Page:Proceedings of the Royal Society of London Vol 1.djvu/235

Rh As a simple ease of entire transfer of force from A to B, it is evi- dent that if A were allowed to ascend to the height due to its ve- locity, and if by any mechanical contrivance, of lever or otherwise, the body B were to be raised by the descent of A, their heights of ascent would be reciprocally as the bodies; consequently, that the sguare of the velocity to be acquired by the free descent of B, would be. to that of A, in the above—mentioned ratio, and the quantity of mechanic force so estimated would be preserved unaltered.

But, on the contrary, the momentum, which is in the simple reci- procal ratio of the bodies, would be increased by such means in the subduplicate ratio of the bodies that might be employed; and if mo- mentum were really a force eﬂicient in proportion to its estimated magnitude, it should not only be capable of reproducing the original quantity. but the additional force, thus acquired, might be employed for counteracting the usual resistances, and perpetual motion would be easily produced. But since the impetus, or mechanic force, re- mains unaltered, it is evident that the utmost that B could eﬁ'ect, in return, would be the reproduction of A's velocity, and restitution of its former 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 effects, or by the square of the velocity which it can produce.

Since we can, at pleasure, by means of any mechanic force, con- of a vis metric extended through a given space, give motion to a body for the purpose of employing its impetus in the production of any sudden eﬂect, or can, on the contrary, occasion a moving body to ascend, and thus resolve its impetus into a moving forCe ready to exert itself through a determinate space of descent, capable of pro- ducing precisely the same quantity of mechanic eﬂect; the force de- pending on impetus may justly be said to be a force of the same kind as any other mechanic force, and may be strictly compared with them as to quantity.

In this manner, the author says, we may even compare the force of a body in motion, with the same kind of force contained in a quantity of gunpowder, and may say that we have the same quantity of mechanic force at command, whether we have one pound of gun- powder, or the weight which it would raise to the height of 30 feet, actually raised to that height, and ready to be let down gradually; or the same weight possessing its original velocity of ascent, to be employed in any sudden exertion.

By employing the same measure, we have a distinct expression for the quantity of mechanic force given to a steam-engine by a peck or by a bushel of coals; and are enabled to compare its effect with the quantity of work which one or more horses may have performed in a day. In short, whether we are considering the sources of extended exertion, or of accumulated energy,—whether we compare the accumulated forces themselves by their gradual or their sudden effects,