﻿Force 
  between 
  Two 
  Coaxial 
  Circular 
  Currents. 
  17 
  

  

  For 
  expressing 
  z 
  in 
  terms 
  of 
  q 
  u 
  we 
  remark 
  that 
  

  

  iH 
  

  

  (A-a) 
  

  

  

  Aa. 
  „ 
  A 
  ( 
  ^ 
  1\ 
  Ka 
  

  

  whence 
  we 
  obtain 
  

  

  *M) 
  

  

  v(o.-^v(o,-^)\ 
  A 
  

   v(o,-J)-v(o,-J)/ 
  U 
  + 
  a;-- 
  ( 
  ' 
  

  

  A 
  similar 
  remark 
  as 
  for 
  (6) 
  applies 
  to 
  the 
  calculation 
  o£ 
  (7) 
  

   in 
  terms 
  of 
  q 
  l3 
  resulting 
  in 
  the 
  expression 
  

  

  -^ 
  = 
  2 
  + 
  64^(1 
  + 
  S 
  gi 
  + 
  44 
  ?1 
  2 
  + 
  192 
  ?1 
  3 
  + 
  718?! 
  4 
  + 
  2400?, 
  5 
  

  

  + 
  7352 
  ?1 
  6 
  + 
  20992^ 
  1 
  7 
  + 
  ....)- 
  ?• 
  (6') 
  

  

  It 
  is 
  generally 
  sufficient 
  to 
  retain 
  q 
  x 
  8 
  , 
  the 
  remaining 
  terms 
  

  

  being 
  negligible 
  even 
  in 
  the 
  most 
  accurate 
  work 
  that 
  can 
  at 
  

  

  present 
  be 
  attempted. 
  

  

  z 
  2 
  

   Squaring 
  (I.) 
  and 
  substituting 
  for 
  t— 
  in 
  (6) 
  and 
  (6'), 
  we 
  

  

  find 
  the 
  required 
  condition 
  to 
  be 
  equivalent 
  to 
  

  

  All 
  the 
  rest 
  is 
  a 
  simple 
  mechanical 
  operation 
  ; 
  the 
  final 
  

   equations 
  for 
  obtaining 
  q 
  or 
  q 
  x 
  from 
  the 
  known 
  ratio 
  of 
  the 
  

  

  A 
  a 
  1 
  

  

  dimensions 
  of 
  the 
  coils 
  r 
  — 
  j- 
  — 
  ( 
  = 
  «+- 
  according, 
  to 
  

  

  Grover's 
  notation) 
  may 
  be 
  presented 
  under 
  the 
  following 
  

   form 
  

  

  r 
  = 
  j- 
  + 
  6'8 
  9-51-6 
  q 
  z 
  + 
  614*4 
  9 
  5 
  -7934'6 
  q 
  7 
  

  

  + 
  103683-6 
  £ 
  9 
  -1353676-4 
  9 
  11 
  + 
  17649300-6? 
  13 
  

  

  -230-1 
  xl0 
  6 
  ^ 
  15 
  + 
  (II.) 
  

  

  Phil. 
  Mag. 
  S. 
  6. 
  Vol. 
  35. 
  No. 
  205. 
  Jan. 
  1918. 
  C 
  

  

  