﻿and 
  the 
  Constitution 
  of 
  the 
  Atom, 
  301 
  

  

  Hence 
  we 
  get 
  for 
  the 
  frequency: 
  

  

  (S-p 
  + 
  q-Sq) 
  2 
  

  

  ^ 
  = 
  J(N-S^-(|-i)(^-S^) 
  2 
  - 
  

  

  92 
  

  

  where 
  B 
  pq 
  and 
  C 
  pq 
  are 
  functions 
  o£ 
  p 
  and 
  q. 
  Independent 
  of 
  

   p 
  and 
  q 
  we 
  get 
  the 
  undoubtedly 
  right 
  factor 
  3/4 
  of 
  N 
  2 
  . 
  

  

  The 
  combination 
  J9 
  = 
  3 
  and 
  #=1 
  represents 
  the 
  solution 
  

   found 
  by 
  Debye. 
  

  

  If 
  q 
  is 
  different 
  from 
  1, 
  there 
  is 
  one 
  and 
  only 
  one 
  other 
  

   possible 
  solution 
  corresponding 
  to 
  

  

  and 
  

  

  p 
  = 
  4- 
  

   which 
  give 
  for 
  the 
  frequency 
  : 
  

  

  <?=4, 
  

  

  ^ 
  = 
  3/4(N-0-9571) 
  ; 
  

  

  (12 
  a) 
  

  

  which 
  is 
  just 
  the 
  formula 
  given 
  by 
  Moseley 
  *. 
  

  

  When 
  we 
  take 
  into 
  account 
  the 
  variation 
  of 
  the 
  mass 
  

   according 
  to 
  equation 
  (10), 
  we 
  easily 
  get 
  from 
  equation 
  (11) 
  : 
  

  

  i=^{\/ 
  1 
  -|( 
  N 
  - 
  s 
  ^-\/ 
  1 
  -' 
  5 
  ( 
  N 
  - 
  S4 
  ) 
  2 
  }'( 
  12 
  *) 
  

  

  or 
  approximately 
  

  

  v/R 
  = 
  3/4(N 
  - 
  S 
  4 
  ) 
  2 
  (l 
  + 
  5/16p(N 
  - 
  S 
  4 
  ) 
  2 
  ). 
  . 
  (12 
  c) 
  

  

  The 
  accuracy 
  of 
  the 
  formula 
  (12 
  c) 
  will 
  be 
  seen 
  from 
  

  

  Table 
  I., 
  where 
  the 
  values 
  of 
  ^ 
  are 
  calculated 
  for 
  a 
  number 
  

   of 
  elements. 
  

  

  

  

  Table 
  I. 
  

  

  

  

  N. 
  

  

  vfR 
  

   obs. 
  

  

  vfR 
  

  

  Debye. 
  

  

  Difference 
  

   in 
  Percent. 
  

  

  vfR 
  

   from 
  12 
  c. 
  

  

  Difference 
  

   in 
  Percent. 
  

  

  15P 
  

  

  147-7 
  

  

  2716 
  

  

  435-4 
  

  

  635-9 
  

  

  880-4 
  

  

  11560 
  

  

  1482-0 
  

  

  1871-0 
  

  

  2290-0 
  

  

  27610 
  

  

  146-4 
  

  

  272-4 
  

  

  437-3 
  

  

  641-5 
  

  

  885-6 
  

  

  11710 
  

  

  14990 
  

  

  1877-0 
  

  

  22970 
  

  

  27770 
  

  

  0-9 
  

   0-3 
  

   0-4 
  

   09 
  

   06 
  

   1-3 
  

   11 
  

   0-3 
  

   0-3 
  

   06 
  

  

  148-4 
  

  

  2736 
  

  

  437-7 
  

  

  641-5 
  

  

  885-9 
  

  

  11720 
  

  

  15020 
  

  

  1876-0 
  

  

  2296-0 
  

  

  2766-0 
  

  

  0-4 
  

   0-7 
  

   0-5 
  

   0-9 
  

   0-6 
  

   1-4 
  

   1-3 
  

   0-3 
  

   0-3 
  

   02 
  

  

  20 
  Ca 
  

  

  25 
  Mn 
  

  

  30 
  Zn 
  

  

  35 
  Br 
  

  

  40 
  Zr 
  ,. 
  

  

  45 
  Rh 
  

  

  50 
  Sn 
  

  

  55 
  0s 
  

  

  60Nd 
  

  

  

  * 
  Loc. 
  cit. 
  

  

  