374  -MK  milner.  on  the  Communication  of 
From  the  proportion  F ap+bp  : ap,  it  appears, 
that  the  force  which  accelerates  the  motion  of  c^,  or  in 
Mr.  smeaton’s  figure,  the  weight  in  the  fcalc  is  to  the. 
natural  force  of  gravity  in  a conftant  and  invariable  pro- 
portion as  long  as  the  quantities  a,  b,  p,  and  p,  remain, 
the  fame;  and  therefore  let  cvdefcend  ever  fo  fiowly,  its 
motion  will  be  uniformly  accelerated  throughout,  and 
the  fpaces  through  which  it  defcends  will  be  as  the 
fquares  of  the  velocities  acquired,  and  the  times  will  be 
as  the  velocities  themfelves ; and  this  is  agreeable  to  what 
Mr.  smeaton  found  them  in  his  fecond  and  third,  fifth 
and  fixth,  eighth  and  ninth  experiments. 
The  general  expreffion  for  the  force  which  accelerates 
the  weight  in  the  fcale  is  > and  will  be  different  ac- 
cording as  the  quantities  a,  />,  or  b,  are  altered;  but  is 
always  eafy  to  be  determined  as  foon  as  thofe  quantities 
are  known.  But  it  is  impoffible  to  determine  the  mag- 
nitude of  the  quantity  b in  the  different  cafes,  unlefs  we 
have  given  the  precife  dimenfions  of  the  whole  machine, 
and  the- fpecific  gravity  of  the  wood  made  ufe  of;  and 
therefore  I confefs  myfelf  to  have  been  puzzled  in  endea- 
vouring to  reconcile  the  firft  and  fecond  and  other  expe- 
1 
riments  with  the  theory : for  though  I could  not  doubt  a 
moment,  that  the  general  expreffion  for  the  force  was 
rightly 
