﻿150 
  Prof. 
  D. 
  N. 
  Mallik 
  on 
  Fermat's 
  Law. 
  

  

  this 
  difficulty 
  can 
  be 
  met, 
  if 
  we 
  suppose 
  that 
  the 
  above 
  

   energy 
  is 
  not 
  localized 
  in 
  each 
  element 
  of 
  volume. 
  But, 
  in 
  

   that 
  case, 
  we 
  must 
  postulate 
  the 
  existence 
  of 
  certain 
  terms 
  

   in 
  the 
  energy 
  function 
  for 
  each 
  such 
  element 
  which 
  disappear 
  

   when 
  integrated 
  throughout 
  the 
  whole 
  volume 
  of 
  the 
  medium. 
  

   We 
  must, 
  that 
  is, 
  admit 
  the 
  existence 
  of 
  a 
  certain 
  amount 
  of 
  

   intrinsic 
  energy 
  in 
  the 
  medium 
  which 
  takes 
  part 
  in 
  the 
  pro- 
  

   pagation 
  of 
  light. 
  This 
  is 
  virtually 
  the 
  view 
  adopted 
  by 
  

   Larmor, 
  who 
  has 
  pointed 
  out 
  that 
  if 
  we 
  could 
  postulate 
  some 
  

   concealed 
  (rotational) 
  phenomenon 
  going 
  on 
  in 
  each 
  element, 
  

   the 
  kinetic 
  reaction 
  of 
  which 
  can 
  give 
  rise 
  to 
  the 
  requisite 
  

   couple, 
  the 
  instability 
  pointed 
  out 
  by 
  Stokes 
  may 
  be 
  pro- 
  

   vided 
  for. 
  He 
  goes 
  on 
  to 
  remark 
  that 
  the 
  explanation 
  of 
  

   gravitation 
  is 
  still 
  outstanding, 
  and 
  necessitates 
  some 
  struc- 
  

   ture 
  or 
  property, 
  quite 
  different 
  from 
  or 
  probably 
  more 
  

   fundamental 
  than 
  simple 
  rotational 
  elasticity 
  of 
  the 
  aether 
  

   and 
  simple 
  molar 
  elasticity 
  of 
  material 
  aggregations 
  in 
  it, 
  

   and 
  this 
  property 
  may 
  be 
  operative 
  in 
  the 
  manner 
  here 
  

   required. 
  

  

  13. 
  No 
  doubt, 
  the 
  "labile 
  aether" 
  theory 
  does 
  not 
  require 
  

   this 
  saving 
  hypothesis, 
  as 
  it 
  only 
  postulates 
  a 
  certain 
  form 
  

   of 
  energy 
  function 
  for 
  a 
  whole 
  volume, 
  not 
  localized 
  in 
  each 
  

   element 
  (together 
  with 
  certain 
  surface 
  integrals, 
  which 
  must 
  

   be 
  supposed 
  to 
  vanish). 
  At 
  the 
  same 
  time, 
  although, 
  on 
  

   this 
  mode 
  of 
  regarding 
  the 
  question, 
  the 
  analytical 
  difficulty 
  

   is 
  met, 
  the 
  hypothesis 
  of 
  " 
  labile 
  " 
  aether 
  leaves 
  the 
  peculiar 
  

   property 
  of 
  the 
  medium 
  somewhat 
  hazy 
  and 
  ill-defined, 
  

   while, 
  on 
  the 
  other 
  hand, 
  if 
  the 
  existence 
  of 
  intrinsic 
  energy 
  

   were 
  admitted, 
  we 
  should 
  have 
  a 
  clearer 
  view 
  of 
  the 
  intimate 
  

   processes, 
  whose 
  resultant 
  alone 
  is 
  exhibited 
  by 
  the 
  final 
  

   analytical 
  result 
  postulated. 
  

  

  14. 
  Finally, 
  as 
  regards 
  the 
  energy 
  function 
  on 
  the 
  electro- 
  

   magnetic 
  theory, 
  the 
  formal 
  similarity 
  of 
  the 
  expression 
  for 
  

   potential 
  energy 
  of 
  the 
  rotationally 
  isotropic 
  medium 
  of 
  

   McCullagh 
  and 
  the 
  electrostatic 
  energy 
  enables 
  us 
  to 
  inter- 
  

   pret 
  the 
  intimate 
  nature 
  of 
  the 
  electric 
  field 
  in 
  the 
  same 
  way, 
  

   that 
  is, 
  on 
  the 
  basis 
  of 
  the 
  same 
  postulate 
  of 
  a 
  certain 
  amount 
  

   of 
  intrinsic 
  energy 
  of 
  the 
  aethereal 
  medium. 
  

  

  15. 
  This 
  same 
  postulate, 
  moreover, 
  serves 
  also 
  to 
  explain, 
  

   in 
  a 
  fairly 
  simple 
  manner, 
  the 
  specific 
  (Faraday-Maxwell) 
  

   property 
  of 
  the 
  electrostatic 
  field. 
  For, 
  since 
  the 
  energy 
  of 
  

  

  Jk 
  

   £— 
  F 
  2 
  dF, 
  we 
  may 
  suppose 
  it 
  to 
  arise 
  from 
  

  

  the 
  stresses 
  given 
  by 
  Maxwell, 
  viz. 
  a 
  tension 
  - 
  — 
  and 
  an 
  

  

  equal 
  pressure 
  — 
  ^— 
  . 
  Now, 
  assuming 
  that 
  the 
  system 
  of 
  

  

  07T 
  

  

  