﻿1014 
  Prof. 
  A. 
  "W. 
  Conway 
  on 
  an 
  Electromagnetic 
  

   The 
  Series 
  Formulae. 
  

  

  If 
  a 
  gas 
  be 
  conceived 
  to 
  be 
  made 
  up 
  of 
  such 
  atoms 
  each 
  

   one 
  having 
  an 
  electron 
  moving 
  in 
  it, 
  those 
  electrons 
  which 
  

   are 
  moving 
  in 
  steady 
  motion 
  give 
  out 
  a 
  radiation 
  of 
  definite 
  

   period. 
  The 
  spectrum 
  of 
  such 
  a 
  gas 
  would 
  be 
  continuous 
  

   within 
  certain 
  limits. 
  We 
  now 
  make 
  the 
  assumption 
  that 
  

   the 
  atom 
  is 
  capable 
  of 
  elastic 
  vibrations 
  in 
  the 
  same 
  way 
  as 
  

   an 
  elastic 
  sphere. 
  Nodal 
  surfaces 
  will 
  be 
  set 
  up, 
  and 
  it 
  is 
  

   only 
  the 
  electrons 
  whose 
  orbits 
  lie 
  on 
  one 
  of 
  these 
  nodal 
  

   surfaces 
  which 
  can 
  give 
  out 
  undisturbed 
  a 
  homogeneous 
  

   radiation. 
  Let 
  us 
  consider 
  as 
  an 
  example 
  that 
  the 
  atom 
  

   vibrates 
  in 
  the 
  same 
  way 
  as 
  a 
  spherical 
  volume 
  of 
  gas 
  under 
  

   constant 
  pressure. 
  The 
  nodal 
  surfaces 
  will 
  then 
  be 
  spheres 
  

   of 
  radii 
  r 
  given 
  by 
  the 
  equations 
  

  

  hr= 
  1-4303 
  tt, 
  2-4590 
  it 
  

  

  where 
  h 
  is 
  determined 
  by 
  an 
  equation 
  of 
  the 
  type 
  

  

  ka 
  = 
  nir 
  

  

  where 
  n 
  is 
  an 
  integer. 
  

  

  Of 
  these 
  nodal 
  spheres, 
  we 
  shall 
  see 
  that 
  only 
  the 
  inner- 
  

   most 
  is 
  likely 
  to 
  be 
  effective 
  in 
  holding 
  the 
  electron. 
  The 
  

   orbirs 
  of 
  electrons 
  which 
  can 
  rotate 
  undisturbed 
  by 
  the 
  

   elastic 
  vibrations 
  are. 
  given 
  by 
  

  

  r 
  = 
  1-4303/w 
  

  

  where 
  n 
  is 
  an 
  integer. 
  Thus 
  the 
  spectrum 
  gets 
  split 
  into 
  

   lines 
  forming 
  a 
  series, 
  the 
  frequencies 
  v 
  being 
  given 
  by 
  the 
  

   formula 
  

  

  s> 
  = 
  e/Z7rm.nY 
  - 
  §/>Oa 
  2 
  (l-4303) 
  2 
  (^n)> 
  2 
  . 
  . 
  (3) 
  

  

  where 
  n 
  is 
  an 
  integer. 
  

  

  This 
  formula 
  is 
  of 
  Balmer's 
  form 
  

  

  r 
  = 
  A-B/n 
  2 
  . 
  

  

  In 
  a 
  similar 
  way 
  we 
  can 
  imagine 
  model 
  atoms 
  which 
  will 
  

   imitate 
  to 
  some 
  extent 
  some 
  of 
  the 
  other 
  properties 
  of 
  series. 
  

   Suppose 
  that 
  the 
  atom 
  or 
  sphere 
  of 
  positive 
  electricity 
  is 
  

   covered 
  with 
  a 
  uniform 
  layer 
  of 
  negative 
  electricity 
  the 
  

   density 
  of 
  which 
  greater 
  than 
  the 
  density 
  of 
  the 
  positive 
  

   electricity. 
  The 
  radial 
  oscillation 
  will 
  be 
  now 
  of 
  two 
  kinds 
  : 
  

   (i.) 
  forced 
  oscillations 
  due 
  to 
  the 
  motion 
  of 
  the 
  surface 
  layer, 
  

   for 
  these 
  oscillations 
  we 
  will 
  have 
  ka 
  = 
  nir\ 
  (ii.) 
  oscillations 
  

   iu 
  which 
  the 
  surface 
  will 
  be 
  a 
  nodal 
  sphere 
  for 
  which 
  

  

  