34.  The  specific  gravity  of  solids  is  determined  by  the
theorem  of  the  renowned  Archimedes,  that  "  when  a  body
is  immersed  in  water,  it  loses  a  portion  of  its  weight  exactly
equal  to  the  weight  of  the  water  displaced."  He  thus  de-
tected the  fraud  of  the  goldsmith  who  fur-
nished to  King  Hiero  of  Syracuse,  as  a  crown
of  pure  gold,  one  fashioned  of  base  metal — the
specific  gravity  of  the  debased  alloy  was  too
small  for  gold.  It  is  plain  that  a  solid  dis-
places, when  immersed,  exactly  its  own  bulk
of  water,  and  loses  weight  to  a  corresponding
amount.  Hence,  if  we  weigh  a  body  first
in  air  and  then  in  water,  the  loss  of  weight  ob-
served, is  equal  to  the  volume  of  water,  cor-
responding to  the  bulk  of  the  solid.  Fig.  19
shows  a  group  of  crystals  of  quartz  suspended
from  the  underside  of  the  scale-pan  by  a  fila-
ment of  silk.  Its  weight  in  air  was  previously
determined.  Its  diminished  weight  in  the
water,  subtracted  from  the  weight  in  air,  gives
^^S-  i9-  a  sum  equal  to  the  bulk  of  water  displaced.
From  these  elements  is  deduced  the  rule  to  find  the  specific
gravity  of  a  solid.      "  Subtract  the  weight  in  water  from

the  weight  in
air,  divide  the
weight  in  air
by  this  dif-
ference, and
the  quotient
will  be  the
specific  gra-
vity." Fig.
20  shows  the
Fig.  20.  balance       ar-


How  is  it  determined  ?  What  is  the  theorem  of  Archimedes  ?    .34.  How
thi.s  illustrated  in  fig.  19  ?     Give  the  rule  for  specific  gravity


WEIGHT    AND    SPECIFIC    GRAVITY.
