30 ESSAYS ann OBSERVATIONS 
formed in. time? That it is inftantaneous, 
will thus appear. A gradual change of mo- 
tion fuppofes, that the foremoft body pafles 
through every degree of velocity from reft till 
it acquires its greateft velocity ; and that the 
motion of the impingeing body is gradually 
retarded in proportion. But this fuppofition 
is inconfiftent with a known fa@t, that the bo- 
dies continue conjoined after conta; whence 
it is evident, that both muft move with the 
fame velocity from the inftant of contact. 
THEsE preliminary points being fettled, the 
operation may be eafily analyzed. Tho’ the 
whole is performed in an inftant, it may, 
however, be diftinguifhed into different fteps. 
The firft is, that, by a certain degree of re- 
fiftance, a proportion of the momentum or 
force of the impingeing body is deftroyed, 
and confequently of its velocity. The next 
ftep is, that, with the remaining force and 
velocity, an impulfe is made upon the body 
at re{t, which now refifts no longer, where- 
by it begins to move with the remaining ve- 
locity of the impingeing body. And the laft 
ftep is, that it is carried on with the fame de- 
gree of velocity by its own vis infita, 
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