﻿310 
  Prof. 
  Lyle 
  on 
  Circular 
  Filaments 
  or 
  Circular 
  

  

  measure 
  with 
  considerable 
  accuracy 
  a 
  point 
  at 
  which 
  the 
  

   previously 
  obtained 
  very 
  sparse 
  rain-like 
  condensations 
  passed 
  

   rapidly 
  into 
  very 
  much 
  denser 
  condensations 
  ; 
  these, 
  however, 
  

   I 
  could 
  scarcly 
  term 
  fogs, 
  as 
  their 
  duration 
  was 
  never 
  very 
  

   great. 
  

  

  My 
  very 
  best 
  thanks 
  are 
  due 
  to 
  Professor 
  Ramsay, 
  at 
  

   whose 
  suggestion 
  these 
  experiments 
  were 
  begun 
  and 
  whose 
  

   advice 
  and 
  assistance 
  were 
  constantly 
  at 
  my 
  disposal. 
  

  

  Chemical 
  Laboratory. 
  University 
  College, 
  London, 
  

   April 
  1901. 
  

  

  XXXII. 
  On 
  Circular 
  Filaments 
  or 
  Circular 
  Magnetic 
  Shells 
  

   equivalent 
  to 
  Circular 
  Coils, 
  and 
  on 
  the 
  equivalent 
  Radius 
  

   of 
  a 
  Coil. 
  By 
  Professor 
  Thomas 
  P. 
  Lyle 
  *. 
  

  

  [Plate 
  VI.] 
  

  

  1. 
  rflHE 
  magnetic 
  potential 
  of 
  a 
  coil, 
  with 
  current 
  C, 
  at 
  any 
  

   A 
  point 
  in 
  its 
  axis 
  is 
  given 
  to 
  a 
  high 
  order 
  of 
  

   approximation 
  by 
  

  

  v=2™c(i-f 
  + 
  |j 
  + 
  ^A) 
  • 
  • 
  *■ 
  

  

  if 
  the 
  dimensions 
  of 
  the 
  cross 
  section 
  are 
  small 
  compared 
  with 
  

   the 
  radius 
  o£ 
  the 
  coil 
  and 
  the 
  winding 
  is 
  uniform 
  ; 
  

   where 
  a 
  = 
  mean 
  radius, 
  

   f 
  = 
  axial 
  breadth, 
  

   rj 
  = 
  radial 
  depth, 
  

  

  x 
  = 
  distance 
  of 
  point 
  on 
  the 
  axis 
  from 
  the 
  centre 
  

   of 
  the 
  coil, 
  

   and 
  p 
  2 
  = 
  a 
  2 
  + 
  x 
  2 
  . 
  

  

  (See 
  Maxwell, 
  sect. 
  700.) 
  

   Expanding 
  in 
  ascending 
  powers 
  of 
  x/a, 
  

  

  _ 
  x 
  5 
  r, 
  o 
  3.5(7^-6/7*) 
  n 
  

   2 
  . 
  4 
  . 
  a" 
  L 
  24a 
  2 
  J 
  

  

  + 
  2.4.6.a 
  7 
  L 
  Ma* 
  J 
  

   — 
  &c 
  &c. 
  > 
  II. 
  

  

  * 
  Communicated 
  by 
  the 
  Physical 
  Society 
  : 
  read 
  December 
  13, 
  1901. 
  

  

  