wide and one foot deep with a current speed of six feet a second, or six feet wide and two feet deep with a current speed of onehalf foot per second, or three feet wide and one foot deep with a current speed of two feet a second, or in any other ratio giving the same total product. The total flow will of course be the same, whether measured at a narrow, contracted point of large velocity or at a point where the current is wide, deep and sluggish.

This method is applicable to streams of any size from the largest rivers down, except very small ditches and brooks, and gives reasonably accurate results (with an error rarely as much. as five per cent) if the stream is flowing in a good straight channel with even and unobstructed flow. It may be used from a bridge, from a small car running on a cable stretched across the river, from a boat, or in a small stream by wading, provided in these last cases that some means is used for holding the meter upstream from the observer, so that it will not be effected by the eddies caused by his feet or by the boat.

This method of measurement can be accurately employed on any artificial channel of appropriate form, such as a ditch or canal, if the speed is sufficient to turn the meter-wheel freely. If the channel is a timber flume or other form not liable to be changed, eroded or obstructed, a careful determination can be made once for all of the quantities of water flowing for various depths in the flume. In large irrigation canals it is a frequent custom to install rating flumes, timber-lined sections of a few rods in length; the side of such a flume is marked at each possible height of water surface with a number indicating the quantity of water flowing when the water rises to that height in the flume. It is then an easy matter for the ditch-rider or gatetender to keep a continuous daily record of the total flow.

In a natural channel, if there are no dams or other obstructions for a considerable distance below the point of measurement and if other conditions are suitable, it will be found that the same amount of water flowing causes always almost the same height of water-surface in the channel, so that, after a series of such measurements of second-feet discharge at different stages of water, a rating-table can be prepared showing with fair precision (say within five per cent) the probable flow for any height of water. It is such representative points that the United States Geological Survey selects for the location of gauging stations. At these stations a vertical gauge rod painted in feet and frac

tions is placed in the water at a bridge pier or at the river margin, or other suitable device is installed, by means of which the height of the water surface may be accurately seen and recorded daily by a local observer. These observations are reported regularly to a district hydrographer who visits the stations from time to time to take soundings, velocity measurements, etc., for the purpose of finding the amount of flow corresponding to different heights of water on the gauge, and thus finally computing the total amount of water flowing down the stream in a year, and the greatest, least, and average flow for each month.

The United States Geological Survey has commenced in this state, chiefly within the past two years, since popular interest in irrigation has arisen here, a comprehensive system of stream measurements of this nature, gauging stations having been established on all the principal streams. At present one of the faculty of the University of North Dakota is the engineer in immediate charge of that branch of work for North Dakota and Minnesota.

The second, or weir-measurement, method affords still more accurate results when the conditions are favorable. A weir is a dam or small barrier with level crest over which the water flows. The depth of water on the crest evidently will be greater for a greater flow, and experiment has shown that the relation between

them can be stated in definite figures if the weir is properly constructed. There are two forms of weir most frequently used, although special circumstances sometimes make other forms more convenient. The rectangular weir has vertical ends; the trapezoidal or Cippoletti weir, as shown in the illustrations (figures 6,

7, and 8) widens above the crest, each end sloping outward one inch in every four inches rise; the second pattern has the simpler formula for computation of flow.

In using the ordinary weir, it should be placed in the middle of the channel at right angles to the stream with its up-stream face in a vertical plane. The crest should be chamfered so as to slope downward on the lower side with an angle of not less than thirty degrees, leaving a sharp edge over which the water can leap freely without retardation by friction, or better still a stiff sheet of thin metal may be placed vertically to form the edge, and the ends should be chamfered likewise. The air thus

has free access under the falling water. In the pond caused by the weir, the water will be brought nearly to rest, and must approach the crest evenly and without cross-currents; this requires that the approaching channel should be straight and even and be at the weir more than twice the depth and at least three times the width of the jet passing over. The length of the weir opening should be three or four times the depth of the jet at the time of the greatest flow.

If the length of the crest of the weir, L, and the depth of water on (or rather, height of the water surface above) the crest, H, be measured in feet and decimals of a foot, the number, Q, of cubic feet of water per second flowing over a rectangular weir can be computed from this formula,

Q=3.33 (L-0.2 H)H√H

and over a Cippoletti weir

Q=3.37 L HVH

The height above the crest of the weir of the level watersurface a few feet behind the weir may be readily found without level or other instrument thus: When the water is first filling

the channel behind the weir, if a stake be driven in the water with attention that the top of the stake be exactly at the water surface at the instant that the water begins to flow over the crest, the subsequent depths of water over the top of this stake will be the required heights.

The formula for the flow is not a complicated one, and for a trapezoidal weir may be expressed in words, "multiply the square root of the depth above the crest by three and three-eighths times the product of the depth and the length of the crest, all being expressed in feet and decimals." But tables are prepared for all the standard sizes of weirs, and may be prepared for any with a few hours work, that give at a glance the amount of flow for each depth of water.

Convenient dimensions for weirs according to the expected amount of flow are given in this table:

For a discharge less than two-thirds second-foot make crest of weir one foot long.

For a discharge between two-thirds and two second-feet make crest of weir one and one-half feet long.

For a discharge between two and four second-feet make crest of weir two feet long.

For a discharge between four and ten second-feet make crest of weir three feet long.

For a discharge between ten and twenty second-feet make crest of weir four feet long.

For a discharge between twenty and forty second-feet make crest of weir five feet long.

Weirs are advantageous for use in canals and ditches whereever sufficient fall can be afforded so that the water leaps freely over the crest without interference from backwater. They are often placed permanently in such cases, for variation in the amount of water flowing in a canal while in use is not great, hence the weir may be small enough to measure accurately the minimum flow, and yet be able to carry the greatest usual flow. In a natural stream, and especially in small streams, the seasonal variations are likely to be greater, and therefore any particular weir will be available for use only at certain stages; while on large streams the cost of constructing a weir would be disproportionately great. Sometimes there are water-power dams on such streams that have level crests and are otherwise so constructed as to permit such measurements; for, although they are not usually sharp-crested as required above, there are suitable form