Page:Conservationofen00stew.djvu/51

Rh Here we have a smooth plane and a weight held upon it by means of a power, as in the figure. Now, if we overbalance by a single grain, we shall bring the weight  from the bottom to the top of the plane. But when this has taken place, it is evident that has fallen through a vertical distance equal to the length of the plane, while on the other hand  has only risen through a vertical distance equal to the height. Hence, in order that the principle of virtual velocities shall hold, we must have multiplied into its fall equal to  multiplied into its rise, that is to say,

$$P \times$$ Length of plane $$= W \times$$ Height of plane,

or $$\frac{P}{W} = \frac{Height.}{Length.}$$

46. The two examples now given are quite sufficient to enable our readers to see the true function of a machine, and they are now doubtless disposed to acknowledge that no machine will give back more energy than is spent upon it. It is not, however, equally clear that it will not give back less; indeed, it is a well-known fact that it constantly does so. For we have supposed our machine to be without friction—but no machine is without friction—and the consequence is that the available out-come of the machine is more or less diminished by this drawback. Now, unless we are able to see clearly