﻿Force 
  between 
  Two 
  Coaxial 
  Circular 
  Currents. 
  

  

  19 
  

  

  The 
  number 
  given 
  by 
  Grover 
  is 
  log 
  q 
  = 
  1*4035322 
  ; 
  the 
  

   value 
  for 
  z/A 
  is 
  0' 
  38353439, 
  while 
  Grover 
  gives 
  for 
  it 
  

   0*3835341, 
  agreeing 
  to 
  within 
  a 
  ten-millionth 
  part. 
  

  

  For 
  the 
  convenience 
  of 
  practical 
  calculation, 
  the 
  foil 
  owing- 
  

   tables 
  of 
  Ar 
  and 
  r 
  are 
  given 
  for 
  different 
  values 
  of 
  q 
  and 
  q 
  1 
  

   respectively, 
  calculated 
  for 
  me 
  by 
  Mr. 
  Shobei 
  Shimizu 
  ; 
  

   Ar 
  in 
  the 
  first 
  table 
  are 
  residuals 
  

  

  614-4 
  q 
  5 
  - 
  7 
  934-6/+ 
  -230*lxl0y 
  5 
  

  

  in 
  (II.), 
  while 
  rin 
  the 
  second 
  table 
  refers 
  to 
  those 
  calculated 
  

   -according 
  to 
  (II'.). 
  

  

  •7- 
  

  

  Ar. 
  

  

  ■ 
  *r 
  

  

  000 
  

  

  o-ooooooo 
  

  

  1 
  

  

  o-oi 
  

  

  o-ooooooi 
  

  

  19 
  

  

  0-02 
  

  

  0-0000020 
  

  

  128 
  

  

  0-03 
  

  

  00000148 
  

  

  469 
  

  

  004 
  

  

  0-0000616 
  

  

  1244 
  

  

  0-05 
  

  

  0-0001860 
  

  

  2705 
  

  

  0-06 
  

  

  0-0004565 
  

  

  5147 
  

  

  0-07 
  

  

  0-0009712 
  

  

  ! 
  

  

  8885 
  • 
  

  

  008 
  

  

  0-0018597 
  

  

  14251 
  

  

  0-09 
  

  

  0-0032848 
  

  

  21574 
  

  

  C10 
  

  

  0-0054422 
  

  

  31175 
  

  

  0-11 
  

  

  0-0085597 
  

  

  

  ?• 
  

  

  r. 
  

  

  A 
  r 
  

  

  0-000 
  

  

  2-0000000 
  

  

  339002 
  

  

  o-ooi 
  

  

  2-0339002 
  

  

  366859 
  

  

  0-002 
  

  

  2-0705861 
  

  

  389351 
  

  

  0-003 
  

  

  2-1095212 
  

  

  409255 
  

  

  0-004 
  

  

  2-1504467 
  

  

  427502 
  

  

  0005 
  

  

  2-1931969 
  

  

  444584 
  

  

  0006 
  

  

  2-2376553 
  

  

  460811 
  

  

  0-007 
  

  

  2-2837364 
  

  

  476382 
  

  

  0008 
  

  

  23313746 
  

  

  491447 
  

  

  0-009 
  

  

  2-3S05193 
  

  

  506120 
  

  

  o-oio. 
  

  

  2-4311313 
  

  

  

  From 
  the 
  table, 
  it 
  will 
  be 
  noticed 
  that 
  the 
  residuals 
  ap- 
  

   parently 
  cover 
  a 
  wide 
  range 
  in 
  the 
  calculation 
  with 
  q 
  : 
  this 
  

   is 
  at 
  once 
  evident 
  from 
  the 
  fact 
  that 
  the 
  range 
  covered 
  by 
  

   the 
  ^-series 
  is 
  very 
  great 
  compared 
  with 
  that 
  in 
  which 
  the 
  

   ^-series 
  are 
  applicable. 
  This 
  is 
  in 
  no 
  way 
  an 
  impediment 
  

   in 
  practical 
  calculations, 
  as 
  the 
  formula 
  in 
  terms 
  of 
  q 
  is 
  

   simpler 
  than 
  that 
  in 
  q 
  Y 
  ; 
  especially 
  in 
  numerical 
  evaluation 
  

   of 
  q 
  from 
  known 
  values 
  of 
  r, 
  the 
  formula 
  (II.) 
  is 
  characterized 
  

   by 
  the 
  great 
  facility 
  with 
  which 
  all 
  the 
  terms 
  can 
  be 
  calcu- 
  

   lated 
  and 
  the 
  required 
  approximations 
  brought 
  to 
  test. 
  As 
  

   all 
  the 
  rest 
  of 
  the 
  calculation 
  depends 
  on 
  the 
  value 
  of 
  q, 
  

  

  Q2 
  

  

  