215 



As a simple case 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 

 square 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 efficient 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 effect, 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- 

 sisting of a v is matrix extended through a given space, give motion 

 to a body for the purpose of employing its impetus in the production 

 of any sudden effect, 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 effect ; 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 given 

 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 ac- 

 cumulated forces themselves by their gradual or their sudden effects, 



