47.  The  pendulum  and  its  teaching.  We  can  demonstrate
the  correctness  of  Galileo's  conclusion  in  still  another  way  —
one  which  he  himself  employed.  If  we  allow  balls  of  iron  and
wood,  for  example,  to  roll  together  down  the  plane  of  Fig.  22,
we  shall  find  that  they  reach  the  bottom  in  almost  exactly  the
same  time.  This  experiment  differs  from  that  with  the  freely
falling  bodies  only  in  that  the  resistance  of  the  air  is  here  more
nearly  negligible  because  the  balls  are  moving  more  slowly.
In  order  to  make  them  move  still  more  slowly  Galileo  sus-
pended them  as  the  bobs  of  long  pendulums  and  observed  that


Fig.  24.  Feather
and  coin  fall

■

together  in  a
vacuum


UNIFOEMLY  ACCELEEATED  MOTION  31

the  periods  of  pendulums  of  equal  lengths,  swinging  through
short  arcs,  are  completely  independent  of  the  weight  or  material
of  the  hols.  Since  in  this  experiment  the  bobs,  as  they  pass
through  any  given  position,  are  merely  moving  very  slowly
down  identical  inclined  planes  (see  Fig.  13),  it  is  evident  that
this  equality  of  periods  proves  in  the  most  exact  way  the
equality  in  the  rates  of  fall  of  different  bodies.  Indeed,  it  is
from  exact  measurements  on  the  periods  and  lengths  of  pendu-
lums that  the  value  of  ^  (980  cm.)  is  most  accurately  determined
(see  Experiment  17,  authors*  manual).
