﻿Hypothesis 
  as 
  to 
  tlie 
  Origin 
  of 
  Scries 
  Spectra. 
  1015 
  

  

  we 
  have 
  tan 
  ha 
  = 
  ka, 
  the 
  higher 
  roots 
  of 
  which 
  are 
  approxi- 
  

   mately 
  given 
  by 
  ka 
  = 
  (n+^)ir. 
  The 
  innermost 
  nodal 
  sphere 
  

   is. 
  in 
  both 
  cases, 
  given 
  by 
  kr 
  = 
  l*43037r. 
  

  

  (iii.) 
  If 
  the 
  negative 
  layer 
  is 
  taken 
  off 
  we 
  have 
  only 
  one 
  

   type 
  of 
  vibration, 
  i. 
  e. 
  ka 
  = 
  nw, 
  whilst 
  the 
  constant 
  A 
  has 
  a 
  

   greater 
  value 
  than 
  before. 
  We 
  thus 
  have 
  three 
  series, 
  the 
  

   formula? 
  for 
  which 
  are 
  of 
  the 
  type 
  

  

  (i.) 
  v 
  = 
  A— 
  — 
  * 
  First 
  subordinate 
  (nebulous) 
  series. 
  

  

  

  (ii.) 
  v 
  = 
  A— 
  -. 
  — 
  -yrg 
  . 
  Second 
  subordinate 
  (sharp) 
  series. 
  

  

  (iii.) 
  v 
  = 
  A' 
  5 
  . 
  Principal 
  series. 
  

  

  n 
  

  

  In 
  reality 
  it 
  may 
  be 
  that 
  the 
  negative 
  layer 
  represents 
  a 
  

   shell 
  or 
  shells 
  of 
  negative 
  electrons, 
  and 
  that 
  the 
  boundary 
  

   conditions 
  in 
  complicated 
  atoms 
  will 
  be 
  slightly 
  different 
  

   although 
  resembling 
  those 
  given 
  above. 
  Any 
  change 
  or 
  

   rearrangement 
  of 
  the 
  shells 
  alters 
  the 
  constants 
  A, 
  which 
  

   thus 
  change 
  from 
  one 
  element 
  to 
  another. 
  The 
  constant 
  B, 
  

   however, 
  in 
  our 
  theory 
  is 
  universal, 
  and 
  thus 
  we 
  get 
  an 
  

   interpretation 
  of 
  Rydberg's 
  constant. 
  

  

  According 
  to 
  the 
  equation 
  

  

  B 
  = 
  fpOa 
  2 
  (l-4303) 
  2 
  (>/m) 
  

  

  we 
  might 
  interpret 
  this 
  by 
  saying 
  that 
  the 
  electrical 
  density 
  

   and 
  the 
  angular 
  velocity 
  of 
  the 
  core 
  of 
  every 
  atom 
  is 
  the 
  

   same. 
  

  

  The 
  Xodal 
  Surfaces. 
  

  

  TVe 
  have 
  now 
  to 
  consider 
  in 
  more 
  detail 
  the 
  question 
  of 
  

   ihe 
  nodal 
  surfaces. 
  If, 
  still 
  following 
  the 
  analogy 
  of 
  the 
  

   elastic 
  sphere, 
  we 
  make 
  the 
  assumption 
  that 
  the 
  change 
  of 
  

   the 
  electrical 
  volume 
  density 
  is 
  proportional 
  to 
  the 
  change 
  

   of 
  density, 
  t. 
  e. 
  proportional 
  to 
  sin 
  krjkr, 
  we 
  get 
  that 
  the 
  

   increase 
  of 
  electrical 
  force 
  at 
  any 
  point 
  due 
  to 
  the 
  oscillations 
  

  

  is 
  proportional 
  to 
  ±irk~ 
  l 
  r~' 
  2 
  \ 
  sinkrrdr, 
  and 
  the 
  condition 
  

  

  that 
  this 
  should 
  vanish 
  is 
  tan 
  kr 
  — 
  kr. 
  Hence 
  the 
  nodal 
  

   surfaces 
  employed 
  above 
  can 
  have 
  a 
  purely 
  electrical 
  origin. 
  

   Coming 
  now 
  to 
  the 
  expressions 
  for 
  the 
  magnetic 
  force, 
  we 
  

   find 
  that 
  the 
  integrals 
  in 
  question 
  are 
  of 
  a 
  less 
  simple 
  

   character 
  on 
  account 
  of 
  the 
  fact 
  that 
  the 
  conditions 
  at 
  the 
  

  

  