Velocities  of  Cannon  Balls,  See. 
81 
f~  T Yeloc.  with 
Veloc.  with 
Veloc,  with 
2 ounces. 
4 ounces. 
8 ounces. 
702 
1068 
1419 
682 
1020 
135^ 
695 
948 
1443 
703 
973 
1360 
725 
957 
1412 
5)3507 
5)4966 
5)69*86 
The  means,  701 
993 
1397 
And  thefe  mean  velocities 
with  two,  four 
, and  eight 
ounces  of  powder,  are  as 
the  numbers  1, 
1.416,  and 
1.993;  but  the  fub-duplicate  ratio  of  the  weights  (two, 
four,  and  eight)  of  powder  gives  the  numbers  1,  1 .414, 
and  2,  to  which  the  others  are  fufficiently  near.  It  is 
obvious,  however,  that  the  greateft  difference  lies  in  the 
laft  number  which  anfwers  to  the  greateft  velocity,  and 
which  is  again  in  defe6t.  It  will  ftill  be  a little  more  in 
defeat  if  we  make  the  allowance  for  the  weights  of  the 
balls;  for  the  mean  weight  of  the  balls  with  the  two 
and  four  ounces  is  1 8|  ounces,  but  of  the  eight  ounces 
it  is  i8|;  diminifhing  therefore  the  number  1.993  in 
the  reciprocal  fub-duplicate  ratio  of  x 8|  to  1 8|,  it  be- 
comes 1.985,  which  falls  fhort  of  the  number  2 by 
.015  or  the  133d  part  of  itfelf;  which  defeat  is  to  be 
Vol.  LXVI1I.  M attri- 
