Velocities  of  Cannon  Balls,  See.  65 
as  the  time. of  a vibration,  it  is  evident  that  the  fri&ion 
in  the  one  cafe  operates  againft  that  in  the  other;  and 
that  the  difference  of  the  two  is  the  real  efficacious  caufe 
of  refiftance,  and  which  therefore  is  either  equal  to  no- 
thing, or  very  nearly  fo. 
Thefe  general  caufes  of  error  in  the  principles  of  the 
experiments  are  therefore  fafely  omitted  in  the  theorem : 
and  our  only  care  muft  he  to  guard  againft  accidental 
errors  in  the  actual  execution  of  the  bufinefs. 
Of  the  experiments. 
The  gun,  with  which  the  experiments  were  made, 
was  of  brafs ; the  diameter  of  the  bore  or  cylinder  at  the 
muzzle  was  if, or  2.16  inches ; but  its  diameter  next  the 
breech  was  a fmall  matter  lefs,  being  there  only  if,  or 
2.08  inches;  fo  that  the  greateft  caft-iron  ball  it  would 
admit  was  juft  1 9^  ounces  avoirdupois,  or  1^  pound  want- 
ing half  an  ounce ; but  fometimes  leaden  balls  were  ufed, 
which  weighed  above  i|  pound,  and  fometimes  long  or 
cylindrical  fhot  which  weighed  near  three  pounds ; the 
length  of  the  bore  was  42]-,  or  42.6  inches,  fo  that  it 
was  nearly  io\  calibers  long. 
The  powder  ufed  was  of  the  fort  which  is  commonly 
made  for  government;  the  quantity  was  two,  four,  or 
Vol.  LXVIII.  K eight 
