Constitution  of  the  Atom.  605 
the  conditions  o£  stability  or  o£  exemption  from  radiation 
may  after  all  really  demand  this  definiteness.  .  .  .  The  fre- 
quencies observed  in  the  spectrum  may  .  .  .  form  an  essential 
part  of  the  original  constitution  of  the  atom  as  determined 
by  conditions  of  stability." 
If  this  were  so,  these  frequencies  would  depend  only  on 
the  constituents  of  the  atom  and  not  on  the  actual  type  of 
motion  taking  place  in  the  atom.  Thus  if  we  regard  the 
atom  as  made  up  of  point-charges  influencing  one  another 
according  to  the  usual  electrodynamical  laws,  the  frequencies 
could  depend  only  on  the  number,  masses,  and  charges  of  the 
point-charges  and  on  the  aether-constant  V.  What  I  wish  to 
point  out  first  is  that  it  is  impossible,  by  combining  these 
quantities  in  any  way,  to  obtain  a  quantity  of  the  physical 
dimensions  of  a  frequency. 
If  to  the  quantities  already  mentioned  we  add  another,  for 
instance  the  energy  of  motion  o£  the  atom,  it  may  be  possible 
to  obtain  frequencies.  Here,  however,  the  frequencies  will 
be  functions  of  the  energy.  And,  as  Lord  Eayleigh  says, 
the  energy  must  change  in  the  course  of  time,  whereas  the 
frequencies,  so  far  as  we  know,  do  not. 
Or,  instead  of  combining  the  original  quantities  with  the 
energy,  we  may  combine  them  with  a  length,  in  such  a  way 
as  to  obtain  frequencies.  Thus  Lord  Rayleigh  obtains  fre- 
quencies in  his  analysis,  but  only  in  virtue  of  having  introduced 
the  radius  of  the  imaginary  sphere  of  positive  electrification. 
If  this  positive  electrification,  instead  of  being  limited  to  an 
invariable  sphere,  were  supposed  free  to  expand  under  its 
self-repulsion,  Lord  Rayleigh's  p0  would  be  indefinite,  as 
would  consequently  be  the  frequencies  also. 
The  situation  with  regard  to  linear  dimensions  is  precisely 
the  same  as  that  with  regard  to  frequencies.  It  is  impossible 
to  derive  a  scale  of  linear  dimensions  from  the  quantities 
permanently  associated  with  point-charges  and  aether.  Thus 
the  atom  would  have  no  definite  size,  but  would  expand  and 
contract  indefinitely  under  external  influences. 
It  seems,  then,  that  we  must  somehow  introduce  new 
quantities — electrons  must  be  regarded  as  something  more 
complex  than  point-charges.  And  when  we  have  once  been 
driven  to  surrendering  the  simplicity  of  the  point-charge 
view  of  the  electron,  is  there  any  longer  any  objection  to 
putting  the  most  obvious  interpretation  on  the  line-spectrum, 
and  regarding  its  frequencies  as  those  of  isochronous  vibra- 
tions about  a  position  of  statical  equilibrium  ?  The  main 
objection  felt,  as  I  understand,  against  this  interpretation, 
lies  in  its  being  inconsistent  with  the  point-charge  view  of  an 
