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_.
+-----------+---------+----------+----------+--------------+
| | | | P. |Difference of |
| Number of | R. | Observed |Calculated| the observed |
|Experiment.| Load | power | power |and calculated|
| | in lbs. | in lbs. | in lbs. | values. |
+-----------+---------+----------+----------+--------------+
| 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.
314. This mode of arriving at the result is a little artificial; it is
more natural to deduce the law directly from the principle of energy.
In a mechanical power of any complexity it would be difficult to trace
exactly the transmission of power from one part to the next, but the
principle of energy evades this difficulty; no matter what be the
mechanical arrangement, simple or complex, of few parts or of many, we
have only to ascertain by trial how many feet the power must traverse
in order to raise the load one foot; the number thus obtained is the
theoretical efficiency of the machine.