﻿Molecules 
  of 
  the 
  Elements 
  and 
  their 
  Compounds. 
  03 
  

   And 
  the 
  second 
  component 
  is 
  

   ys 
  ixee'aa'ai 
  2 
  r3aa' 
  . 
  p' 
  2 
  3 
  D 
  l 
  

  

  + 
  ^Ccos 
  2 
  7 
  + 
  — 
  2 
  Dsin7-f- 
  ^Esm2 
  7 
  J. 
  . 
  . 
  (25) 
  

  

  where 
  

  

  A 
  = 
  - 
  (r 
  2 
  + 
  2</ 
  2 
  ) 
  + 
  2(r 
  2 
  + 
  # 
  2 
  -f 
  if) 
  cos 
  a 
  + 
  2.i-r 
  sin 
  a 
  

  

  — 
  (r 
  2 
  + 
  2x 
  2 
  ) 
  cos 
  2 
  a 
  — 
  2a?2 
  sin 
  a 
  cos 
  a, 
  

  

  B 
  = 
  3a 
  2 
  .r 
  + 
  a 
  2 
  f 
  4- 
  d 
  2 
  f 
  4- 
  (a 
  2 
  # 
  2 
  + 
  3a 
  2 
  j/ 
  2 
  + 
  3a' 
  2 
  j/ 
  2 
  ) 
  cos 
  a 
  

  

  + 
  6a'*£2 
  sin 
  a 
  cos 
  a 
  + 
  3a' 
  2 
  «tf 
  2 
  cos 
  2 
  a 
  -f- 
  2a' 
  2 
  xz 
  sin 
  a 
  cos 
  2 
  a 
  

   -t- 
  a' 
  2 
  .r 
  2 
  cos 
  3 
  a 
  4- 
  a' 
  2 
  z 
  2 
  sin 
  2 
  a 
  cos 
  a 
  f 
  3a'V 
  2 
  sin 
  2 
  a, 
  

  

  C 
  = 
  r 
  2 
  + 
  2 
  < 
  y 
  2 
  + 
  2(?' 
  2 
  + 
  <r 
  2 
  + 
  ?/ 
  2 
  )cosa 
  + 
  2^sin« 
  

   + 
  (r 
  2 
  4- 
  2# 
  2 
  ) 
  cos 
  2 
  a 
  + 
  2^^ 
  sin 
  a 
  cos 
  a, 
  

  

  D 
  = 
  — 
  2a 
  2 
  ^y 
  + 
  2xy(a 
  2 
  4- 
  a' 
  2 
  ) 
  cos 
  a 
  + 
  2a' 
  2 
  yz 
  sin 
  a 
  

  

  — 
  2a' 
  2 
  xy 
  cos 
  2 
  a 
  — 
  2a' 
  2 
  yz 
  sin 
  a 
  cos 
  a, 
  

  

  E 
  = 
  2^ 
  — 
  4ry 
  cos 
  a 
  — 
  2yz 
  sin 
  a 
  + 
  2ys 
  sin 
  a 
  cos 
  a 
  + 
  2xy 
  cos 
  2 
  a. 
  

  

  77t£ 
  Third 
  and 
  Fourth 
  Component 
  Forces. 
  

  

  It 
  will 
  now 
  be 
  shown 
  that 
  the 
  sum 
  of 
  the 
  third 
  and 
  the 
  

   fourth 
  component 
  forces 
  when 
  averaged 
  over 
  a 
  lono- 
  time 
  is 
  

   zero 
  under 
  any 
  conditions 
  of 
  the 
  motion 
  of 
  the 
  charges. 
  The 
  

   consequence 
  is 
  that 
  the 
  translational 
  force 
  due 
  to 
  these 
  com- 
  

   ponent 
  forces 
  is 
  always 
  zero 
  upon 
  any 
  atom 
  containing 
  a 
  

   number 
  of 
  revolving 
  electrons, 
  and 
  need 
  not 
  be 
  considered 
  

   further. 
  The 
  instantaneous 
  values 
  of 
  course 
  do 
  not 
  vanish, 
  

   but 
  as 
  far 
  # 
  as 
  the 
  equilibrium 
  positions 
  of 
  the 
  atoms 
  are 
  con- 
  

   cerned 
  they 
  may 
  be 
  completely 
  determined 
  by 
  considering 
  the 
  

   first 
  and 
  second 
  component 
  forces 
  alone. 
  The 
  effects 
  of 
  the 
  

   third 
  and 
  fourth 
  component 
  forces 
  are 
  felt 
  in 
  the 
  atoms 
  

   because 
  the 
  moments 
  of 
  the 
  forces 
  do 
  not 
  vanish, 
  and 
  they 
  

   control 
  the 
  position 
  of 
  the 
  plane 
  of 
  the 
  orbit, 
  and 
  of 
  the 
  

   individual 
  electrons 
  within 
  the 
  orbits, 
  thereby 
  conferring 
  a 
  

   certain 
  rigidity 
  upon 
  the 
  whole 
  system. 
  

  

  The 
  third 
  and 
  fourth 
  component 
  instantaneous 
  forces 
  

   expressed 
  as 
  vectors 
  are 
  

  

  F 
  fife 
  

  

  F 
  4 
  = 
  — 
  fxee 
  

  

  '(f)* 
  

  

  