Motion  by  Impact  and  Gravity.  355 
B X 4BG2  + 4-BG x AB.  Add  to  both  fides  AX  A^?  + B x AB% 
and  we  fhall  have  ax  ad2  + b x abj=ax  a^'+bx  ab  + 2bg\ 
We  are  not  to  wonder,  therefore,  upon  making  trials 
with  perfectly  elaftic  bodies,  if  any  fuch  exifted,  were  we 
always  to  find  their  vires  viva,  as  the  foreigners  exprefs 
themfelves,  neither  increafed  nor  diminifhed  by  the 
ftroke.  They  define  the  force  of  bodies  in  motion,  or 
their  vis  viva,  to  be  in  a compound  ratio  of  their  quan- 
tities of  matter,  and  the  fquares  of  their  velocities;  and 
certainly  fuch  a definition  implies  no  contradi&ion  or 
impofiibility.  The  term  force,  in  a loofe  and  ordinary 
way  of  fpeaking,  conveys  to  us  no  determinate  idea  at 
all,  and  therefore,  until  it  be  defined,  is  incapable  of 
being  ufed  to  any  good  purpofe  in  philofophy:  whe- 
ther this  or  that  definition  come  nearer  to  the  general 
fenfe  in  which  it  is  ufed  indiftindtly  enough  in  common 
language,  is  entirely  another  queftion.  We  may  go  far- 
ther, and  add,  that  in  their  ufe  of  the  words,  becaufe  the 
fum  of  the  forces  of  elaftic  bodies  is  never  affected  by 
the  ftroke,  it  is  not  unnatural  to  fay,  that  acftion  is  there- 
fore equal  to  re-a<ftion,  and  that  no  force  is  loft  by  one 
body  but  what  is  communicated  to  the  other.  But  if  we 
will  go  fo  far,  and  thereby  change  the  meaning  of  the 
terms  action  and  re-aftion  and  their  meafures,  we  ought 
at  leaft  to  guard  our  readers  from  miftakxng  us,  however 
Vol.  LXVIII.  Z z convenient 
