﻿328 
  Prof. 
  Lyle 
  on 
  Circular 
  Filaments 
  or 
  Circular 
  

  

  respectively, 
  that 
  the 
  mean 
  value 
  of 
  

  

  5- 
  3 
  was 
  = 
  2-60070. 
  

   Hence 
  (see 
  §§10 
  and 
  13) 
  as 
  the 
  ratio 
  of 
  the 
  equivalent 
  radii 
  

  

  "^-n.R.l 
  2W 
  «2 
  2 
  /i 
  

   we 
  get 
  

  

  -} 
  = 
  ~ 
  x 
  2-60070 
  x 
  1-001044, 
  

  

  24-81295 
  ,„ 
  .„„. 
  

   r2=: 
  -M2053 
  = 
  10 
  ' 
  25104 
  - 
  

  

  The 
  force 
  between 
  the 
  suspended 
  and 
  one 
  of 
  the 
  fixed 
  coils 
  

   is 
  now 
  equal 
  to 
  the 
  sum 
  of 
  the 
  four 
  forces 
  between 
  two 
  

   coaxal 
  circular 
  filaments 
  of 
  radii 
  24*81295 
  and 
  10*25104 
  

   [each 
  small 
  filament 
  carrying 
  current 
  =^n 
  2 
  G 
  and 
  each 
  large 
  

   filament 
  carrying 
  current 
  ^wiC] 
  at 
  the 
  four 
  different 
  distances 
  

  

  a? 
  + 
  A+/3 
  2 
  , 
  » 
  —A— 
  A? 
  

  

  that 
  is 
  13-006, 
  11-994, 
  12*436, 
  12*564. 
  

  

  The 
  parameter 
  y 
  for 
  each 
  of 
  these 
  pairs 
  will 
  be 
  

  

  58°31'-74, 
  59°23 
  / 
  -88, 
  59° 
  l'*29, 
  58°54'*69, 
  

  

  which 
  give 
  respectively 
  for 
  -= 
  — 
  the 
  values 
  

  

  1-032198, 
  1-055872, 
  1*046662, 
  and 
  1*043648 
  

  

  whose 
  mean 
  value 
  is 
  

  

  1*044595. 
  

  

  Lord 
  Eayleigh's 
  value 
  for 
  the 
  same 
  was 
  

  

  1*044627. 
  

  

  26. 
  If, 
  in 
  the 
  above 
  calculation, 
  I 
  made 
  allowance 
  for 
  tho 
  

   length 
  of 
  the 
  small 
  magnet 
  used 
  in 
  comparing 
  the 
  equivalent 
  

   radii 
  of 
  the 
  coils, 
  there 
  would 
  be 
  a 
  very 
  appreciable 
  difference 
  

   in 
  the 
  result 
  even 
  if 
  the 
  needle 
  were 
  very 
  short. 
  I 
  do 
  not 
  know 
  

  

  