Electrical  Vibrations  and  Constitution  of  the  Atom.        117 
The  full  line  curves  Q  and  P  show  the  stress  at  the  bottom 
and  tjp  ends  of  the  rope  respectively.  The  height  OP. 
represents  36,000  lb.  per  sq.  inch.  the  dotted  curve  P 
shows  what  both  of  those  would  be  according  to  the  approxi- 
mate solution.     In  all  cases  gravitational  forces  are  neglected. 
As  was  to  be  expected,  the  approximate  solntion  is  quite 
different  from  the  other  when  the  rope  is  long,  and  seems  to 
agree  with  the  other  better  and  better  as  the  rope  is  shorter. 
Also  it  is  evident  that  if  internal  friction  in  the  rope  or  any 
other  cause  is  likely  to  destroy  the  discontinuities  which  we 
observe  at  the  times  of  refiVxion,  then  the  approximate  solution 
is  probably  more  correct  than  the  other. 
VII.  On  Electrical  Vibrations  and  the  Constitution  of  the  Atom. 
By  Lord  Rayleigh,  O.M.,  F.R.S* 
IN  illustration  of  the  view,  suggested  by  Lord  Kelvin, 
that  an  atom  may  be  represented  by  a  number  of  nega- 
tive electrons,  or  negatively  charged  corpuscles,  enclosed 
in  a  sphere  of  uniform  positive  electrification,  Prof.  J.  J. 
Thomson  has  given  some  valuable  calculations  t  of  the 
stability  of  a  ring  of  such  electrons,  uniformly  spaced,  and 
either  at  rest  or  revolving  about  a  central  axis.  The  cor- 
puscles  are  supposed  to  repel  one  another  according  to  the 
law  of  inverse  square  of  distance  and  to  be  endowed  with 
inertia,  which  may,  however,  be  the  inertia  of  aether  in  the 
immediate  neighbourhood  of  each  corpuscle.  The  effect  of 
the  sphere  of  positive  electrification  is  merely  to  produce  a 
field  of  force  directly  as  the  distance  from  the  centre  of  the 
sphere.  The  artificiality  of  this  hypothesis  is  partly  justified 
by  the  necessity,  in  order  to  meet  the  facts,  of  introducing 
from  the  beginning  some  essential  difference,  other  than  of 
mere  sign,  between  positive  and  negative. 
Some  of  the  most  interesting  of  Prof.  Thomson's  results 
depend  essentially  upon  the  finiteness  of  the  number  of 
electrons  ;  but  since  the  experimental  evidence  requires 
that  in  any  case  the  number  should  be  very  large,  I  have 
thought  it  worth  while  to  consider  what  becomes  of  the 
theory  when  the  number  is  infinite.  The  cloud  of  electrons 
may  then  be  assimilated  to  a  fluid  whose  properties,  however, 
must  differ  in  many  respects  from  those  with  which  we  are 
most  familiar.  We  suppose  that  the  whole  quantities  of 
positive   and    negative  are    equal.     The   difference   between 
*  Communicated  bv  the  Author, 
t  Phil.  Mag.  vii.  p.237  (1904), 
