﻿that 
  Rontgen 
  Rays 
  are 
  Ordinary 
  Light* 
  535 
  

  

  Accordingly 
  the 
  radiation 
  from 
  the 
  target 
  against 
  which 
  

   the 
  kathode 
  rajs 
  impinge, 
  along 
  with 
  repetitions 
  of 
  the 
  

   same 
  at 
  intervals 
  of 
  a 
  day, 
  may 
  be 
  resolved 
  into 
  the 
  coexist- 
  

   ence 
  of 
  component 
  undulations, 
  each 
  filling 
  the 
  whole 
  of 
  

   space, 
  and 
  each 
  consisting 
  of 
  an 
  unlimited 
  train 
  of 
  uniform 
  

   plane 
  pendulous 
  wavelets. 
  The 
  periodic 
  times 
  of 
  these 
  will 
  

   be 
  T 
  and 
  its 
  integer 
  submultiples. 
  

  

  Next 
  form 
  the 
  series 
  of 
  ascending 
  prime 
  numbers, 
  viz 
  : 
  — 
  

  

  2, 
  3, 
  5, 
  7, 
  11, 
  13, 
  17, 
  19, 
  &c, 
  

  

  and 
  call 
  the 
  continued 
  product 
  of 
  the 
  first 
  n 
  of 
  these 
  

  

  M». 
  

  

  Then 
  instead 
  of 
  repeating 
  the 
  Rongten 
  events 
  at 
  intervals 
  of 
  

   a 
  day, 
  let 
  them 
  bo 
  repeated 
  at 
  intervals 
  of 
  M 
  ;i 
  days. 
  Thereby 
  

   the 
  period 
  of 
  the 
  Fourier's 
  series 
  becomes 
  M 
  n 
  T 
  ; 
  and 
  the 
  

   radiation 
  of 
  the 
  Rongten 
  experiment, 
  repeated 
  at 
  these 
  longer 
  

   intervals, 
  is 
  represented 
  by 
  the 
  coexistence 
  of 
  series 
  of 
  pen- 
  

   dulous 
  terms 
  of 
  which 
  the 
  periods 
  are 
  

  

  M 
  n 
  T, 
  and 
  its 
  integer 
  submultiples. 
  

  

  If 
  n 
  be 
  changed 
  into 
  n-(-l, 
  these 
  series 
  will 
  include 
  new 
  

   terms. 
  

  

  The 
  limit 
  of 
  this 
  process, 
  when 
  n 
  is 
  increased 
  without 
  

   limit, 
  is 
  that 
  the 
  series 
  can 
  contain 
  terms 
  with 
  periodic 
  times 
  

   of 
  amj 
  period, 
  whether 
  commensurable 
  or 
  incommensurable 
  

   with 
  T. 
  

  

  And 
  that 
  it 
  then 
  represents 
  the 
  Rongten 
  event 
  isolated 
  — 
  

   i. 
  e. 
  without 
  any 
  repetition. 
  It 
  is 
  obvious 
  that 
  one 
  condition 
  

   which 
  must 
  be 
  fulfilled 
  by 
  a 
  series 
  of 
  the 
  nature 
  of 
  Fourier's 
  

   series 
  in 
  order 
  that 
  it 
  may 
  be 
  competent 
  to 
  represent 
  an 
  event 
  

   of 
  limited 
  duration 
  without 
  repetitions 
  of 
  the 
  same, 
  is 
  that 
  it 
  

   shall 
  contain 
  terms 
  the 
  periodic 
  times 
  of 
  which 
  are 
  incommen- 
  

   surable 
  with 
  one 
  another. 
  

  

  Hence, 
  finally, 
  the 
  impulses 
  which 
  are 
  propagated 
  through 
  

   the 
  aether, 
  as 
  the 
  consequence 
  of 
  the 
  kathode 
  hedge-firing 
  

   however 
  irregular, 
  may 
  be 
  resolved 
  into 
  the 
  coexistence 
  of 
  

   component 
  undulations 
  travelling 
  in 
  the 
  various 
  directions, 
  

   each 
  of 
  which 
  is 
  a 
  train 
  of 
  perfectly 
  similar 
  plane 
  wavelets, 
  

   and 
  of 
  which 
  there 
  need 
  be 
  only 
  one 
  of 
  each 
  wave-length 
  in 
  

   each 
  direction. 
  

  

  It 
  follows 
  from 
  the 
  known 
  properties 
  of 
  Fourier's 
  expan- 
  

   sions 
  that 
  the 
  more 
  abrupt 
  and 
  irregular 
  the 
  hedge-firing 
  is, 
  

   the 
  more 
  prominent 
  a 
  place 
  will 
  terms 
  furnishing 
  undulations 
  

   of 
  very 
  short 
  wave-length 
  have 
  in 
  the 
  final 
  expansions, 
  

  

  If 
  we 
  choose 
  we 
  can 
  compound 
  these 
  undulations 
  of 
  short 
  

  

  2 
  2 
  

  

  