﻿326 
  Prof. 
  Lyle 
  on 
  Circular 
  Filaments 
  or 
  Circular 
  

   so 
  we 
  have 
  to 
  determine 
  the 
  four 
  M's 
  where 
  

  

  

  Radii. 
  

  

  Distance. 
  

  

  1... 
  

  

  13*8054 
  and 
  13'7854 
  

  

  6*534 
  

  

  2... 
  

  

  13-8054 
  „ 
  13-5988 
  

  

  6-534 
  

  

  3... 
  

  

  13-6188 
  „ 
  13-7854 
  

  

  6-534 
  

  

  4... 
  

  

  13-6188 
  „ 
  13-5988 
  

  

  6-534 
  

  

  From 
  which 
  we 
  get 
  (see 
  Maxwell, 
  .chap, 
  xiv.) 
  

   7l 
  =76° 
  40'Jj* 
  7 
  2 
  = 
  76°34'|| 
  7a==76 
  35^ 
  v^l&wgg 
  

  

  M 
  1 
  = 
  161-2805 
  

  

  M 
  2 
  = 
  159-1388 
  M^nn 
  M— 
  1 
  WIJW 
  

   M 
  3 
  = 
  159-1642 
  ivi-ioj 
  ibot. 
  

  

  M 
  4 
  = 
  157-1594 
  

  

  Mutual 
  Inductance 
  = 
  n 
  1 
  n 
  2 
  M. 
  

  

  = 
  3775250. 
  

   .Rowland's 
  value 
  for 
  the 
  same 
  pair 
  o£ 
  coils 
  was 
  

  

  3775500. 
  

  

  24. 
  In 
  determining 
  the 
  constant 
  of 
  a 
  current-balance 
  of 
  

   the 
  type 
  used 
  by 
  Lord 
  Eayleigh 
  and 
  Mrs. 
  Sidgwick 
  in 
  their 
  

   determination 
  of 
  the 
  electrochemical 
  equivalent 
  of 
  silver, 
  

   and 
  of 
  which 
  the 
  coils 
  should 
  preferably 
  be 
  single-shell 
  ones, 
  

   we 
  should 
  first 
  determine 
  the 
  equivalent 
  radii 
  of 
  the 
  two 
  

   large 
  coils 
  and 
  of 
  the 
  suspended 
  coil 
  by 
  the 
  method 
  I 
  have 
  

   explained 
  above, 
  which 
  involves 
  in 
  the 
  first 
  instance 
  deter- 
  

   mining 
  the 
  ratios 
  of 
  these 
  equivalent 
  radii. 
  

  

  It 
  is 
  possible 
  also 
  to 
  realize 
  an 
  accuracy, 
  if 
  due 
  care 
  be 
  

   taken, 
  that 
  is 
  comparable 
  with 
  what 
  can 
  be 
  obtained 
  in 
  

   measuring 
  a 
  straight 
  line 
  by 
  the 
  well-known 
  methods. 
  

  

  We 
  can 
  now 
  imagine 
  the 
  coils 
  replaced 
  by 
  their 
  equivalent 
  

   filaments 
  and 
  calculate 
  for 
  each 
  pair 
  of 
  attracting 
  or 
  repelling 
  

   filaments 
  the 
  value 
  of 
  the 
  parameter 
  7 
  where 
  

  

  sin 
  ^7= 
  -7 
  -rf- 
  — 
  - 
  a 
  as 
  before. 
  

  

  (fi 
  + 
  ^J 
  +# 
  2 
  

  

  From 
  Lord 
  Rayleigh's 
  Table 
  * 
  we 
  get 
  the 
  value 
  of 
  

  

  corresponding 
  to 
  each 
  value 
  of 
  7 
  and 
  thence 
  -7— 
  for 
  the 
  

   * 
  Phil. 
  Trans. 
  1884. 
  

  

  