Galvano-        Let  now  the  galvanometer  resistance  be  capable  of  variation,
meter  Re-     We  shall  assume  that  the  mass  of  wire  in  the  galvanometer  and
sistance     the  channel  in  which  it  is  wound  remain  constant.    When  this  is
Variable,    the  case  the  electromagnetic  force  at  the  needle  is,  as  will  be
proved  in  Vol.  II.,  proportional  to  the  square  root  of  the  resist-
ance of  the  galvanometer.     Hence  for  a  given  value  of  y5  the
deflection  of  the  needle  may  be  put  equal  to  ayb  vV6  where  a  is  a
constant.     Hence


SENSIBILITY  OF  BRIDGE  METHOD.  333

We  have  in  this  case  to  find  when  D/r^r^  N//-5  is  a  minimum.  Galvano
This  can  be  put  into  the  form  (m  -f-  nr^/k^/r^  where  tn,  n,  k,
do  not  involve  r5.  Equating  tlie  first  differential  coefficient  of
this  quantity  to  zero,  we  get  for  a  minimum  rb  =  mjn,  or  after
reduction  r5  =  fj(r4  +  r3)/(rj  +  r2).  This  value  of  r5  taken,  along
with  the  already  found  values  of  r^  and  r3  gives  'maximum
sensibility  to  the  bridge  arrangement  when  the  battery  only  is
kept  constant.
