﻿534 
  Dr. 
  G. 
  Johnstone 
  Stoney 
  on 
  Evidence 
  

  

  wavelets. 
  These 
  wavelets 
  are 
  of 
  unlimited 
  extent 
  laterally, 
  

   each 
  is 
  uniform 
  throughout, 
  and 
  they 
  propagate 
  themselves 
  

   forward 
  through 
  the 
  medium 
  without 
  undergoing 
  change. 
  

   One 
  of 
  them 
  advances 
  perpendicularly 
  to 
  itself 
  in 
  each 
  of 
  the 
  

   directions 
  towards 
  which 
  the 
  spherical 
  wave 
  advances 
  (see 
  

   Phil. 
  Mag. 
  for 
  April 
  1897, 
  p. 
  273). 
  

  

  Use 
  polar 
  coordinates 
  and 
  consider 
  some 
  one 
  direction 
  6(f). 
  

   One 
  of 
  the 
  plane 
  impulsive 
  wavelets 
  is 
  propagated 
  in 
  that 
  

   direction 
  from 
  each 
  of 
  the 
  impacts 
  of 
  the 
  hedge-firing 
  on 
  the 
  

   shield 
  ; 
  and 
  those 
  which 
  happen 
  to 
  travel 
  from 
  all 
  the 
  

   impacts 
  in 
  the 
  direction 
  6(j>, 
  form 
  an 
  undulation 
  of 
  some 
  

   kind 
  travelling 
  in 
  that 
  direction. 
  It 
  obviously 
  consists 
  of 
  an 
  

   irregular 
  succession 
  of 
  uniform 
  plane 
  impulsive 
  wavelets. 
  

  

  The 
  whole 
  of 
  this 
  irregular 
  undulation 
  travelling 
  in 
  any 
  

   one 
  direction 
  may 
  be 
  represented 
  by 
  the 
  equations 
  

  

  T 
  2 
  = 
  F 
  2 
  (r-vt)j 
  <■ 
  ' 
  

  

  where 
  Tj 
  and 
  t 
  2 
  are 
  resolved 
  parts 
  of 
  the 
  transversal 
  in 
  two 
  

   planes 
  parallel 
  to 
  the 
  radius-vector 
  and 
  at 
  right 
  angles 
  to 
  one 
  

   another 
  ; 
  where 
  v 
  is 
  the 
  velocity 
  of 
  light 
  ; 
  and 
  where 
  the 
  

   forms 
  of 
  the 
  functions 
  Fj 
  and 
  F 
  2 
  vary 
  with 
  the 
  vector 
  6(f). 
  

  

  Next 
  let 
  all 
  the 
  events 
  of 
  the 
  Hongten 
  experiment 
  be 
  

   regarded 
  as 
  repeated 
  at 
  definite 
  equal 
  intervals 
  of 
  time, 
  say 
  

   at 
  intervals 
  of 
  a 
  day 
  — 
  i. 
  e. 
  of 
  86,400 
  seconds. 
  

  

  The 
  functions 
  ¥ 
  1 
  and 
  F 
  2 
  are 
  thereby 
  rendered 
  periodic 
  

   functions 
  ; 
  the 
  period 
  being 
  

  

  T 
  = 
  86,400 
  seconds. 
  

  

  These 
  functions 
  then 
  become 
  resolvable 
  by 
  Fourier's 
  theorem 
  

   into 
  pendulous 
  terms, 
  of 
  which 
  the 
  periods 
  are 
  T 
  and 
  integer 
  

   submultiples 
  of 
  T. 
  

  

  Equations 
  (1) 
  when 
  thus 
  expanded 
  by 
  Fourier's 
  theorem 
  

   represent 
  the 
  plane 
  wavelet 
  component 
  in 
  the 
  direction 
  6(f> 
  

   of 
  the 
  whole 
  motion 
  in 
  the 
  setter 
  due 
  to 
  the 
  radiation 
  from 
  the 
  

   target, 
  along 
  with 
  the 
  same 
  component 
  of 
  previous 
  and 
  sub- 
  

   sequent 
  repetitions 
  of 
  this 
  motion 
  in 
  the 
  setter 
  at 
  intervals 
  of 
  

   a 
  day. 
  

  

  Each 
  term 
  of 
  the 
  expansions 
  represents 
  physically 
  a 
  com- 
  

   plete 
  undulation 
  consisting 
  of 
  an 
  unlimited 
  train 
  of 
  exactly 
  

   similar 
  plane 
  pendulous 
  wavelets 
  of 
  some 
  one 
  wave-length, 
  

   filling 
  the 
  whole 
  of 
  space*, 
  and 
  advancing 
  with 
  the 
  velocity 
  v 
  

   in 
  the 
  direction 
  6(f). 
  

  

  * 
  If 
  it 
  fill 
  the 
  whole 
  of 
  space, 
  what 
  is 
  represented 
  by 
  it 
  includes, 
  in 
  

   addition 
  to 
  the 
  actual 
  radiation, 
  that 
  preceding 
  condition 
  of 
  the 
  sethev 
  

   which 
  would 
  have 
  produced 
  the 
  radiation 
  without 
  external 
  aid. 
  

  

  