309. We can see the reason why the wheel and axle overhauls—that is, runs down of its own accord—when allowed to do so; it is because less than half the applied energy is expended upon friction.
310. A series of experiments which have been carefully made with this wheel and axle are recorded in Table XVIII.
Wheel of wood; axle of iron, in oiled brass bearings; weight of wheel and axle together, 16·5 lbs.; effective circumference of wheel, 88"·5; effective circumference of axle, 2"·87; velocity ratio, 31; mechanical efficiency, 22; useful effect, 70 per cent.; formula, P = 0·204 + 0·0426 R.
| Number of Experiment. | R. Load in lbs. | Observed power in lbs. | P. Calculated power in lbs. | Difference of the observed and calculated powers. |
|---|---|---|---|---|
| 1 | 28 | 1·4 | 1·4 | 0·0 |
| 2 | 42 | 2·0 | 2·0 | 0·0 |
| 3 | 56 | 2·6 | 2·6 | 0·0 |
| 4 | 70 | 3·2 | 3·2 | 0·0 |
| 5 | 84 | 3·7 | 3·8 | +0·1 |
| 6 | 98 | 4·4 | 4·4 | 0·0 |
| 7 | 112 | 5·0 | 5·0 | 0·0 |
By the method of the Appendix a relation connecting the power and the load has been determined; it is expressed in the form—
P = 0·204 + 0·0426 R.
311. Thus for example in experiment 5 a load of 84 lbs. was found to be raised by a power of 3·7 lbs. The value calculated by the formula is 0·204 + 0·0426 × 84 = 3·8. The calculated value only differs from the observed value by 0·1 lb., which is shown in the fifth column. It will be seen from this column that the values calculated from the formula represents the experiments with fidelity.
312. We have deduced the relation between the power and the load from the principle of energy, but we might have obtained it from the principle of the lever. The wheel and axle both revolve about the centre of the axle; we may therefore regard the centre as the fulcrum of a lever, and the points where the cords meet the wheel and axle as the points of application of the power and the load respectively.
313. By the principle of the lever of the first order ([Art. 237]), the power is to the load in the inverse proportion of the arms; in this case, therefore, the power is to the load in the inverse proportion of the radii of the wheel and the axle. But the circumferences of circles are in proportion to their radii, and therefore the power must be to the load as the circumference of the axle is to the circumference of the wheel.