upon the Colli f on of 'Bodies, ^ ^ 
according to all the eftablifhed rules, both of perfectly ei attic 
and perfectly non-elaftic fojt bodies ; rules which muft fail in 
the perfectly non-elaftic hard bodies, if their velocity after the 
ltroke is to the velocity of the ftriking body as one is to the 
fquare root of 2 ; for then the center of gravity of the two 
bodies will by the ftroke acquire a velocity greater than the 
center of gravity the two bodies had before the ftroke in 
that proportion, which is proved thus. 
At the outlet of the ftriking body, the center of gravity of 
the two bodies in our cafe will be exactly in the middle be- 
tween the two ; and when they meet it will have moved from 
their halt diftance to their point of contaCt, fo the velocity of 
the center of gravity before the bodies meet will be exaCtly 
one half of the velocity of the ftriking body; and, therefore, 
if the velocity of the ftriking body is 2, the velocity of the 
center of gravity of both will be one. After the ftroke, ns both 
bodies arefuppofed to move in contact, the velocity of the cen- 
ter of gravity will be the fame as that of the bodies ; and as 
their velocity is proved to be the fquare root of 2, the velocity 
of their center of gravity will be increafed from 1 . to the fquare 
root of 2. ; that is, from 1. to 1.414, &c. 
The fair inference from thefe contradictory conclufions there- 
fore is, that an unelaftic hard body (perfectly fo) is a repugnant 
idea, and contains in itfelf a contradiction; for to make it 
agree with the fair conclufions that may be drawn on each fide, 
from clear premifes, .we fhall be obliged to define its proper- 
ties thus : that in the ftroke of unelaftic hard bodies they cannot 
pnjjibly lofe any mechanic power in the ftroke ; becaufe no other 
impreflion is made than the communication of motion ; and 
yet they muji lofe a quantity of mechanic power in the ftroke ; 
becaufe, if they do not, their common center of gravity, as 
Vol. LXXIJ. A a a above 
