﻿318 
  Prof. 
  Lyle 
  on 
  Circular 
  Filaments 
  or 
  Circular 
  

  

  Thus 
  i£ 
  Rj 
  and 
  R 
  2 
  be 
  the 
  resistances 
  of 
  the 
  parallel 
  branches 
  

   in 
  which 
  the 
  two 
  coils 
  r 
  v 
  n± 
  and 
  r 
  2 
  , 
  n 
  2 
  are 
  included 
  when 
  the 
  

   needle 
  at 
  their 
  common 
  centre 
  is 
  unaffected, 
  then 
  

  

  r* 
  w 
  9 
  R, 
  

  

  and 
  if 
  the 
  distance 
  2A, 
  between 
  the 
  poles 
  of 
  the 
  small 
  magnet 
  

   be 
  taken 
  into 
  account 
  (see 
  Maxwell, 
  § 
  711), 
  

  

  r 
  2 
  ^Ki 
  L 
  V'l 
  r 
  2 
  J 
  J 
  

  

  where 
  for 
  r 
  1 
  and 
  r 
  2 
  on 
  the 
  right 
  side 
  the 
  mean 
  radii 
  a 
  x 
  and 
  a 
  2 
  

   got 
  by 
  approximate 
  measurement 
  may 
  be 
  substituted. 
  

   In 
  general 
  we 
  have 
  

  

  Ri 
  Gi 
  

  

  R 
  2 
  G 
  2 
  

  

  i^ib-m 
  

  

  where 
  R 
  1? 
  E 
  2 
  are 
  the 
  resistances 
  of 
  the 
  two 
  parallel 
  branches 
  

   in 
  which 
  the 
  coils 
  lie, 
  and 
  G 
  j5 
  G 
  2 
  their 
  galvanometer 
  constants 
  

   given 
  in 
  terms 
  of 
  equivalent 
  radius, 
  breadth 
  or 
  depth 
  in 
  § 
  10. 
  

   14. 
  The 
  proposed 
  electrical 
  method 
  of 
  measuring 
  the 
  equi- 
  

   valent 
  radius 
  of 
  a 
  coil 
  will 
  be 
  easily 
  understood 
  from 
  the 
  

   following. 
  If, 
  with 
  the 
  apparatus 
  used 
  in 
  Bosscha's 
  method 
  

   for 
  determining 
  the 
  ratio 
  of 
  the 
  equivalent 
  radii 
  of 
  two 
  coils, 
  

   some 
  arrangement 
  be 
  made 
  by 
  means 
  of 
  which 
  the 
  smaller 
  

   coil 
  can 
  slide 
  to 
  either 
  side 
  of 
  the 
  larger 
  one, 
  still 
  remaining 
  

   coaxal 
  with 
  and 
  parallel 
  to 
  it, 
  then 
  if 
  the 
  former 
  be 
  moved 
  a 
  

   distance 
  x 
  to 
  either 
  side, 
  and 
  if 
  the 
  resistances 
  be 
  readjusted 
  

   so 
  that 
  the 
  magnet 
  at 
  the 
  centre 
  of 
  the 
  large 
  coil 
  is 
  not 
  

   affected, 
  we 
  have 
  

  

  Jh 
  = 
  n 
  2 
  r 
  2 
  2 
  

  

  rM 
  H/to 
  1 
  + 
  «")*' 
  [ 
  } 
  

  

  if 
  the 
  coils 
  be 
  single-shell 
  ones, 
  where 
  R/ 
  and 
  E 
  2 
  / 
  are 
  the 
  new 
  

   resistances 
  in 
  the 
  parallel 
  branches. 
  If 
  with 
  the 
  same 
  resist- 
  

   ances 
  R 
  1 
  / 
  and 
  R/ 
  in 
  the 
  branches, 
  balance 
  is 
  obtained 
  with 
  

   the 
  small 
  coil 
  first 
  at 
  one 
  side 
  and 
  then 
  at 
  the 
  other, 
  the 
  distance 
  

   between 
  the 
  two 
  positions 
  of 
  the 
  small 
  coil 
  will 
  be 
  2x 
  ; 
  and 
  as 
  

   the 
  ratio 
  of 
  r^ 
  to 
  r 
  2 
  determined 
  by 
  the 
  method 
  in 
  the 
  last 
  

   section 
  is 
  known 
  and 
  given 
  by 
  

  

  '-^=^| 
  2 
  (ii.) 
  

  

  r 
  2 
  n 
  2 
  ii 
  2 
  K 
  ' 
  

  

  we 
  can 
  from 
  equations 
  I. 
  and 
  II. 
  determine 
  both 
  i\ 
  and 
  r 
  2 
  in 
  

   terms 
  of 
  2x 
  and 
  the 
  two 
  ratios 
  of 
  resistances. 
  

  

  