Velocities  of  Cannon  Halls , <kc.  83 
We  may  now  collect  into  one  view  the  principal  in- 
ferences that  have  x'efulted  from  thefe  experiments. 
1.  And  firft,  it  is  made  evident  by  them,  that  powder 
fires  almoft  inftantaneoufly,  feeing  that  almoft  the  whole 
of  the  charge  fires  though  the  time  be  much  dimi- 
nifhed. 
a.  The  velocities  communicated  to  balls,  or  foot  of 
the  fame  weight,  with  different  quantities  of  powder, 
are  nearly  in  the  fub-duplicate  ratio  of  thofe  quantities. 
A very  fmall  variation,  in  defect,  taking  place  when  the 
quantities  of  powder  become  great. 
3.  And  when  fhot  of  different  weights  are  fired  with 
the  fame  quantity  of  powder,  the  velocities  communi- 
cated to  them  are  nearly  in  the  reciprocal  fub-duplicate 
ratio  of  their  weights. 
4.  So  that,  univerfally,  fhot  which  are  of  different 
weights,  and  impelled  by  the  firing  of  different  quanti- 
ties of  powder,  acquire  velocities  which  are  directly  as 
the  fquare  roots  of  the  quantities  of  powder,  and  in- 
verfely  as  the  fquare  roots  of  the  weights  of  the  fhot, 
nearly. 
5 . It  would  therefore  be  a great  improvement  in  ar- 
tillery to  make  ufe  of  fhot  of  a long  form,  or  of  heavier 
matter;  for  thus  the  momentum  of  a fhot,  when  fired 
M 2 with 
