fit  Mr.  hutton  on  the  initial 
of  the  truth  in  fuch  cafes  as  generally  happen.  But  fince 
bk  x is  ufually  hut  about. the  300th  or  400th  part  of 
pg,  and  that  bk  differs  from  bk  x h~-  but  by  about  the 
80th  or  1 ooth  part  of  itfeif,  therefore  pg+bk  is  within 
h —L.  k 
about  the  20000m  or  30000th  part  of  pg+bk x — 7-  . 
2 O 
Confequently  v is  — 8 .0  a c x P-jt~  very  nearly.  Or, 
^ • 
farther,  if  g be  written  for  k in  the  laft  term  bky  then 
finally  u is  = 8.0a cg\/^b'y.pg~g,  or  V-  5.67  icgVh x y~, 
which  is  an  eafy  theorem  to  be  iifed  on  all  occafions;  ‘ 
-and  being  within  about  the  3000th  part  of  the  truth,  it 
is  fufficiently  exasSt  for  all  practical  purpofes  whatever. 
Where  it  muft  be  obferved,  that  c,  g,  k,  r,  may  be  taken 
in  any  meafures,  either  feet  or  inches,  &c.  provided  they 
be  but  all  of  the  fame  kind ; but  h muft  be  in  feet, 
becaufe  the  theorem  is  adapted  to  feet. 
scholium.  As  the  balls  remain  in  the  pendulum 
during  the  time  of  making  one  whole  fet  of  experi- 
ments, by  the  addition  of  their  weight  to  it,  both  its 
weight  and  the  centers  of  gravity  and  ofcillation  will  be 
changed  by  the  addition  of  each  ball  which  is  lodged  in 
the  wood,  and  therefore  p,  g,  and  h,  muft  be  corrected 
after  every  fhot  in  the  theorem  for  determining  the  ve- 
locity v.  Now  the  fucceeding  value  of  p is  always  p+b% 
or 
