﻿■324 
  Prof. 
  Lyle 
  on 
  Circular 
  Filaments 
  or 
  Circular 
  

  

  by 
  A 
  and 
  B, 
  A 
  being 
  on 
  the 
  side 
  o£ 
  the 
  magnetometer 
  furthest 
  

   from 
  the 
  observer. 
  

  

  1. 
  Coil 
  adjusted 
  at 
  A 
  so 
  as 
  to 
  give 
  a 
  balance, 
  then 
  

   drawn 
  to 
  other 
  side 
  o£ 
  magnetometer 
  and 
  adjusted 
  

   similarly 
  at 
  B. 
  Distance 
  A 
  to 
  B 
  = 
  8*7280 
  cm 
  

  

  2. 
  Similarly, 
  but 
  pushing 
  the 
  coil 
  from 
  B 
  to 
  A 
  position. 
  

  

  Distance 
  B 
  to 
  A 
  =8' 
  7258 
  cm. 
  

  

  3. 
  Same 
  as 
  1. 
  „ 
  A 
  to 
  B 
  = 
  8*7278 
  cm. 
  

  

  4. 
  Same 
  as 
  2. 
  „ 
  B 
  to 
  A=8'7255 
  cm. 
  

  

  It 
  will 
  be 
  seen 
  that 
  there 
  is 
  a 
  nearly 
  constant 
  difference 
  

   between 
  the 
  results 
  obtained 
  when 
  the 
  slide-bar 
  is 
  drawn 
  

   towards 
  the 
  observer 
  from 
  the 
  A 
  to 
  the 
  B 
  position, 
  and 
  when 
  it 
  

   is 
  thrust 
  from 
  the 
  observer 
  from 
  the 
  B 
  to 
  the 
  A 
  position. 
  

   There 
  was, 
  I 
  found, 
  considerable 
  friction 
  between 
  the 
  slide- 
  

   bar 
  and 
  the 
  far 
  upright 
  which 
  fully 
  accounted 
  for 
  this 
  

   discrepancy, 
  as 
  the 
  force 
  of 
  a 
  few 
  pounds 
  was 
  sufficient 
  to 
  

   compress 
  that 
  part 
  of 
  the 
  bar 
  (it 
  was 
  not 
  a 
  very 
  thick 
  one) 
  

   between 
  the 
  coil 
  and 
  the 
  far 
  upright, 
  in 
  which 
  it 
  slid, 
  by 
  an 
  

   amount 
  equal 
  to 
  the 
  discrepancy. 
  

  

  20. 
  From 
  the 
  theory 
  established 
  in 
  the 
  early 
  sections 
  of 
  

   this 
  paper, 
  it 
  is 
  obvious 
  that 
  the 
  determination 
  of 
  the 
  mutual 
  

   inductance 
  of 
  any 
  two 
  coaxal 
  circular 
  coils 
  is 
  reduced 
  to 
  that 
  

   of 
  coaxal 
  circular 
  filaments 
  ; 
  and 
  in 
  this 
  method 
  no 
  terms 
  

   are 
  neglected 
  of 
  order 
  lower 
  in 
  small 
  quantities 
  than 
  the 
  

   fourth 
  power 
  of 
  the 
  ratio 
  of 
  the 
  cross 
  section 
  to 
  the 
  radius. 
  

  

  Hence 
  by 
  using 
  Maxwell's 
  tables 
  (see 
  Maxwell, 
  Chap. 
  xiv. 
  

  

  M 
  

  

  Appendix) 
  for 
  log 
  -: 
  -= 
  as 
  a 
  function 
  of 
  7, 
  where 
  

  

  4*77 
  yr 
  x 
  r 
  2 
  

  

  r 
  l 
  and 
  r 
  2 
  being 
  the 
  radii 
  of 
  the 
  filaments, 
  and 
  x 
  the 
  distance 
  

   between 
  their 
  planes, 
  we 
  can 
  quickly 
  and 
  accurately 
  determine 
  

   the 
  mutual 
  induction 
  of 
  two 
  coils. 
  

  

  21. 
  For 
  single-shell 
  coils 
  of 
  equivalent 
  radii 
  r 
  1 
  and 
  r 
  2 
  and 
  

   distance 
  x 
  apart 
  the 
  process 
  is 
  very 
  expeditious, 
  for 
  M, 
  

   determined 
  as 
  in 
  § 
  20, 
  has 
  only 
  to 
  be 
  multiplied 
  by 
  n^ 
  to 
  

   get 
  the 
  mutual 
  inductance 
  of 
  the 
  coils. 
  

  

  22. 
  To 
  determine 
  the 
  mutual 
  inductance 
  of 
  two 
  double-shell 
  

   coaxal 
  coils, 
  we 
  replace 
  the 
  coils 
  by 
  their 
  equivalent 
  filaments, 
  

   determine 
  the 
  M 
  ; 
  s 
  as 
  in 
  § 
  20 
  for 
  the 
  four 
  pairs 
  got 
  by 
  

   combining 
  a 
  filament 
  of 
  one 
  coil 
  with 
  a 
  filament 
  of 
  the 
  other, 
  

   and 
  multiply 
  the 
  mean 
  of 
  these 
  by 
  n 
  Y 
  n 
  2 
  . 
  

  

  