﻿78 
  Dr. 
  A. 
  C. 
  Crehore 
  on 
  the 
  Formation 
  of 
  the 
  

  

  The 
  other 
  (n 
  — 
  1) 
  electrons 
  in 
  the 
  ring 
  give 
  similar 
  ex- 
  

   pressions. 
  If 
  F', 
  F", 
  and 
  F'" 
  denote 
  the 
  resultants 
  of 
  all 
  

   the 
  forces 
  in 
  the 
  ring 
  due 
  to 
  F 
  l5 
  F 
  2 
  , 
  and 
  F 
  3 
  respectively, 
  we 
  

  

  find 
  

  

  ,2 
  

  

  F' 
  = 
  -,. 
  .y 
  a 
  S, 
  a 
  repulsion 
  from 
  0, 
  . 
  . 
  (66) 
  

   F''=,-^ 
  2 
  (2P-S), 
  ........ 
  (67) 
  

  

  Vue'q' 
  

  

  F"' 
  = 
  ^(2P-S), 
  (6$) 
  

  

  wnere 
  

  

  o 
  7T 
  2lT 
  37T 
  # 
  / 
  i\ 
  7 
  '" 
  //j 
  \ 
  

  

  b 
  = 
  cosec 
  — 
  +- 
  cosec 
  1- 
  cosec 
  — 
  + 
  . 
  . 
  . 
  . 
  cosec( 
  n 
  — 
  I 
  > 
  — 
  [ov) 
  

  

  n 
  n 
  n 
  ' 
  n 
  

  

  F= 
  sin 
  — 
  f- 
  sm 
  [- 
  sin 
  — 
  + 
  sin 
  (n 
  — 
  1) 
  — 
  . 
  liv) 
  

  

  ?i 
  n 
  /t 
  ' 
  w 
  

  

  More 
  than 
  One 
  Ring 
  of 
  Electrons. 
  

  

  The 
  effect 
  upon 
  the 
  outside 
  ring 
  of 
  electrons 
  of 
  an 
  inside 
  

   ring 
  is 
  approximately 
  the 
  same 
  as 
  if 
  all 
  the 
  electrons 
  in 
  the 
  

   inside 
  ring 
  were 
  situated 
  at 
  the 
  centre 
  of 
  the 
  sphere. 
  If 
  the 
  

   total 
  number 
  in 
  all 
  electrons 
  in 
  inside 
  rings 
  is 
  u, 
  supposed 
  

   to 
  be 
  at 
  the 
  centre 
  of 
  the 
  sphere, 
  the 
  force 
  of 
  repulsion 
  

   which 
  they 
  exert 
  upon 
  the 
  single 
  electron 
  at 
  A 
  in 
  the 
  outside 
  

  

  This 
  must 
  be 
  added 
  to 
  the 
  sum 
  of 
  the 
  three 
  forces 
  {66), 
  (67), 
  

   and 
  (68) 
  to 
  obtain 
  the 
  whole 
  force 
  upon 
  A 
  due 
  to 
  all 
  the 
  

   rings 
  of 
  electrons. 
  

  

  Sphere 
  of 
  Positive 
  Electrification. 
  

  

  If 
  it 
  is 
  assumed 
  that 
  the 
  electrons 
  are 
  within 
  a 
  sphere 
  of 
  

   positive 
  electrification 
  of 
  radius 
  b, 
  its 
  attraction 
  upon 
  the 
  

   electron 
  at 
  A, 
  assuming 
  uniform 
  density, 
  is 
  

  

  6 
  ~ 
  K6 
  3 
  ~ 
  Kb" 
  ' 
  

   where 
  p 
  is 
  the 
  total 
  number 
  of 
  electrons 
  in 
  the 
  atom. 
  

  

  