106. In the foregoing table, experiments 4, 5, 6, and 7, were made with the wheel still; the brake was screwed up tight, and the pressure of the water upon the buckets, was measured by weights in the scale. In experiments 4 and 7, the weights were sufficient to balance the effect of the pressure of the water on the buckets, and also to overcome the friction of the apparatus; in other words, the weights were the least that would cause the scale to preponderate over the active and passive forces. In experiments 5 and 6, the weights in the scale were the greatest that the pressure upon the buckets would raise, and overcome the friction of the apparatus; consequently, the force of the water acting upon the buckets, may be considered as balanced by the average of the weights in the fourth and fifth experiments, and, also, by the average in the sixth and seventh experiments.
To obtain the true weight that would balance the pressure, we must reduce the weights in the different experiments to what they would have been, if the fall acting upon the wheel had been constant.
The following table shows the weights reduced to a uniform fall of 2.5 feet, obtained by simple proportion; thus, in the fourth experiment,
| Number of experiment. | Actual fall acting upon the wheel, in feet. | Weight in scale by experiment, in pounds. | Weight reduced to a uniform fall of 2.5 feet. | Quantity of water discharged, reduced to uniform fall of 2.5 feet, in cubic feet per second. |
|---|---|---|---|---|
| 4 | 2.5180 | 25.750 | 25.586 | 1.9651 |
| 5 | 2.5074 | 19.375 | 19.318 | 1.9567 |
| 6 | 2.4405 | 19.250 | 19.719 | 1.9568 |
| 7 | 2.3735 | 24.125 | 25.411 | 1.9584 |
| Means | 22.5085 | 1.9592 |
The mean reduced weight, when the weights preponderated, is . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
25.4985 pounds. | |
and when the pressure on the buckets preponderated, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
19.5185pounds.„ | |
Difference, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
5.9800 pounds. | |
Half of this difference, or 2.99 pounds, may be considered as the measure of the passive resistances, or, rather, of the friction of the apparatus.
107. In experiment 13, the brake was entirely removed, and the wheel allowed to run without load; with the brake, the counterbalance was necessarily
