﻿6$ 
  Dr. 
  A. 
  C. 
  Crehore 
  on 
  the 
  Formation 
  of 
  the 
  

  

  Thus, 
  since 
  a 
  Q 
  — 
  l 
  

  

  i 
  

   we 
  have 
  

  

  « 
  2 
  = 
  2 
  

  

  

  

  1 
  

  

  3 
  

   4 
  

  

  

  1 
  

  

  «6 
  = 
  2 
  

  

  3 
  

  

  ' 
  4 
  ' 
  

  

  5 
  

   6 
  

  

  Instead 
  of 
  retaining 
  a, 
  a', 
  7% 
  5, 
  and 
  % 
  in 
  the 
  equations, 
  it 
  is 
  

   better 
  to 
  use 
  the 
  quantities 
  m 
  ) 
  n, 
  v, 
  and 
  \, 
  which 
  may 
  be 
  

   defined 
  by 
  the 
  equations 
  

  

  a 
  =a 
  ,m. 
  

  

  

  s 
  = 
  a*A 
  _1 
  where 
  A= 
  (v 
  2 
  + 
  m? 
  + 
  n 
  2 
  )-%, 
  

   iV 
  =a*vcosX. 
  

  

  It 
  is 
  convenient 
  to 
  refer 
  all 
  distances 
  to 
  some 
  radius 
  a* 
  as 
  

   unity 
  instead 
  of 
  to 
  a 
  centimetre, 
  and 
  a* 
  may 
  be 
  taken 
  to 
  be 
  

   the 
  radius 
  of 
  the 
  orbit 
  of 
  the 
  electrons 
  in 
  a 
  simple 
  atom, 
  say 
  

   that 
  of 
  hydrogen. 
  For 
  brevity 
  let 
  cos 
  A 
  = 
  A, 
  cos7=T, 
  

   ?rt 
  2 
  + 
  n 
  2 
  = 
  cr, 
  and 
  mn 
  = 
  B. 
  With 
  these 
  substitutions, 
  an 
  

   examination 
  of 
  (40) 
  shows 
  that 
  

  

  F 
  ' 
  =-T^{^-ATl| 
  r 
  A 
  3 
  +? 
  2A 
  5 
  (mncos 
  7 
  + 
  ? 
  ;AT) 
  

   Along 
  r 
  -^ 
  I 
  L 
  J 
  L 
  Z 
  

  

  Along 
  

  

  3 
  5 
  

   2*4 
  

  

  + 
  9- 
  1 
  .2W( 
  „ 
  y 
  

  

  3 
  5 
  7 
  

   + 
  -.-. 
  . 
  2 
  3 
  AV 
  V 
  

  

  4 
  6 
  

  

  ■] 
  }' 
  (41) 
  

  

  where, 
  after 
  multiplying 
  the 
  brackets, 
  T 
  n 
  is 
  to 
  be 
  replaced 
  

   by 
  zero 
  if 
  n 
  is 
  odd, 
  and 
  T 
  2n 
  by 
  a 
  2n 
  g 
  n 
  , 
  where 
  g 
  = 
  m 
  2 
  + 
  ?i 
  2 
  

   — 
  2mn 
  cos 
  y=a 
  — 
  2BF. 
  By 
  performing 
  the 
  operations 
  

  

  