ON PERCUSSION. 37 



entire mechanic force neither increased nor diminished, Considerations 

 excepting Jby the necessary imperfection of machinery, respecting mc- 

 The possibility of perpetual motion is consequently in- ^ ^^^'^ 

 consistent with those principles which measure the quan- 

 tity 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 

 HuYQENs; for if the body A were allowed to ascend to 

 the height due to its velocity, and if by any simple me- 

 chanical 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 B would be in that 

 ratio, and the quantity of mechanic force would be, pre- 

 served 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 from the centre ; 

 , and since the space through which the body would move 

 to lose its whole velocity would be reciprocally as the re- 

 tarding force, the angular motion of the lever and space 

 through which the spring must bend, would be the same, 

 .at. whatever point of the lever the body acted. And 

 conversely, the reaction of the spring upon any other 

 body B, would in all positions communicate to it the 

 same velocity. 



It may be remarked, however, that the times in which 

 these total eifects arc produced may be varied at pleasure 

 in proportion to the distances at which the bodies are 



placed 



