57. Column 6. Duration of the experiment, is obtained by taking the differences of the times of the beginning, and ending of the experiment, as given in column 5.
58. Column 7. Total number of revolutions of the wheel during the experiment. This is obtained from the note-book of the "speed of the wheel," by counting the number of observations of the times at which the bell was struck; this number, less one, multiplied by 50, which is the number of revolutions of the wheel to each stroke of the bell, gives the number of revolutions during the experiment.
59. Column 8. Number of revolutions of the wheel per second, is obtained by dividing the total number of revolutions of the wheel, by the duration of the experiment.
60. Column 9. The weight in the scale, requires no explanation.
61. Column 10. Useful effect, or the friction of the brake, in pounds avoirdupois, raised one foot per second. This is obtained by multiplying together the weight in the scale, and the velocity that the point of application of the weight, tends to take. Or, in other words, the product of the weight into the velocity that the weight would actually take, if, for an infinitely short time, the brake, and the apparatus connecting it with the weight, were rigidly connected with the friction pulley.
The effective length of the brake, including the leverage due to the different lengths of the arms of the bell crank, was 10.827778 feet (art. 50). The circumference of a circle of this radius is 68.0329 feet. This circumference is a constant for all the experiments in which any useful effect was produced, and column 10 was obtained by the product of this constant, the weight, and the number of revolutions of the wheel per second. The computation was performed by logarithms, and if the results given in the tables should be verified by actual multiplications, minute differences would, no doubt, be detected.
62. Columns 11 and 12. Heights of the water in the forebay and in the wheelpit. These heights are all referred to the top of the weir, consequently, the differences give the fall acting upon the wheel.
63. Column 13. Total fall acting upon the wheel. These are the differences referred to in the last sentence. In experiments 27 and 28, observations were taken in the ventilating pipe G, plate I., for the purpose of estimating the loss of fall to this part of the supply pipe; — it was not convenient, however, to measure these heights with complete accuracy. In experiment 27, the height of the water in the ventilating pipe was 0.106 feet below the level in the forebay; — in experiment 28 the difference was found to be 0.102 feet; — in experiment 30, which gave the maximum coefficient of effect, the quantity of water discharged by the wheel, was a little less than in either experiment 27, or 28. We may, therefore,
