﻿Hypothesis 
  as 
  to 
  the 
  Origin 
  of 
  Series 
  Spectra. 
  1011 
  

  

  increases 
  asn 
  increases 
  and 
  becomes 
  infinite 
  with?i 
  ; 
  (iii.) 
  the 
  

   amount 
  of 
  radiation 
  given 
  out 
  must 
  obey 
  Planck's 
  law. 
  As 
  

   regards 
  (i.), 
  as 
  pointed 
  out 
  by 
  Lord 
  Hayleigh, 
  the 
  difficulty 
  

   can 
  be 
  overcome 
  by 
  making 
  the 
  frequency 
  depend 
  on 
  the 
  

   ■magnetic 
  force 
  ; 
  and 
  as 
  to 
  (ii.) 
  this 
  paper 
  is 
  intended 
  to 
  point 
  

   out 
  a 
  mode 
  of 
  connexion 
  between 
  the 
  vibrations 
  of 
  elastic 
  

   bodies 
  and 
  the 
  above 
  law. 
  The 
  question 
  of 
  energy 
  being- 
  

   radiated 
  according 
  to 
  Planck's 
  law 
  is 
  dealt 
  with 
  in 
  the 
  last 
  

   section 
  of 
  the 
  paper, 
  in 
  which 
  it 
  is 
  shown 
  that 
  the 
  kinetic 
  

   energy 
  radiated 
  is 
  homogeneous 
  and 
  of 
  amount 
  hv 
  where 
  h 
  

   is 
  a 
  constant 
  having 
  the 
  value 
  6*8 
  X 
  10 
  ~ 
  27 
  (Planck's 
  constant 
  

   being 
  6*5 
  x 
  10~ 
  27 
  ). 
  The 
  atom 
  considered 
  is 
  a 
  " 
  Thomson 
  " 
  

   atom 
  rotating 
  with 
  a 
  constant 
  angular 
  velocity. 
  It 
  is 
  shown 
  

   that 
  all 
  single 
  negative 
  electrons 
  having 
  circular 
  orbits 
  in 
  

   such 
  atoms 
  have 
  a 
  constant 
  angular 
  momentum 
  h/ir. 
  If 
  the 
  

   atom 
  is 
  supposed 
  capable 
  of 
  executing 
  elastic 
  vibrations, 
  

   reasons 
  are 
  given 
  for 
  supposing 
  that 
  the 
  innermost 
  nodal 
  

   sphere 
  in 
  any 
  mode 
  will 
  capture 
  the 
  electron. 
  A 
  frequency 
  

   formula 
  of 
  the 
  type 
  

  

  F=A--.B/(n 
  + 
  /*) 
  1 
  

  

  is 
  arrived 
  at, 
  A 
  depending 
  on 
  the 
  external 
  structure 
  of 
  the 
  

   atom, 
  B 
  being 
  the 
  same 
  for 
  all 
  atoms, 
  and 
  yu, 
  depending 
  on 
  

   the 
  nature 
  of 
  the 
  surface 
  conditions 
  for 
  the 
  elastic 
  waves. 
  

   The 
  simplest 
  form 
  of 
  atom— 
  the 
  sphere 
  — 
  and 
  the 
  simplest 
  

   mode 
  of 
  vibration 
  — 
  the 
  radial— 
  is 
  considered. 
  It 
  is 
  possible 
  

   that 
  more 
  complex 
  conditions 
  will 
  give 
  better 
  results, 
  and 
  

   that 
  this 
  paper 
  may 
  suggest 
  a 
  mode 
  of 
  attacking 
  this 
  problem 
  

   from 
  this 
  standpoint. 
  

  

  The 
  question 
  of 
  the 
  Zeeman 
  effect 
  is 
  not 
  considered, 
  but 
  

   for 
  a 
  discussion 
  for 
  this 
  type 
  of 
  atom 
  we 
  may 
  refer 
  to 
  Ritz 
  

   (Annalen 
  der 
  PhysiJc, 
  7. 
  xxv. 
  1908, 
  p. 
  660). 
  

  

  The 
  Internal 
  Forces. 
  

  

  Let 
  the 
  volume 
  density 
  p 
  of 
  the 
  spherical 
  atom 
  be 
  a 
  func- 
  

   tion 
  of 
  r 
  only 
  the 
  distance 
  from 
  the 
  centre, 
  and 
  let 
  12 
  be 
  

   the 
  angular 
  velocity 
  of 
  the 
  sphere 
  supposed 
  moving 
  as 
  a 
  

   rigid 
  body, 
  the 
  axis 
  of 
  rotation 
  being 
  taken 
  as 
  the 
  axis 
  of 
  z.- 
  

   The 
  rotation 
  of 
  the 
  sphere 
  produces 
  a 
  magnetic 
  force 
  

   (a, 
  /3, 
  7) 
  which 
  is 
  the 
  curl 
  of 
  a 
  vector 
  potential 
  (F, 
  G, 
  H) 
  

   defined 
  inside 
  the 
  sphere 
  by 
  the 
  equations 
  

  

  V 
  2 
  F 
  = 
  4<7rp% 
  ; 
  V 
  2 
  G 
  =-47r/Dfi 
  t 
  r 
  ; 
  V 
  2 
  H 
  = 
  0, 
  

   Outside 
  the 
  sphere 
  F. 
  G, 
  and 
  H 
  are 
  harmonic 
  and 
  on 
  the 
  

  

  