On the Force of Percussion. 235 
for counteracting the usual resistances, and perpetual motion 
would be easily effected. But since the impetus remains 
unaltered, it is evident that the utmost which the body B 
could effect in return would be the reproduction of A’s ve- 
locity. and restitution of its entire mechanic force neither 
increased nor diminished, excepting by the necessary im- 
perfection of machinery. The possibility of perpetual mo- 
tion 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 pro- 
duce upon another at rest, the same result is obtained by 
employing impetus as ascensional force, according to Huy- 
gens ; for if the body A were allowed to ascend to the height 
due to its velocity, and if by any simple mechanical con- 
trivance 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 preserved as before unaltered. 
It may be of use also to consider another application of 
the same energy, and to show 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 ad- 
vantage or disadvantage ; although the time of action might 
by that means be increased or decreased in any desired pro-+ 
portion. For instance, if the body supposed to be in mos 
tion 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 retarding 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 
