Lever. ' 97 



bodies act respectively ; we must have, therefore^ in order that 27 - 

 there may be an equilibrium, 



w m : wn : : FE : FC, 



that is, 



m : n : : FE : FC ; 



therefore, in order that there may be an equilibrium between 

 two bodies which are urged only with the force of gravity, or 

 between any two bodies that tend to move with equal velocities ; 

 it is sufficient that the masses of these bodies be in the inverse 

 ratio of the distances of their directions from the fulcrum. 



167. But if the velocities with which the bodies tend to move, 

 be unequal, it is not the masses, but the products of the masses 

 into the velocities, which must be in the inverse ratio of the dis- 

 tances of their directions from the fulcrum. 



168. If two finite and heavy masses m, n, are urged by finite 

 and unequal velocities, according to the directions Im, Kn; as 

 the velocity which gravity is capable of giving in an instant (or 

 infinitely small portion of time) is infinitely small ; in order that 

 the two finite velocities may mutually destroy each other, it is 

 sufficient that the quantities of motion which the two bodies 

 would have in virtue of these velocities should be in the inverse 

 ratio of FE, FC. But this equilibrium would not exist except 

 for an instant ; for when these velocities are mutually destroyed, 

 the bodies m, n, subjected to the action of gravity, would receive 

 quantities of motion, which would be in the simple ratio of the 

 masses, and which consequently would no longer be in the in- 

 verse ratio of the distances FE, FC. 



We hence see the difference between an equilibrium among 

 bodies urged by gravity only, and an equilibrium among bodies 

 urged by unequal finite velocities. 



It may be remarked, moreover, that it is impossible to put 

 in equilibrium a body urged by gravity only with a body urged 

 by a finite velocity ; and we may hence conclude, that if the 

 weight p is in equilibrium with a force q exerted by an animal, Fig- 7] 

 this last does not tend to move the point D, except with a velo- 

 city infinitely small. If on the contrary the force q, applied at 

 Mcch. 1 3 



