﻿430 
  MR 
  W. 
  J. 
  M. 
  RANIUNE 
  ON 
  THE 
  CENTRIFUGAL 
  THEORY 
  OF 
  ELASTICITY, 
  

  

  ±dd> 
  

  

  (6.) 
  

  

  fffdzdi/dz=kM.V 
  A 
  ^Ld(p 
  

  

  £ 
  being 
  a 
  specific 
  constant, 
  and 
  4- 
  and 
  w 
  functions 
  of 
  <j>, 
  and 
  of 
  the 
  nature 
  and 
  

   density 
  of 
  the 
  substance. 
  

  

  The 
  lower 
  limit 
  of 
  integration 
  of 
  </> 
  must 
  be 
  made 
  -co, 
  that 
  it 
  may 
  include 
  

   orbits 
  of 
  indefinitely 
  small 
  magnitude 
  described 
  round 
  the 
  atomic 
  centre. 
  

  

  The 
  nature 
  of 
  the 
  function 
  4* 
  is 
  limited 
  by 
  the 
  following 
  condition, 
  

  

  l 
  = 
  kj 
  e 
  -±d<t> 
  (7.) 
  

  

  — 
  CO 
  t'i 
  

  

  Let 
  ^+1 
  = 
  6 
  

   h 
  k 
  

  

  Then 
  these 
  transformations 
  give 
  the 
  following 
  result 
  for 
  the 
  pressure 
  at 
  the 
  bound- 
  

   ins: 
  surface 
  of 
  an 
  atom 
  : 
  — 
  

  

  J 
  — 
  CO 
  i 
  

  

  h 
  fJL 
  6 
  Wj 
  

  

  (8.) 
  

  

  MV 
  w' 
  w", 
  w"' 
  

  

  Wl 
  ""6 
  + 
  6* 
  l*"*" 
  &c 
  ' 
  

  

  w'u 
  &,c. 
  being 
  the 
  successive 
  differential 
  coefficients 
  of 
  w 
  with 
  respect 
  to 
  k 
  4>, 
  when 
  

  

  4> 
  = 
  <Pv 
  

  

  (4.) 
  The 
  following 
  transformation 
  will 
  be 
  found 
  useful 
  in 
  the 
  sequel. 
  

  

  Let 
  A 
  be 
  the 
  indefinite 
  value 
  of 
  log 
  e 
  V, 
  and 
  \ 
  l 
  its 
  actual 
  value 
  in 
  the 
  case 
  

  

  under 
  consideration. 
  Let 
  G 
  be 
  the 
  same 
  function 
  of 
  A 
  which 
  w 
  is 
  of 
  k 
  <£, 
  and 
  let 
  

  

  G', 
  G", 
  &c. 
  be 
  its 
  successive 
  differential 
  coefficients 
  with 
  respect 
  to 
  X. 
  

  

  r>\ 
  >(*-*i) 
  G 
  G' 
  G" 
  

  

  R 
  l= 
  f 
  I 
  GdX=^-^ 
  + 
  ^ 
  r 
  ~&c. 
  

  

  Then 
  

  

  '=^% 
  ... 
  (9.) 
  

  

  The 
  function 
  H 
  has 
  the 
  following 
  properties, 
  which 
  will 
  be 
  afterwards 
  referred 
  

   to 
  — 
  

  

  Sxr 
  + 
  ^- 
  G 
  -° 
  \ 
  

  

  (10.) 
  

  

  X, 
  TT 
  _ 
  rfHj 
  

  

  dd 
  

  

  r\ 
  

  

  '— 
  00 
  

  

  