188     Mr.  G.  K.  Winter  on  Testing  the  Metal-resistance  of 
tical  with  equation  (5),  is  much  more  complicated  and  tedious 
to  solve,  owing  to  the  attempt  to  isolate  the  unknown  quantity 
in  the  literal  equation,  which  is,  I  think,  a  mistake  in  this  case. 
The  above  correction  to  the  Wheatstone-bridge  method  of 
testing  line-resistance,  however,  is  only  true  so  long  as  the  ratio 
E' 
-^  remains  constant  during  the  two  tests.     We  have  not  much 
fear  of  the  electromotive  force  of  the  testing  battery  changing ; 
but  earth- currents  are,  as  a  rule,  continually  varying  in  strength ; 
for  this  reason  I  have  always  considered  the  bridge  method  of 
testing  line-resistance  unreliable.  There  are  at  least  two  me- 
thods which  are  much  to  be  preferred.  One  is  Mance's  method, 
given  in  the  Number  of  this  Magazine  for  April  last  (p.  314), 
and  the  other  a  modification  of  Varley's  method  of  testing  the 
internal  resistance  of  a  cell  by  the  differential  galvanometer. 
In  both  these  methods  the  cable  or  line,  together  with  its  two 
earth-plates,  is  considered  as  an  electromotor,  and  its  internal 
resistance  is  measured. 
I  need  scarcely  say  that  in  every  method  of  measuring  the  in- 
ternal resistance  of  an  electromotor,  unless  its  electromotive 
force  is  known,  two  observations  are  necessary  ;  and  if  this  force 
is  liable  to  vary,  the  more  quickly  these  observations  follow  each 
other  the  greater  the  chance  of  accuracy.  In  the  two  tests  just 
referred  to,  the  first  observation  is  simply  the  noting  of  a  deflec- 
tion, and  the  second  is  simply  seeing  that  the  deflection  does 
not  alter  when  we  press  a  key  in  one  case  and  raise  a  key  in  the 
other.  In  land-lines  there  is  usually  no  interval  at  all  between 
the  two  observations ;  but  in  cables  the  alteration  in  the  resist- 
ance of  the  circuit  causes  a  sudden  difference  in  the  dynamic 
charge  of  the  cable,  and  hence  a  sudden  flow  through  the  galva- 
nometer. We  have  therefore  merely  to  wait  till  the  needle 
comes  to  rest  before  the  second  observation  can  be  taken. 
Mance's  method  was  so  fully  described  in  the  April  Number  of 
this  Journal  that  I  need  not  further  refer  to  it ;  so  I  will  pro- 
ceed at  once  to  the  second  method,  which  is  more  applicable  to 
measuring  the  resistance  of  land-lines. 
The  instrument  I  use  for  the  purpose  is  a  double-shunt  dif- 
ferential galvanometer  having  the  resistance  and  magnetic  effect 
of  its  coils  equal.  The  connexions  will  be  readily  understood 
from  fig.  2  (Plate  II.).  C  is  a  thick  wire  offering  comparatively 
no  resistance.  The  key  is  first  pressed,  so  that  the  earth-cur- 
rent flows  through  only  one  coil  of  the  galvanometer,  and  the 
in  which  a  and  b  are  the  branch  resistances,  W  the  adjusted  resistance 
with  a  positive,  W"  that  with  a  negative,  and /the  resistance  of  the  test- 
ing battery. 
