Velocities  of  Cannon  Balls,  &c.  5 5- 
given,  its  verfed  fine  becomes  known,  which  is  the 
height  perpendicularly  defcended  by  the  correfponding 
point  of  the  pendulum.  The  height  defcended  being 
thus  known,  the  velocity  acquired  in  falling  through 
that  height  becomes  known  from  the  common  rules  for 
the  defcent  of  bodies  by  the  force  of  gravity;  and  this  is 
the  velocity  of  that  point  of  the  pendulum  : this  velocity 
of  any  known  point  whatever  is  then  to  be  reduced  to 
the  velocity  at  the  center  of  ofcillation,  by  the  propor- 
tion of  their  radii  or  diftances  from  the  axis  of  motion; 
and  the  velocity  of  this  center,  thus  obtained,  is  to  be 
efteemed  the  velocity  of  the  whole  pendulum  itfelf ; 
which  being  now  given,  that  of  the  ball  before  the  ftroke 
becomes  known  from  the  given  weights  of  the  ball  and 
pendulum.  Thus  then  the  menfuration  of  the  very 
great  velocity  of  the  ball  is  reduced  to  the  obfervation  of 
the  magnitude  of  the  arch  defcribed  by  the  pendulum, 
in  confequence  of  the  blow  ftruclc.  This  arch  may  be- 
meafured  after  various  ways  : in  the  following  experi- 
ments it  was  afcertained  by  meafuring  the  length  of  its 
chord  by  means  of  a piece  of  tape  or  fmail  ribband,  the 
one  end  of  which  was  fattened  to  the  bottom  of  he  pen- 
dulum, and  the  reft  of  it  made  to  Hide  through  a fmail 
machine  contrived  for  the  purpofe,  which  will  be  here- 
after defcribed  ; for  thus  the  length  of  the  tape  drawn 
