Velocities  of  Cannon  Balls , See.  ■ 6 3 
or  p muft  be  corrected  by  the  continual  addition  of  b : 
and  g is  corrected  by  taking  always  g+j^b,  or  g+*-~  b 
nearly  for  each  fucceffive  value  of  g\  or  g is  corrected 
p cr  t 
by  adding  always  —ffb  to  the  next  preceding  value  of 
and  laftly,  h is  corrected  by  taking  for  its  new  values 
fucceffively  or  by  adding  always  bf  ox~-  b 
nearly,  to  the  preceding  value  of  h ; fo  that  the  three 
corrections  are  made  by  adding  always, 
b to  the  value  of  p, 
f——  x b to  the  value  of  g, 
fo 
— x b to  the  value  of  h. 
Before  we  proceed  to  the  experiments  it  may  not  be 
improper  to  take  notice  of  three  feeming  caufes  of  error, 
which  have  not  been  brought  to  account  in  our  theorem 
for  determining  the  velocity  of  the  fhot ; and  to  examine 
here  whether  their  effedts  can  fenlibly  afreet  the  conclu- 
fion.  Thefe  are  the  penetration  of  the  ball  into  the 
wood  of  the  pendulum,  the  refiftance  of  the  air  to  the 
back  of  it,  and  the  fridtion  on  the  axis  : by  each  of  thefe 
three  caufes  the  motion  of  the  pendulum  feems  to  be 
retarded.  The  principle  on  which  our  rule  is  founded 
fuppofes  the  momentum  of  the  ball  to  be  communicated 
fo  the  pendulum  in  an  inftant  ; but  this  is  not  accurately 
a the. 
