122       Electrical  Vibrations  and  Constitution  of  the  Atom. 
sought,  unless  we  introduce  another  reflecting  surface.  For 
the  enclosed  space  thus  defined,  we  find  of  course  undissipated 
vibrations,  and  jo  becomes  wholly  real. 
In  the  calculation  of  frequencies  given  above  for  a  cloud 
of  electrons  the  undisturbed  condition  is  one  of  equilibrium, 
and  the  frequencies  of  radiation  are  those  of  vibration  about 
this  conditiou  of  equilibrium.  Almost  every  theory  of  this 
kind  is  open  to  the  objection  that  I  put  forward  some  years 
ago*,  viz.  thatp2,  and  notjo,  is  given  in  the  first  instance.  It  is 
difficult  to  explain  on  this  basis  the  simple  expressions  found 
for  p,  and  the  constant  differences  manifested  in  the  formulae 
of  Rydberg  and  of  Kayser  and  Kunge.  There  are,  of  course, 
particular  cases  where  the  square  root  can  be  taken  without 
complication,  and  Ritzf  has  derived  a  differential  equation 
leading  to  a  formula  of  this  description  and  capable  of  being 
identified  with  that  of  Eydberg.  Apart  from  the  question 
whether  it  corresponds  with  anything  mechanically  possible, 
this  theory  has  too  artificial  an  appearance  to  inspire  much 
confidence. 
A  partial  escape  from  these  difficulties  might  be  found  in 
regarding  actual  spectrum  lines  as  due  to  difference  tones 
arising  from  primaries  of  much  higher  pitch, — a  suggestion 
already  put  forward  in  a  somewhat  different  form  by  Julius. 
In  recent  years  theories  of  atomic  structure  have  found 
favour  in  which  the  electrons  are  regarded  as  describing 
orbits,  probably  with  great  rapidity.  If  the  electrons  are 
sufficiently  numerous,  there  may  be  an  approach  to  steady 
motion.  In  case  of  disturbance,  oscillations  about  this  steady 
motion  may  ensue,  and  these  oscillations  are  regarded  as  the 
origin  of  luminous  waves  of  the  same  frequency.  But  in  view  of 
the  discrete  character  of  electrons  such  a  motion  can  never 
be  fully  steady,  and  the  system  must  tend  to  radiate  even 
when  undisturbed  J.  In  particular  cases,  such  as  some  con- 
sidered by  Prof.  Thomson,  the  radiation  in  the  undisturbed 
state  may  be  very  feeble.  After  disturbance  oscillations 
about  the  normal  motion  will  ensue,  but  it  does  not  follow 
that  the  frequencies  of  these  oscillations  will  be  manifested 
in  the  spectrum  of  the  radiation.  The  spectrum  may  rather 
be  due  to  the  upsetting  of  the  balance  by  which  before  dis- 
turbance radiation  was  prevented,  and  the  frequencies  will 
conespond  (with  modification)  rather  to  the  original  dis- 
tribution of  electrons  than  to  the  oscillations.     For  example, 
*  Phil.  Mag.  xliv.  p.  362,  1897;  'Scientific  Papers/  iv.  p.  S4o. 
t  Drude,  Ann.  Bd.  xii.  p.  264,  1P0.°>. 
%  Confer  Larnior.  '  Matter  and  -Pother.' 
