 ....... 1.05 1.09 Ui4 ....... 1. 72 1. 78 2.13 ....... 2.38 2.46 

.37 ....... .41 .43 .96 ....... 1.07 1.10 1.55 ....... 1. 73 1. 79 2.14 ....... 2.39 2.47 

.38 ....... 1 .43 .44 .97 ....... 1.08 1.12 1.56 ....... 1. 74 1.80 2.15 ....... 2.40 2.48 

.39 ....... . 44 . 45 .98 ....... 1.09 1.13 1.57 ....... 1. 75 1.81 2.16 ....... 2.41 2.49 

:!~=~==:=:1 .45 . 46 .99 ....... 1.10 1.14 1.58 ....... 1. 76 1.82 2.17 ....... 2.42 2.50 

.46 . 47 1.00 ....... 1.11 1.15 1.59 ....... 1. 77 1.83 2.18 ....... 2.43 2.51 

.42 ....... .47 . 48 1.01. ...... 1.13 1.16 1 60 ....... 1. 79 1.84 2.19 .•••••• 2.44 2.52 

.43 ..... .48 . 49 1.02 ....... 1.14 1.18 1.61. ...... 1.80 1.86 2.20 ....... 2.45 2.54 

.44 ....... .49 . 51 1.03 ....... 1.15 1.19 1.62 ...... 1. 81 1.87 2.21. ...... 2.47 2.55 

.45 ....... .50 . 52 1.04 ....... 1.16 1.20 1.63 ....... 1. 82 1. 88 2. 22 ....... 2.48 2.&5 

.46 ....... . 52 .53 1.05 .. 1.17 1.21 1.64-....... 1.83 1.89 2. 23.- --··· 2.49 2.57 

.47 ....... .53 .5! 1.06 ... ::~: 1.18 1.22 1.65 ....... 1. 84 1.!10 2.24 ....... 2.50 2.58 

.48 ....... .54 . 55 1.07 ....... 1.19 1.23 1.66 ....... 1.85 1. fl1 2.25 ....... 2.51 2.59 

.49 ....... .55 .56 1.08 ....... 1.20 1.25 1. 67 ....... 1. 86 1. 93 2.26 ....... 2.52 2.61 

.50 ....... .56 :58 1.09 ....... 1.22 1.26 1.68 ....... 1.87 1. 9± 2.27.. ..... 2.53 2.62 

.51. ...... .57 .59 1.10 ....... 1.23 1.27 1.69 ....... 1.89 1. 95 2. 28 ....... 2.54 2.63 

.52 ....... .58 . 60 1.11 ....... 1.24 1.28 1.70 ....... 1.90 1. 96 2.29 ....... 2.55 2.64 

.53 ....... .59 .61 1.12 ....... 1.25 1.29 1. 71 ....... 1.91 1. 97 2.30 ....... 2.57 2.65 

.54 ....... .60 .62 1.13 ....... 1.26 1.30 1. 72 ....... 1.92 1. 98 2.31. ...... 2.58 2.66 

.55 ....... . 61 .63 1.14 ....... 1.27 1.31 1.73 ....... 1.93 1. 99 2.32 ....... 2.59 2.69 

.56 ....... 6') . 64 1.15 ....... 1.28 1.33 1. 74 ....... 1.94 2.01" 2.33 ....... 2.60 2.67 

.57 ....... 1 .6J .66 1.16 ....... 1.29 1.34 1. 75 ....... 1. 95 2.02 2.34 ....... 2.61 2.70 

.58 ....... .64 .67 1.17 ....... 1.31 1.35 1. 76 ....... 1.96 2.03 2.35 ....... I 2.62 2. 71 

.59 ....... .65 .68 1.18 ....... 1. 3:! 1.36 I 1.77 ....... 1.97 2.04 2.36 ....... 2.63 2.72 
NOTES .AND COMPUTATIONS. 49 

Table for converting run-off in second-feet per square mile, etc.-Continued. 

i3econd- Second- 30 • Second- Secondfeet per 30 31 feet per 31 feet per 30 31 feet per 30 31 

square days. days. square days. days. square days. days. square days. days. mile. mile. mile. mile. 

-- Inch. Inch. lnch. Inch. Inch. Inch. lnch. Inch. 

2.37 .•••... 2.64 2. 73 12. 78 .•••.•. 3.10 3.21 3.19 .•••... 3.56 3.60 3.60 _______ 4.02 4.15 

2.38 .••.... 2.66 2.74 2. 79 _______ 3.11 3.22 3.20 .••••.. 3.57 3.68 3.61. ...... 4.00 4.16 

2.39 ...•.•. 2.67 2. 76 . 2.80 ....... 3.12 3.23 3.21. ••...• 3.58 3. 79 3.62 ....... 4.04 4.17 

2.40.------ 2.68 2.77 2.81. •..... 3.14 3.24 3.22 ....... 3.59 3. 71 3.63 _______ 4.05 4.18 2.41. ______ 2.69 2. 78 2.82 _______ 3.15 3.25 3.23 _______ 3.60 3. 72 3.64 ........ 4.06 4.20 

2.42 .•..... 2.70 2. 79 2.83 ....... 3.16 3.26 3.24 _______ 3.61 3. 74 3.65 _______ 4.07 4.21 2.43 _______ 2. 71 2.80 2.84 _______ 3.17 3.27 3.25 ....... 3.63 3.75 3.66 _______ 4.08 4.22 2.44 _______ 2.72 2.81 2.85 _______ 3.18 3.29 3.26 _______ 3.64 3. 76 3.67 _______ 4.09 4.23 2.45 _______ 2. 73 2.82 2.86 _______ 3.19 3.30 3.27 _______ 3.65 3. 77 3.68 .. ----- 4.11 4.24 2.46 _______ 2. 74 2.84 2.87 ....... 3.20 3.31 3.28_ ------ 3.66 3. 78 3.69.------ 4.12 4.25 2.47 _______ 2. 76 2.85 2.88 _______ 3.21 3.32 3.29 _______ 3.67 3. 79 3.70 _______ 4.13 4.27 

2.48 .••.... 2. 77 2.86 2.89 _______ 3.22 3.33 3.30 ....... 3.68 3.80 3.71. ______ 4.14 4.28 

:~.49- ------ 2.78 2.87 2.90 _______ 3.2<l 3.34 3.31. ...... 3.69 3.82 3. 72.------ 4.15 4.29 

2.50 ....... 2. 79 2.88 2.91. •..... 3.25 3.35 3.32 _______ 3.70 3.83 3. 73.------ 4..16 4.30 

2.51. ...... 2.80 2.89 2.92 ....... 3.26 3.37 3.33 _______ 3. 71 3.84 3. 74- .•••••• 4.17 4.31 2.52 _______ 2.81 2.91 2.93 _______ 3.27 3.38 3.34 ....... 3. 73 3.85 3. 75.------ 4.18 4.32 

2.53 ....... 2.82 2.92 2. 94.------ 3.28 3.39 3.35_. _____ 3. 74 3.86 3. 76 _______ 4.20 4.33 2.54, _______ 2.83 2.93 2.95 _______ 3.29 3.40 3.36 _______ 3. 75 3.87 3.77------- 4.21 4.35 

2. 5,5_- ----- 2.85 2.94 2. 96_ ...... 3.30 3.41 3.37 .•..... 3. 76 3.89 3.78 _______ 4.22 4.36 2.56 _______ 2.86 2.95 2.97 ..•.•.• 3.31 3.42 3.38 _______ 3. 77 3.90 3. 79 _______ 4.23 4.37 2.57 _______ 2.87 2.96 2.98 _______ 3.32 3.44 3.39 _______ 3. 78 3.91 3.80 _______ 4.24 4.38 2.58 _______ 2.88 2.97 2.99.------ 3.34 3.45 3.40 _______ 3. 79 3.92 3.81. ______ 4.25 4.39 

2.59 .•....• 2.89 2.99 3.00 .•..... 3.35 3.46 3.41. ______ 3.80 3.93 3.82 _______ 4.26 4.40 2.60 _______ 2.90 3.00 3. 01 .. ----- 3.36 3.47 3.42_ ------ 3.82 3.94 3.83 _______ 4.27 4.42 

2.61. ••..•. 2.91 3.01 3,02 _______ 3.37 3.48 3.43 _______ 3.83 3.95 3.84 .•..... 4.28 4.43 

2.62 .•..... 2.92 3.02 3.03 3.38 3.49 3.44 _______ 3.84 3.97 3.85 .•...•. 4.30 4.44 2.63 _______ 2.93 3.03 3.04 .••.... 3.39 3.50 3.45 _______ 3.85 3.98 3.R6 ........ 4.31 4.45 

2.64 .•....• 2.95 3.04 3.0.1)_ ------ 3.40 3.52 3.46 .. ----- 3.86 3.99 3.87.. ..... 4.32 4.46 

2. 65.------ 2.96 3.06 3.06 _______ 3.41 3.53 3.47.------ 3.87 4.00 3.88 _______ 4.33 4.47 

2.66 .•.••.. 2.97 3.07 3.07.------ 3.43 3.M 3.4,8 ______ 3.88 4.01 3. 89 _______ 4.34 4.48 

2. 67------- 2.98 3.08 3.08 ....... 3.44 3. 5.5 3.49 _______ 3.89 4.02 3.90 _______ 4.35 4.50 2.68 _______ .2. 99 3.09 3. 09.------ 3.45 3.56 3.50.------ 3.90 4.04 3.91_ ______ 4.36 4.51 2.69 _______ 3.00 3.10 3.10.------ 3.46 3.57 3.51. .•.•.. 3.92 4.05 3.92 _______ 4.37 4.52 

2.70 .••.... 8.01 3.11 '3.11 .•••..• 3.47 3.59 3.52 ......• 3.93 4.06 3.93 .•••.•. 4.38 4.53 2.71. ______ 8.02 3.12 1 3.12 ....... 3.48 3.60 3. 53_------ 3.94 4.07 3.94 _______ 4.40 4. 

2.72 ....... 3.03 3.14 3.13 _______ 3.49 3.61 3.54, _______ 3.95 4.08 3. 95. ------ 4.41 4.55 

2. 73.------ 3.05 3.15 3.14 _______ 3.50 3.62 3. 5.5. -----· 3.96 4..09 3.96 _______ 4.42 4.57 

2. 74.------ 3.00 3.16 3.15 .•..... 3.51 3.63 3.56 _______ 3.97 4.10 3.97 _______ 4.43 4.58 2.75 _______ 3.07 3.17 3.16 _______ 3.53 3.64 3.57 ....•.. 3.98 4.12 3.98 _______ 4.44 4.59 

2.76 .•••.•• 3.08 3.18 3.17 .•. --- 3.M 3. 6.1) 3.58 _______ 3.99 4.13 3.99 ....... 4.45 4.60 

2. 77 ....... 3.09 3.19 3.18 ....... 3. 5.5 3.67 3.59 _______ 4.01 4.14 4.00.------ 4.46 4.61 

INSTRUCTIONS TO COMPUTERS. 

GAGE HEIGHTS. 

A careful inspection of tabulated gage heights frequently will 

reveal errors made in reading t .... e rod or subsequently introduced by 

transcribing, which on the face·of them are incongruities or physical 

impossibilities. For example, take the accompanying table of the 

low-water flow of Coosa River at Rome, Ga., during part of the month 

of October, 1899. An inspection will reveal at once that the gage 

October, 1899. height for October 11 is to be viewed with suspicion. 

L ....... 0

·

40 Although a sudden rise of 1.30 feet in twenty-four hours 

2 •••• ---- . 30 

3________ .30 might be expected, at this low stage of the river a drop of 

4-------- ·

30 1 foot in the next twenty-four hours would be a very 5 •••• ---- . 30 

6________ 50 improbable occurrence. Upon looking up the original 

7-------- · 70 record it will be found that the correct gage height for that 

8........ . 70 d . 1 f 9________ .so ay Is oot. -

Io ________ .oo In working up gage heights and records of discharge 

~::~::::: 1:: measurements computers should always be on their guard 

13 ••••••••. 70 for errors -of this nature, although the data bear check 

~:::::::: :~ marks or initials indicating revision. In cases of this kind 

16 ......... oo the stage and locality of the river should be taken into 

IRR56-01-4 
50 METHODS OF STREAM MEASUREMENT. 

account, for a fluctuation similar to that just illustrated would be 

quite characteristic of the river at a higher stage, say during the 

spring-flood season; or, again, it would be entirely compatible with 

the erratic behavior of streams in the arid regions, as, for instance, 

Queen Creek, Ariz., at any season of the year. Many errors in gage 

reading are due to observers mistaking feet for tenths or tenths for 

hundredths. A careful scrutiny of the general behavior of the stream 

and. the exercise of a little judgment will often be found fruitful in 

determining the true relations. 

RATING TABLES. 

Rating tables should be made in all respects complete. They should 

contain the discharges for the lowest as well as for the highest gage 

heights occurring during the period to which they are applicable. If 

the gage at a station has been read to tenths of a foot only, the discharge in the rating table should be given for every tenth, and where 

gage readings are carried out to hundredths of a foot the rating table· 

should give values for each half tenth. In applying rating tables of 

the latter class the gage readings are mentally reduced to the nearest 

half tenths and the corresponding discharge values are taken from 

the rating table. This applies to all rivers and creeks, with the 

exception of small streams and canals the observations on which have 

•been made with special care, in which cases the rating tables should 

be constructed to furnish values for single hundredths. 

In constructing rating tables great stress is laid on the necessity of 

avoiding the occurrence of negative second differences. The increments of the differences between the discharges of successive increasing· gage heights may vary from a given quantity down to zero, as in 

the case of a rating curve changing into a straight line, but in no 

instance should the values of these increments or second differences 

become negative, implying the occurrence of a reverse curve in any 

portion of a rating curve. Although theoretically not impossible, the 

occurrence of a reverse curve is only admissible under certain peculiar local conditions existing in the stream channel at or near the 

gaging station, eonditions which are generally avoided in establishing 

stations. 

AVERAGES, RUN-OFFS, ETC. 

Great care should be exercised in obtaining the mean monthly flow 

in second-feet to divide the total for a month by the actual n'lllmber 

of dc.tys recorded in that month, i.e., not necessarily by the total number of days in the month, 28, 29, 30, or 31, as the case may be, but by 

the number of days for which the gage heights are given. Omissions 

in gage readings, due to a variety of causes, give rise to frequent gaps 

in the records, and these should not escape the attention of the 

computer. From the monthly means or averages so obtained are com-
NOTES AND COMPUTATIONS. 51 

puted the run-off per square mile, the run-off, in inches, on the watershed, and the total number of acre-feet for the month. In case of 

fractional months or incomplete records the monthly average should 

be treated as the average for a full month whenever the character of 

the partial record is such as fairly to represent the flow of the river 

during the entire month. 

Thus an incomplete record of flow for a month during the low-water 

season may in most cases, without appreciable error, be given the 

weight of a full recorCi, and the average run-offs and acre-feet be 

treated accordingly. On the other hand, a gap of six days in the 

record for a high-water month may frequently mean the omission of a 

large flood, perhaps too large to be measured and recorded, and the 

amount of water discharged during those six days may have equaled 

the total discharge of the river for the remainder of the month. Considering the mean of such a record as the mean for the entire month 

would evidently introduce here an error of 100 per cent. In such a 

case the proper method of procedure is to compute the run-offs and 

acre-feet for the exact number of days recorded, and insert a footnote stating the number of days that they represent. 

Again, four or five readings taken at intervals during a winter 

month, when the river is partly frozen and its flow practically devoid 

of material fluctuations, will be ample upon which to base general 

figures of run-offs and acre-feet. The mean in such ·a case, however, 

will not be the arithmetical mean of the four or five records available, 

but an approximation, in round numbers, to that arithmetical mean. 

Such a figui'e should always be·accompanied by a footnote stating 

that it is approximate. 

0 

.1