It will be noticed that the coefficient differs even less from the curve than of my own meters. Beyond the velocities given in this table there are a few observations, and they plot on each side of a tangent to the ellipse drawn through the intersection of the minor axis, showing apparently that the coefficient follows a straight line in greater velocities than are given by the curve. This meter having been tested by a measured amount of water passing it in a given time, makes this coincidence of its coefficient with the curve quite important, as it in a measure proves the corrections of the still water observations, and also the general application of this method to the computation of the coefficient of all meters, though I have not as yet been able to obtain the observations made by other engineers. M. Morin says in this connection, "If certain engineers in using instruments of this kind have found that the relation between the velocities and number of revolutions should be represented by a curved line of the parabolic form, it comes no doubt from the fact that in the instruments they used the friction notably increased with the velocity." But when the appliances are light and the surfaces of the blades of the screw are sufficiently large, as in the meter we have been examining, the friction will remain very small and then the number of revolutions will increase proportionally to the velocity. I also do not think that the experiments which have furnished results different from those of M. Lapointe have been as extended, nor made with a precision comparable to the observations of this engineer. As will be seen from the tables above, the Lapointe meter stops at a velocity of 1.5 foot per second, while the float meter moves at 0.3 foot per second. M. Dubuat gives the resistance of a sphere as 0.35 of that experienced by its great circle when drawn through still water; and Beaufoy with velocities from two to twelve feet per second found the resistance to vary from 0.325 to 0.359, giving a mean of 0.342. It was upon these results that Robinson constructed his anemometer, now so generally used in meteorological observations, in which he called the velocity of the cups one-third that of the wind moving them. Obtaining the same ratio of resistances from the observed revolution of the float meter, given in table II, we find for the mean of the whole 0.360, which is nearly the same as that above, while for the velocity of 4.5 feet per second it is only 0.189; therefore the velocities given by the anemometer when the wind is blowing over two or three miles an hour will be much too small. To test the corrections of the coefficient, the float meter was compared with floats in a small canal at Ogdensburg, conveying water from the dam to certain mills. A straight reach was chosen below the dam and above the mill sluices so as to have the minimum of disturbance. Wires were stretched across the canal 200 feet apart, and the time of passage of the floats past the wires was telegraphed to the recorder, who had a chronometer before him and noted the time to the nearest tenth of a second. The floats were run at mid-depth of the canal and as nearly in the center as possible, and the meter was run continuously at the same depth midway between the wires. The wind was quite strong in the direction contrary to the flow of the water in the canal during all the observations, but its force being broken by the surrounding buildings, the effect upon the floats was very small. TABLE IV.-Showing the comparison between the floats and meter in the canal at Ogdensburg. From this it will be seen that the difference between the mean velocity, as determined by the floats and the meter, is small, though the range of velocities, as given by single floats, is quite large. I have not as yet been able to test the coefficient of the meter by measuring the quantity of water passing it in a given time, though the observations on Lapointe's meter, given above, seem to show the corrections of the general curve. The following table shows the comparison between the meter and floats at different depths taken in the St. Clair River: The floats were run past the same base line and in the same manner as in the previous year. (Report 1867-28.) TABLE V.-Comparison of floats with Saxton's meter No. 2, in the St. Clair river, 1868. The meter was located midway between the sections, as near the path of the floats as possible, and run continuously at each five feet depth during the whole time the floats were passing at the same depth. There are not enough of these observations to give the true difference between the floats and meter for all depths, and, therefore, we cannot yet reduce the observations taken in 1867, but they are sufficient to show that while near the surface in a calm the meter and floats give nearly the same velocity, while as we approach the bottom the velocity determined by floats is greater than that given by the meter; and, though the range of difference shows that a large number of observations will be required to give the law of variation, yet there are enough to show that the errors of float measurement are in the direction heretofore pointed out, and that sub-surface velocities given by the double floats will be too large. I think that I have shown that the meter gives velocities as nearly correct as is possible with any apparatus when the coefficient is known, and that it is as accurate in the measurement of velocities at all depths as Mr. Darcy's modification of Petot's tube is in canals and small streams. In table A, at end of report, are given the reduced meter observations for 1868. In these tables two different methods of observation are given; one for determining the vertical curve and the other for determining the horizontal. In the first case the boat was anchored in one place long enough to allow the meter to run for any required length of time at each five feet of depth; thus occupying only a few positions in a day. In the second the meter was only run at two or three depths and then moved about two hundred feet, thus going across the whole river in one day. These latter observations were taken to find the horizontal curve for a single day, by means of which the vertical curves taken on different days could be reduced to the center of the two hundred feet division into which the river was divided, in order to give the discharge more accurately, as noticed in the last report. But it was found that the velocity changed as much from day to day as it did in the whole season, so that the horizontal curves were constructed from the whole observations by plotting the daily velocities obtained at each five feet of depth in their proper relative distance from the base line. A free hand curve was drawn through these points and a connection found which was applied to each observed velocity to reduce it to the center of the division in which it was taken. The velocities for Niagara vary greatly; this is due partly to the eddies and partly to the flow over the falls, hereafter noticed. The velocities for each five feet of depth reduced to the center of each division are given in the following tables: The surface velocities at St. Clair and Niagara were not properly taken. The meter being at the stem of the boat the true velocity could not be obtained, as the friction of the current against the bottom of the boat would retard it very much, and, therefore, give its velocity too small. At Ogdensburg there were too few taken to be of any importance. The bottom velocities, given in the tables, were obtained by plotting the velocities on a large scale, and continuing the curve they indicated till it intersected the line representing the bottom of the river. These are probably too large. |