﻿Molecules 
  of 
  the 
  Elements 
  and 
  their 
  Compounds. 
  61 
  

   or, 
  substituting 
  the 
  values 
  of 
  A, 
  &c, 
  

   R 
  . 
  r 
  = 
  r 
  2 
  — 
  ax 
  sin 
  (at 
  + 
  6) 
  —ay 
  cos 
  {tot 
  + 
  6) 
  + 
  a' 
  z 
  sin 
  a 
  sin 
  {a't 
  + 
  0') 
  

  

  -fay 
  cos 
  ((o't 
  + 
  6') 
  -\-a'x 
  cos 
  a 
  sin 
  (a't-\-0') 
  (16) 
  

  

  By 
  (11) 
  we 
  find 
  

  

  ^-- 
  3 
  a+«r 
  l 
  -K 
  1 
  -l 
  u+ 
  ¥" 
  s 
  -r6» 
  s+ 
  Si" 
  4 
  -2-S« 
  5+ 
  ---) 
  

  

  • 
  • 
  • 
  (") 
  

  

  Upon 
  substitution 
  of 
  (17) 
  and 
  (16) 
  in 
  (14), 
  the 
  complete 
  

   value 
  of 
  F 
  x 
  when 
  resolved 
  along 
  the 
  vector 
  r, 
  from 
  to 
  0', 
  

   becomes 
  

  

  Fj 
  = 
  j, 
  3 
  J 
  %2—ax 
  sin 
  (cot 
  + 
  0) 
  — 
  ay 
  cos 
  (at 
  -\- 
  0) 
  -\- 
  a' 
  z 
  sin 
  a 
  sin 
  (a't 
  + 
  0') 
  

  

  — 
  r- 
  O 
  

  

  + 
  ay 
  cos 
  (at 
  + 
  (9') 
  + 
  a'x 
  cos 
  a 
  sin 
  (a/* 
  + 
  6') 
  1 
  — 
  ^w 
  

  

  15 
  — 
  35 
  3 
  315 
  4 
  

  

  > 
  * 
  olo 
  4 
  1 
  

  

  + 
  ^' 
  r 
  16 
  

  

  The 
  Second 
  Component 
  Force 
  resolved 
  along 
  the 
  direction 
  r. 
  

  

  The 
  value 
  of 
  the 
  second 
  component 
  of 
  the 
  force 
  (2) 
  has 
  

   the 
  same 
  form 
  as 
  the 
  first 
  component, 
  or 
  electrostatic 
  force, 
  

   except 
  for 
  the 
  factor 
  qq 
  cos 
  y. 
  If 
  q 
  and 
  q' 
  denote 
  the 
  vector 
  

   velocities, 
  this 
  factor 
  is 
  q 
  . 
  q', 
  and 
  may 
  be 
  obtained 
  by 
  differ- 
  

   entiating 
  (5) 
  and 
  (6), 
  and 
  then 
  taking 
  the 
  direct 
  product. 
  

   The 
  differentials 
  of 
  rj 
  and 
  r 
  2 
  with 
  respect 
  to 
  the 
  time 
  are 
  

  

  1 
  =^=« 
  a 
  ,^[cos(<»« 
  + 
  ff)](0-[sin(< 
  8 
  * 
  + 
  ^]0-)} 
  • 
  (19) 
  

  

  q'= 
  J 
  =aV|[cos 
  («'t 
  + 
  e')](i')-l>in 
  (<»'<+0')]W 
  } 
  (20) 
  

  

  and 
  their 
  direct 
  product 
  

  

  q 
  . 
  q'=aa'sDo>'[cos 
  «cos 
  (at 
  + 
  &) 
  cos 
  (a't 
  + 
  0') 
  

  

  + 
  sm(a>t 
  + 
  0)sm(a>'t+0')] 
  .... 
  (21) 
  

  

  The 
  second 
  component 
  force 
  (2) 
  when 
  resolved 
  along 
  the 
  

   vector, 
  r, 
  is 
  therefore, 
  

  

  F 
  2 
  =^(R.r)(q.q> 
  .... 
  (22) 
  

  

  