126  Tlie  Constitution  of  Natural  Radiation. 
We  have  next  to  consider  the  resultant  of  the  components 
PQ.  Here  again  the  phases  are  distributed  in  all  directions. 
The  amplitudes,  however,  are  no  longer  equal,  but  they  are 
small  relatively  to  unity.  Although  the  contrary  is  not 
impossible,  it  would  seem  that  in  all  probability  the  resultant 
amplitude  of  the  PQ's  is  small  in  comparison  with  that  of  the 
OP's,  from  which  it  follows  that,  exceptional  cases  apart,  the 
amplitude  and  phase  of  the  resultant  remain  but  little  changed 
at  the  end  of  a  time  t,  such  that  the  changes  of  phase  of  the 
individual  components  are  small. 
From  the  above  discussion  I  am  disposed  to  infer  that  a 
Fourier  element  of  radiation  necessarily  possesses  in  large 
degree  the  characteristic  which  (if  1  rightly  understand  him) 
Prof.  Larmor  associates  with  white  light  in  contrast  to 
Pontgen  radiation.  Of  course,  after  the  lapse  of  a  sufficient 
time  the  final  phases  of  the  components  lose  all  simple 
relation  to  the  initial  phases.  The  final  phase  of  the  resultant 
is  then  without  relation  to  the  initial  phase,  and  the  amplitudes 
may  differ  finitely,  but  in  all  probability  within  >omewhat 
restricted  limits.  From  this  variation  it  seems  to  me  white 
light  cannot  be  exempt. 
In  the  above  and,  so  far  as  I  remember,  in  what  I  have 
written  previously,  the  question  is  purely  kinematical.  In 
saying  that  Fourier's  theorem  is  competent  to  answer  any 
question  that  may  be  raised  respecting  the  action  of  a  dis- 
persive medium,  1  take  for  granted  that  the  law  of  dispersion 
is  given  in  its  entirety.  I  quite  admit  that  if  there  are  any 
wave-lengths  for  which  the  behaviour  of  the  medium  is 
unknown,  a  corresponding  uncertainty  must  attach  to  the 
fate  of  any  aggregate  in  which  these  are  included.  Doubt- 
less a  complete  statement  of  the  law  of  dispersion  may  involve 
the  case  of  wave-lengths  for  wrhich  the  medium  is  not  trans- 
parent. 
As  regards  the  passage  quoted  from  Sir  G.  Stokes,  his 
object  was,  1  think,  to  explain  the  absence  of  refraction  when 
Pontgen  rays  traverse  matter.  Taking  light  of  ordinary  and 
absolutely  definite  wave-length  incident  upon  transparent 
matter,  he  contemplates  the  lapse  of  10,000  periods  before 
harmony  is  established  between  the  aetherial  and  molecular 
vibrations,  that  is,  as  I  understand  it,  before  regular  refraction 
is  possible.  At  this  rate  the  light  from  a  soda  flame  would 
be  incapable  of  regular  refraction,  for  the  vibrations  are 
certainly  not  regular  for  more  than  500  periods.  Indeed 
Stokes's  argument  appears  better  adapted  to  prove  that 
Pontgen  rays  could  not  traverse  material  media  at  all  in  a 
regular  manner,  than  that  they  would  do  ^o  without  change  of 
wave-velocitv. 
