370  Mr.  milner  on  the  Communication  of 
by  the  force /,  will  be  the  motion  loft  in  the  fame 
body  Q_by  the  diminution  of  its  gravity.  Let  a be  any 
prifmatic  particle  of  the  body,  and  ad  its  diftance  from 
the  axis ; the  velocity  of  this  particle  will  be  ; its 
motion  — r— j- — , and,  by  the  nature  of  the  lever,  the 
motion  which  Q_muft  lofe  to  generate  fuch  an  effedt  in  a 
n - AXad’Xv  . vabp  ~ ^ 
mult  be  — -t . The  quantity  -r-  reprefents  the  fum 
of  all  the  quantities — — — ; and  therefore  the  motion, 
which  Q.has  loft  by  its  adtion  on  the  body,  is  precifely 
equal  to  the  motion  gained  by  the  different  parts  of  that 
body  after  a proper  allowance  is  made  for  the  lengths  of 
the  levers,  ad,  &c. 
Thus  it  appears,  that  there  is  no  neceffity  in  account- 
ing for  the  time  of  qJs  defcent  and  the  velocity  it  ac- 
quires, of  having  recourfe  to  the  confervatio  vis  viva,  or 
any  fuch  perplexed  hypo  thefts.  By  purfuing  the  ana- 
lytic method  far  enough,  we  have  been  led  diredtly  to 
that  fundamental  law  of  motion,  that  adtion  is  equal  to 
re-adlion,  and  in  the  contrary  diredtion. 
A diftindtion,  however,  is  always  to  be  made  between 
the  adtions  of  bodies  when  at  liberty,  and  when  they  re- 
solve about  a center  or  axis.  In  the  firft  cafe  the  motion 
loft 
