﻿14 
  Prof. 
  H. 
  Nagaoka 
  on 
  the 
  Calculation 
  of 
  Maximum 
  

  

  by 
  Grover, 
  this 
  difficulty 
  is 
  overcome 
  by 
  finding 
  the 
  approxi- 
  

   mate 
  value 
  of 
  the 
  distance 
  by 
  means 
  of 
  Rayleigh's 
  formula, 
  

   and 
  by 
  using 
  a 
  relation 
  which 
  is 
  rather 
  empirical, 
  and 
  the 
  

   ultimate 
  result 
  is 
  arrived 
  at 
  after 
  a 
  number 
  of 
  successive 
  

   approximations. 
  

  

  The 
  process 
  which 
  I 
  am 
  now 
  going 
  to 
  develop 
  is 
  similar 
  

   to 
  that 
  already 
  used 
  in 
  my 
  former 
  papers 
  and 
  is 
  characterized 
  

   by 
  giving 
  the 
  value 
  of 
  q 
  corresponding 
  to 
  the 
  maximum 
  force 
  

   by 
  a 
  simple 
  relation 
  ; 
  it 
  does 
  not 
  necessitate 
  the 
  knowledge 
  

   of 
  the 
  approximate 
  value 
  of 
  the 
  required 
  distance, 
  but 
  by 
  

   two 
  or 
  three 
  processes 
  of 
  approximation 
  in 
  finding 
  the 
  value 
  

   of 
  q, 
  it 
  leads 
  to 
  results 
  which 
  can 
  be 
  used 
  in 
  measurements 
  of 
  

   great 
  accuracy 
  even 
  in 
  the 
  most 
  unfavourable 
  case. 
  

  

  Denote 
  the 
  radii 
  of 
  the 
  coils 
  by 
  a 
  and 
  A, 
  the 
  distance 
  

   between 
  them 
  by 
  z, 
  then 
  the 
  mutual 
  inductance 
  is 
  given 
  by 
  

  

  C" 
  co*6d0 
  

  

  M 
  = 
  47rAa| 
  , 
  , 
  9 
  9 
  9 
  ., 
  . 
  =^, 
  . 
  . 
  (1) 
  

   J 
  VA 
  2 
  + 
  a 
  2 
  + 
  z 
  2 
  — 
  2Aacos<9' 
  v 
  J 
  

  

  whence 
  the 
  force 
  between 
  the 
  unit 
  currents 
  passing 
  through 
  

   them 
  is 
  given 
  by 
  

  

  BM 
  . 
  . 
  f» 
  cos 
  0cW 
  , 
  ON 
  

  

  ^ 
  Jo 
  (A» 
  + 
  a» 
  + 
  ^-2Aacostf)*- 
  * 
  () 
  

  

  For 
  evaluating 
  (1) 
  and 
  (2), 
  we 
  have 
  to 
  put, 
  as 
  usual, 
  

  

  ±(s-e 
  l 
  )(s-e 
  2 
  )(s-e 
  3 
  ) 
  = 
  ±s*-cj 
  2 
  s-g 
  3 
  = 
  S, 
  

  

  where 
  

  

  2/9 
  1-/3 
  1+0 
  

  

  13: 
  

  

  and 
  

  

  (2 
  \i 
  

  

  \Aa) 
  ' 
  

  

  u= 
  I 
  — 
  - 
  or 
  s 
  = 
  f(^(u). 
  

  

  Js 
  vs 
  6 
  ' 
  

  

  A 
  2 
  + 
  a 
  2 
  + 
  z' 
  

   6Aa 
  

  

  ds 
  

  

  We 
  easily 
  find 
  that 
  (2) 
  is 
  given 
  by 
  

  

  J 
  t 
  

  

  <°i 
  — 
  T? 
  \k 
  — 
  t\ 
  (^ 
  + 
  ei< 
  °y> 
  [ 
  

  

  (3) 
  

  

  