60  Mr.  hutton  on  the  initial 
v the  original  velocity  of  the  ball, 
c the  chord  of  the  arch  meafured  by  the  tape,  and 
r its  radius,  or  the  diftance  from  the  axis  to  the  bot- 
tom of  the  pendulum. 
Then  the  effect  of  the  blow  ftruclc  by  the  ball  is  as 
or,  as  kk  :gb  ::p : g-jj  = the  weight  of  a body,  which, 
being  placed  at  the  point  ftruck,  would  acquire  the 
fame  velocity  from  the  blow  as  the  pendulum  does 
at  the  fame  point.  Here  then  are  two  bodies,  b and 
the  former  of  which,  with  the  velocity  v,  ftrikes  the 
latter  at  reft,  fo  that  after  the  blow  they  both  proceed 
uniformly  forward  together  with  the  velocity  z\  in. 
which  cafe  it  is  well  known,  that  b : b & jp  : : Z'.v,  and! 
therefore  the  velocity  z.  is  - jprpjb}  • ®ut  becaufe  °f  the 
acceffion  of  the  ball  to  the  pendulum,  the  place  of  the 
center  of  ofcillation  will  be  changed;  and  from  the 
known  property  of  that  point  we  find  = to  its  dif- 
tance from  the  axis.  Gall  this  diftance  of  the  center  of 
ofcillation,  of  the  mafs  compounded  of  the  ball  and 
pendulum,  H.  Then,  fince  z is  the  velocity  of  the 
point  whofe  diftance  is  b,  we  have  this'  proportion,  as 
Z VL  b k *1) 
ft  : h : : z : -p-  = = the  velocity  of  this  compound 
center  of  ofcillation. 
Again* 
