76.  Density  of  a  heavy  solid.  The  density
of  a  Ixidy  is  by  definition  its  mass  divided  by
its  volume.  It  is  always  possible  to  obtain
the  mass  of  a  body  by  weighing  it,  but  it  ia
not,  in  general,  possible  to  obtain  the  volume
of  an  irregular  body  from  measurements  of
its  dimensions.  Archimedes'  principle,  how-
ever, furnishes  an  accurate  and  easy  method
for  obtaining  the  volume  of  any  solid,  how-
ever irregular,  for  by  the  preceding  paragraph  this  volume  is
numerically  equal  to  the  loss  of  weight  in  water.  Hence  the
equation  which  defines  density,  namely.
Fio.  47.  Method  of
weighing  a  body
nnder  water


I


PEESSUEE  IN  LIQUIDS


Loss  of  weight  in  water


77,  Density  of  a  solid  lighter  than  water.
may  still  obtain  ita  volume  by
forcing  it  beneath  the  surface
with  a  sinker.  Thus  suppose
w^  represents  the  weight  on
the  right  pan  of  the  balance
when  the  body  is  in  air  and  the
sinker  in  water,  as  in  Fig.  48;
while  Wj  is  the  weight  on  the
right  pan  when  both  body  and
sinker  are  under  water.  Then
w,— Wj  is  obviously  the  buoy-
ant effect  of  the  water  on  the
body  alone,  and  is  therefore
equal  to  the
weight  of  the

displaced  wat«r  wMch  is  numerically  equal  to

the  volume  of  the  body.
