64  Mr.  hutton  on  the  initial 
the  cafe,  becaufe  that  this  force  is  communicated  during 
the  fmall  time  in  which  the  ball  makes  the  penetration  ; 
but  as  this  is  generally  effected  before  the  pendulum  has 
moved  one-tenth  of  an  inch  out  of  its  vertical  petition, 
and  ufually  amounts  to  fcarcely  more  than  the  200th 
part  of  a fecond,  its  effedt  will  be  quite  imperceptible,  and 
therefore  it  may  fafely  be  negledted  in  thefe  experi- 
ments. As  to  the  fecond  retarding  force,  or  the  refiftance 
of  the  air  to  the  back  of  the  pendulum,  it  is  manifeft 
that  it  will  be  quite  infenfible,  when  it  is  confidered  that 
= its  velocity  is  not  more  than  three  feet  in  a fecond,  that 
its  furface  is  but  about  twenty  inches  fquare,  and  that  its 
weight  is  four  or  five  hundred  pounds.  Neither  can  the 
effedt  of  the  laft  caufe,  or  the  fridtion  on  the  axis,  ever 
amount  to  a quantity  confiderable  enough  to  be  brought 
into  account  in  thefe  experiments : for,  befides  that  care 
was  taken  to  render  this  fridtion  as  fmall  as  poffible,  the 
effedt  of  the  little  part  which  does  remain  is  nearly  ba- 
lanced by  the  effedt  it  has  on  the  diftance  of  the  center  of 
ofcillation ; for  as  this  center  was  determined  from  the 
adtual  vibrations  of  the  pendulum,  the  fridtion  on  the  axis 
would  a little  retard  its  motion,  and  caufe  its  vibrations  to 
be  flower,  and  the  confequent  diftance  of  this  center  to 
be  greater;  fo  that  the  other  parts  of  our  theorem  being 
multiplied  by  \/ h,  or  the  root  of  this  diftance,  which  is 
a$ 
