﻿70 
  Dr. 
  A. 
  C. 
  Crehore 
  on 
  the 
  Formation 
  of 
  the 
  

  

  Where 
  the 
  numerical 
  coefficients 
  are 
  related 
  as 
  follows 
  : 
  — 
  

  

  A 
  ,o 
  =1 
  

  

  A 
  2,0 
  = 
  '> 
  Aq 
  

  

  

  

  

  

  Ai.o 
  = 
  ^ 
  ^ 
  2 
  ,0 
  

  

  A4, 
  2 
  — 
  A4,o 
  

  

  

  

  

  Ae,o 
  = 
  3 
  A4 
  } 
  o 
  

  

  A 
  6 
  ,2 
  = 
  7A 
  4>2 
  

  

  

  

  

  ^8,0 
  = 
  4 
  A 
  6r 
  o 
  

  

  As, 
  2 
  = 
  2 
  ^ 
  6 
  . 
  2 
  

  

  As, 
  4 
  — 
  2 
  X 
  

  

  3 
  A 
  

  

  

  A 
  U 
  A 
  

  

  Aio,o 
  — 
  5" 
  ^8,0 
  

  

  A 
  10, 
  2= 
  "3 
  A 
  8#2 
  

  

  Aio,4= 
  11 
  

  

  Ag, 
  4 
  

  

  

  A 
  13 
  A 
  

  

  -^12,0 
  — 
  ~g 
  -^10,0 
  

  

  A 
  - 
  13 
  A 
  

  

  Ai2,2 
  — 
  '4-^.10, 
  2 
  

  

  A 
  13 
  

  

  Al2,4= 
  2" 
  

  

  Aio,4 
  

  

  A 
  2 
  3 
  5 
  A 
  

   Ai2,6=2 
  *4*6 
  

  

  B2.2 
  =| 
  

  

  

  

  

  

  B 
  4 
  , 
  2 
  =5 
  

  

  

  

  

  

  Be, 
  2 
  =: 
  2 
  Be, 
  4 
  

  

  = 
  4 
  B 
  6i2 
  

  

  

  

  

  Bg,2 
  = 
  g" 
  B 
  8 
  ,4 
  

  

  = 
  9 
  B.,4 
  

  

  

  

  

  Blo,2— 
  4" 
  Bio, 
  

  

  11 
  R 
  tt 
  3 
  ! 
  R 
  

  

  4 
  == 
  ~2 
  - 
  - 
  D 
  8,4 
  ^lO^— 
  4 
  (j^lO^ 
  

  

  

  

  Bi2,2= 
  5- 
  B 
  12 
  , 
  

  

  4= 
  7j~ 
  Bio, 
  4 
  B12 
  

  

  6= 
  13 
  Bio,6 
  

  

  

  

  Bu,2= 
  ^r 
  B 
  14 
  , 
  

  

  1= 
  -4 
  B^.4 
  Bi4, 
  6 
  = 
  ^ 
  B 
  ]2 
  ,6 
  

  

  Bl4,8 
  = 
  

  

  3 
  5,1. 
  

   = 
  4*5 
  g^ 
  14 
  ' 
  2 
  ' 
  

  

  12,0. 
  

  

  The 
  Average 
  Force 
  perpendicular 
  to 
  r. 
  

  

  From 
  (33) 
  we 
  find 
  the 
  average 
  value 
  of 
  the 
  first 
  com- 
  

   ponent 
  force 
  resolved 
  in 
  the 
  meridian 
  plane 
  perpendicular 
  

   to 
  r 
  to 
  be 
  

  

  F 
  = 
  

  

  perp.r 
  

  

  lim 
  

  

  t 
  = 
  co 
  t 
  

  

  ff-K? 
  sin 
  x 
  [~ 
  T 
  ] 
  [l+ 
  1-7 
  2 
  (-'-s7+..t)] 
  

  

  <fr 
  

  

  (43) 
  

  

  Upon 
  comparing 
  this 
  with 
  the 
  equation 
  (40) 
  it 
  may 
  be 
  

   shown 
  that 
  

  

  F, 
  = 
  tan 
  X- 
  

  

  perp. 
  r 
  

  

  ^A 
  3 
  r 
  

  

  B 
  2 
  , 
  2 
  c/A 
  2 
  A 
  2 
  

  

  B 
  4 
  , 
  2 
  sr 
  „„ 
  A 
  4 
  

  

  B 
  6 
  , 
  2 
  8 
  2 
  P„„A 
  6 
  + 
  B 
  M 
  <y 
  2 
  AVA 
  6 
  

  

  B 
  M 
  ST»„„A 
  8 
  +B 
  8 
  ,4gr 
  „„„A 
  8 
  

  

  B 
  10 
  , 
  2 
  § 
  4 
  r 
  4 
  ,. 
  „ 
  A 
  10 
  + 
  Bi 
  0)4 
  £ 
  2 
  r 
  2 
  „ 
  „ 
  „ 
  a 
  io 
  +b 
  10 
  , 
  6 
  ..,avA 
  10 
  

  

  