VOL. LXXII.] PHILOSOPHICAL TRANSACTIONS. 305 



Respecting bodies unelastic and perfectly hard, we must infer, that since we 

 are unavoidably led to a conclusion concerning them, which contradicts what is 

 esteemed a truth capable of the strictest demonstration ; viz. that the velocity of 

 the centre of gravity of no system of bodies can be changed by any collision 

 among them, something must, be assumed that involves a contradiction. This 

 perfectly holds, according to all the established rules, both of perfectly elastic 

 and perfectly non-elastic soft bodies ; rules which must fail in the perfectly non- 

 elastic hard bodies, if their velocity after the stroke is to the velocity of the 

 striking body, as 1 is to the square root of 2 ; for then the centre of gravity of 

 the two bodies will by the stroke acquire a velocity greater than the centre of 

 gravity the two bodies had before the stroke in that proportion ; which is proved 

 thus. 



At the outset of the striking body, the centre of gravity of the two bodies in 

 our case will be exactly in the middle between the two ; and when they meet it 

 will have moved from their half distance to their point of contact, so that the 

 velocity of the centre of gravity before the bodies meet will be exactly one half 

 of the velocity of the striking body ; and therefore, if the velocity of the strik- 

 ing body be 2, the velocity of the centre of gravity of both will be ] . After 

 the stroke, as both bodies are supposed to move in contact, the velocity of the 

 centre of gravity will be the same as that of the bodies ; and as their velocity is 

 proved to be the square root of 2, the velocity of their centre of gravity will be 

 increased from 1, to the square root of 2 ; that is, from 1 to 1 .414 &c* 



The fair inference from these contradictory conclusions therefore is, that an 

 unelastic hard body (perfectly so) is a repugnant idea, and contains in itself a 

 contradiction ; for to make it agree with the fair conclusions that may be drawn 

 on each side, from clear premises, we shall be obliged to define its properties 

 thus : that in the stroke of unelastic hard bodies they cannot possibly lose any 

 mechanic power in the stroke ; because no other impression is made than the 

 communication of motion ; and yet they must lose a quantity of mechanic 

 power in the stroke ; because, if they do not, their common centre of gravity, 

 as above shown, will acquire an increase of velocity by their stroke on each 

 other. In like manner, the idea of a perpetual motion perhaps, at first sight, 

 may not appear to involve a contradiction in terms ; but we shall be obliged to 

 confess that it does, when, on examining its requisites for execution, we find we 

 shall want bodies having the following properties; that when they are made to 

 ascend against gravitation their absolute weight shall be less ; and that when they 

 descend by gravitation, through an equal space, their absolute weight shall be 

 greater ; which, according to all we know of nature, is a repugnant or contra- 

 dictory idea. 



* Here is another false conclusion, drawn in consequence of a former mistake. 



VOL. XV. R R 



