Motion  by  Impact  and  Gravity . 369 
a propofition  of  this  kind.  The  mutual  actions  of  bodies 
upon  one  another,  efpecially  when  their  gravity  is  taken 
into  the  queftion,  depends  upon  fo  many  con  fi  derations, 
and  the  cafes  which  may  be  put  are  capable  of  fuch  an 
infinite  variation,  that  it  is  impoffible  almoft  to  draw  a 
general  inference  of  this  nature.  Even  when  experi- 
ments are  produced,  which  feem  to  prove  the  point,  one 
is  apt  to  fufpedl  the  univerfality  of  the  conclufion,  and  to 
imagine  that  it  may  poffibly  be  owing  to  fome  particular 
circumftance  which  we  have  not  attended  to,  or  been 
able  to  diftinguifh  from  others  not  fo  effential.  In  the 
example  we  are  confidering  it  is  clearly  proved  from  ex- 
El/2, 
perience,  that  pxv2  is  equal  to  pv2  + ~-r ; but  whether 
that  be  true  in  every  other  cafe  that  may  be  conceived, 
can  never  be  determined  from  fuch  an  experiment ; nor 
is  it  poffible  to  make  any  diftin£lions  about  it,  until  we 
have  demonftrated  its  connexion  with  fome  other  princi- 
ple, which  is  more  fimple  and  lefs  contefted. 
Retaining  the  fame  fymbols,  let  f reprefent  the  force 
of  gravity,  and/ the  force  which  accelerates  the  body 
in  its  motion.  From  what  has  been  already  fhewn  it  ap- 
pears, that  F ap+b?  : ap  and  F-f:f::bv:ap:i 
a-~p-:pv',  and  becaufe  pv  is  the  motion  generated  in  o_ 
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