HYDRAULICS.] HYDROMECHANICS 505 diminish. The one channel gradually absorbs the whole of the water supply, while the other branches silt up. Bui as the mouth of the new main channel extends seaward the resistance increases both from the greater length of the channel and the formation of shoals at its mouth, and the river tends to form new bifurcations AC or AD (fig. 135), and one of these may in time become the main channel of the river. 122. Field Operations preliminary to a Study of River Improve ment. There are required (1) a plan of the river, on which the positions of lines of levelling and cross sections are marked ; (2) a longitudinal section and numerous cross sections of the river ; (3) a series of gaugings of the discharge at different points and in different conditions of the river. Longitudinal Section. This requires to be carried out with great accuracy. A line of stakes is planted, following the sinuosities of the river and chained and levelled. The cross sections are referred to the line of stakes, both as to position and direction. To determine the slope of the water surface great care is necessary. 123. Cross Sections. A stake is planted flush with the water, and its level relatively to some point on the line of levels is determined. Then the depth of the water is determined at a series of points (if possible at uniform distances) in a line starting from the stake and perpendicular to the thread of the stream. To obtain these, a wire may be stretched across with equal distances marked on it by hang ing tags. The depth at each of these tags may be obtained by a light wooden staff, with a disk-shaped shoe 4 to 6 inches in diameter. If the depth is great, soundings may be taken by a chain and weight. To ensure the wire being perpendicular to the thread of the stream, it is desirable to stretch two other wires similarly graduated, one above and the other below, at a distance of 20 to 40 yards. A number of floats being then thrown in, it is observed whether they pass the same graduation on each wire. For large and rapid rivers the cross section is obtained by sound ing in the following way. Let AC (fig. 136) be the line on which soundings are required. A base line AB is measured out at right angles to AC, and ranging staves are set up at AB and at D in line with AC. A boat is allowed to drop down stream, and, at the moment it ?omes in line with A D, the lead is dropped and an ob- server in the boat takes, with ^. a box sextant, the angle AEB subtended by AB. The sounding line may have a weight of 14 lt> of lead, and, if the boat drops down stream slowly, it may hang near the bottom, so that the observation is made instant ly. In extensive surveys of the Mississippi observers with theodolites were sta tioned at A and B. The theo dolite at A was directed to wards C, that at B was kept on the boat. When the boat came on the line AC, the observer at A signalled, the sounding line was dropped, and the ob server at B read off the angle ABK. By repeating observations a number of soundings are obtained, which can be plotted in their proper position, and the form of the river bed drawn by connecting the extremities of the lines. From the section can be measured the sectional area of the stream ft and its wetted perimeter x ! an d from these the hydraulic mean depth m can be calculated. 124. Measurement of the Discharge of Rivers. The area of cross section multiplied by the mean velocity gives the discharge of the stream. The height of the river with reference to some fixed mark should Vie noted whenever the velocity is observed, as the velocity an 1 area of cross section are different in different states of the river. To determine the mean velocity various methods may be adopted ; and, since no method is free from liability to error, either from the difficulty of the observations or from uncertainty as to the ratio of the mean velocity to the velocity observed, it is desirable that more than one method should be used. INSTRUMENTS FOR MEASURING THE VELOCITY OF WATER. 125. Surface Floats are convenient for determining the surface velocities of a stream, though their use is difficult near the banks. The floats may be small balls of wood, of wax, or of hollow metal, so loaded as to Iloat nearly flush with the water surface. To render them visible they may have a vertical punted stem. In experi ments on the Seine, cork balls If inches diameter were used, loaded to float flu>h with the water, and provided with a stem. In Captain Cunningham s observations at Roorkec, the floats were thin circular disks of English deal, 3 inches diameter and J inch thick. For observations near the banks, floats 1 inch diameter and inch thick were used. To render them visible a tuft of cotton wool was used loosely /ixcd in a hole at the centre. Fig. 136. B D 4- The velocity is obtained by allowing the float to be carried down, and noting the time of passage over a measured length of the stream. If v is the velocity of any float, t the time of passing over a length I, then v . To mark out distinctly the length of stream over which the floats pass, two ropes may be stretched across the stream at a distance apart, which varies usually from 50 to 250 feet, accord ing to the size aud rapidity of the river. In the Rooikee experi ments a length of run of 50 feet was found best for the central two- fifths of the width, and 25 feet for the remainder, except very close to the banks, where the run was made 12 feet only. The longer the run the less is the proportionate error of the time observations, but on the other hand the greater the deviation of the floats from a straight course parallel to the axis of the stream. To mark the precise position at which the floats cross the ropes, Captain Cun ningham used short white rope pendants, hanging so as nearly to touch the surface of the water. In this case the streams were 80 to 180 feet in width. In wider streams the use of ropes to mark the length of run is impossible, and recourse must be had to box sex tants or theodolites to mark the path of tire floats. Let AB (fig. 137) be a measured base line strictly parallel to the thread of the stream, and AA 1( BB X lines at right angles to AB marked out by ranging rods at A l and Bj. Suppose observers stationed at A and B with sextants or theodo- lites, and let CD be the path of any float down stream. As the float ap proaches AA 1; the observer at B keeps it on the cross wire of his in strument. The observer at A observes the instant of the float reaching the line AAj, and signals to B who then reads off the angle ABC. Similarly, as the float approaches BB ]; the ob server at A keeps it in sight, and when signalled to by B reads the angle BAD. The data so obtained are suf ficient for plotting the path of the float and determining the distances AC, BD. The time taken by the float in pass ing over the measured distance may be observed by a chronograph, started as the float the lower. ^ meters were sometimes used, the lime of passing one end of the run being noted on one, and that of passing the other end of the run being noted on the other. The chronometers were compared im mediately before the observations. In other cases a single chrono meter was used placed midway of the run. The moment of the floats passing the ends of the run was signalled to a timekeeper at the chronometer by shouting. It was found quite possible to count the chronometer beats to the nearest half second, and in some cases to the nearest quarter second. 126. Sub-surface Floats. The velocity at different depths below the surface of a stream may be obtained by sub-surface floats, used precisely in the same way as surface floats. The most usual arrange ment is to have a large float, of slightly greater density than water, connected with a small and very light surface float. The motion of the combined arrangement is not sensibly different from that of the large float, and the small surface __/^%__ float enables an observer to note the W ;Mj|gp== path and velocity of the sub-surface : ~ float. The instrument is, however, not free from objection. If the large submerged float is made of very nearly the same density as water, then it is liable to be thrown up wards by very slight eddies in the water, and it does not maintain its position at the depth at which it is intended to float. On the other hand, if the large float is made sen sibly heavier than water, the indicat ing or surface float must be made rather large, and then it to some ex tent influences the motion of the submerged float Fig. 138 shows one form of sub-surface float. It con sists of a couple of tin plates bent at a right angle and soldered together at the angle. This is connected with a wooden ball at the surface by a very thin wire or cord. As the tin alone makes a heavy submerged float, it is better to attach to the tin float some pieces of wood to diminish its weight in water. Fig. 139 shows the form of submerged float used by Captain Cunningham. It consists of a hollow metal ball connected to a slice of cork, which serves as the surface float. XT - C>A Fig. 137. at passes the upper rope or line, and stopped when it passes r. In Captain Cunningham s observations two chrono-
Fig. 138.
