upon the ColUjion of Bodies. 343 
fquare root of which being 10, will be the velocity of the two 
non-elaftic loft bodies after the ftroke, being juft one half of 
the original velocity, as it is conftantly found to be. But in 
the non-elaftic hard bodies, no power being loft in the ftroke, 
the mechanic power will remain after it, as before it, = 3200; 
this, in like manner, being divided by 16, the double quantity 
of matter, will give 200 for the fquare of the velocity, the 
fquare root of which is 14. 14, &c. lor their velocity alter the 
ftroke, which is to 10, the velocity of the non-elaftic foft bodies 
after the ftroke, as the fquare root of 2 to 1 ; or as the diagonal 
of a fquare to its fide. 
It remains, therefore, now to be proved, that precilely half 
of the mechanic power is loji in the colliiion ol non-elaftic foft 
bodies ; for which purpofe my mind fuggefted the following 
refieftions. I11 the colliiion ol elaftic bodies the effect feem- 
ingly inftantaneous, is yet performed in time ; during which 
time the natural fprings redding in elaftic bodies, and which 
conftitute them fuch, are bent or forced, till the motion of 
the ftriking body is divided between ltfelf and the body at reft ; 
and in this ftate the two bodies would then proceed together, as 
in the cafe of non-elaftic foft bodies ; but as the fprings will 
immediately reftore themfelves in an equal time, and with the 
fame degree of impuljive force , wherewith they were bent in 
this re-aftion, the motion that remained in the ftriking body 
will be totally deftroyed, and the total exertion of the two 
fprings, communicated to the original refting body, will caufc 
it to fly off with the fame velocity wherewith it was ftruck. 
Upon this idea, if we could con ft r u<ft a couple of bodies in 
fuch a way that they fhould either aft as bodies perfeftly elaftic ; 
or, that their fprings fhould at pleafui-e be hooked up, 
retained, or prevented from reftoring themfelves, when at 
their extreme degree of bending ; and if the bodies under theie 
VOL. 
T 
Z z 
circum 
