Page:Philosophical Transactions - Volume 096.djvu/32

20 that the utmost which the body B could effect in return would be the reproduction of A's velocity, and restitution of its entire mechanic force neither increased nor diminished, excepting by the necessary imperfection of machinery. The possibility of perpetual motion is consequently inconsistent with those principles which measure the quantity of force by the quantity of its extended effect, or by the square of the velocity which it can produce.

In estimating the utmost effect which one body can produce upon another at rest, the same result is obtained by employing impetus as ascensional force, according to Christiaan Huygens; for if the body A were allowed to ascend to the height due to its velocity y and if by any simple mechanical contrivance of a lever or otherwise the body B were to be raised by the descent of A, it is well known that the heights of ascent would be reciprocally as the bodies; and consequently that the square of the velocity to be acquired by free descent of R would be in that ratio, and the quantity of mechanic force would-be preserved as before unaltered.

It may be of use also to consider another application of the same energy, and to shew more generally that the same quantity of total effect would be the consequence not only of direct action of bodies upon each other, but also of their indirect action through the medium of any mechanical advantage or disadvantage; although the time of action might by that means be increased or decreased in any desired proportion. For instance, if the body supposed to be in motion were to act by means of a lever upon a spring placed at a certain distance from the centre of motion, the retarding force opposed to it would be inversely as the distance of the body