372  Mr.  milner  on  the  Communication  of 
now  pretty  weii  agreed  upon,  that  the  neglect  of  this 
circumftance  is  one  caufe  of  that  material  error,  which 
Sir  Isaac  newton  himfelf  is  fuppofed  to  have  fallen 
into  in  the  thirty-ninth  propofition  of  the  third  book  of 
his  Principia. 
I had  feveral  reafons  for  infilling  fo  particularly  oil 
the  demonftration  of  this  third  cafe.  It  is  in  itfelf  one  of 
the  molt  neat  and  elegant  problems  we  have;  and,  what 
isof  more  confequence,  it  admits  of  an  experimental  proof 
and  illuftration.  It  is  obvious,  that  the  motion  of  the 
body  amb  may  be  made  fo  flow,  that  the  time  of  c£s 
defcent  through  any  aflignable  fpace  may  be  meafured 
to  the  greateft  exaiftnefs.  The  velocity  of  Q^may  alfo  be 
inferred  with  the  fame  eafe  by  obferving  the  velocity  of 
any  particular  point  in  the  body  to  which  the  velocity  of 
Q_always  bears  an  invariable  ratio.  Such  experiments,  it 
muft  be  owned,  feem  very  unfit  for.  the  fir  ft  difcovery  of 
the  laws  of  nature;  though,  as  I have  fhewn,  it  is  not 
impoflible  to  collect  them  that  way ; but  after  they  are 
difcovered,  the  application  of  them  to  the  folution  of 
fuch  intricate  problems  is  both  entertaining  and  inftruc- 
tive,  and  then  the  agreement  of  the  experiments  them- 
felves  with  the  theory  becomes  a folid  argument  for  the 
certainty  of  our  principles. 
We 
i 
