﻿Prof. 
  D. 
  N. 
  Mallik 
  on 
  Fermat's 
  Law. 
  153 
  

  

  where 
  k 
  is 
  the 
  specific 
  inductive 
  capacity, 
  E 
  is 
  Young's 
  

   modulus, 
  and 
  a 
  is 
  Poisson's 
  ratio, 
  and 
  

  

  ?xy 
  = 
  0, 
  &c. 
  

  

  EL 
  & 
  

  

  *»" 
  87rE' 
  &C 
  * 
  

   Applying 
  the 
  compatibility 
  equations, 
  we 
  have 
  

  

  (-S 
  + 
  Cl 
  + 
  2.)g)p 
  2 
  = 
  0, 
  

  

  * 
  F 
  =0, 
  & 
  c. 
  

  

  Hence 
  F 
  2 
  = 
  a«r 
  + 
  ^ 
  + 
  cr+ 
  constant, 
  which 
  is, 
  obviously, 
  

   impossible. 
  

  

  If, 
  however, 
  the 
  phenomena 
  are 
  not 
  statical, 
  the 
  above 
  

   argument 
  does 
  not 
  apply. 
  

  

  21. 
  It 
  should 
  be 
  remarked, 
  however, 
  what 
  indeed 
  experi- 
  

   ments 
  seem 
  to 
  indicate, 
  that 
  the 
  distribution 
  of 
  electrostatic 
  

   stress 
  in 
  a 
  dielectric 
  medium 
  is 
  not 
  so 
  simple 
  as 
  Maxwell 
  

   supposed, 
  so 
  that 
  the 
  assumption 
  virtually 
  made 
  by 
  Maxwell 
  

   that 
  the 
  principal 
  axes 
  of 
  stress 
  (agreeably 
  to 
  Faraday's 
  

   views) 
  are 
  along 
  and 
  perpendicular 
  to 
  the 
  lines 
  of 
  force, 
  

   seems 
  to 
  be 
  only 
  a 
  first 
  approximation. 
  

  

  Experiments 
  moreover 
  suggest, 
  as 
  has 
  been 
  remarked 
  by 
  

   J. 
  J. 
  Thomson, 
  that 
  there 
  must 
  be 
  forces 
  in 
  the 
  electric 
  field 
  

   not 
  recognized 
  by 
  Maxwell's 
  theory. 
  These 
  peculiarities 
  of 
  

   the 
  field 
  seem 
  to 
  be 
  intimately 
  related 
  to 
  the 
  fact 
  that 
  the 
  

   field 
  is 
  essentially 
  one 
  of 
  kinetic 
  energy. 
  

  

  22. 
  AVe 
  may 
  picture 
  to 
  ourselves 
  the 
  intimate 
  processes 
  

   going 
  on 
  in 
  an 
  sethereal 
  medium 
  which 
  is 
  the 
  seat 
  of 
  electrical 
  

   or 
  optical 
  energy, 
  by 
  means 
  of 
  the 
  moving 
  Faraday 
  tubes 
  of 
  

   J. 
  J. 
  Thomson. 
  On 
  this 
  view, 
  the 
  Faraday 
  tubes 
  are 
  

   supposed 
  to 
  move 
  with 
  the 
  velocity 
  of 
  light 
  and 
  both 
  

   electric 
  and 
  magnetic 
  forces 
  and 
  electric 
  polarization, 
  and 
  

   therefore 
  the 
  state 
  of 
  energy 
  of 
  the 
  field, 
  can 
  be 
  completely 
  

   represented 
  by 
  these 
  motions. 
  (' 
  Recent 
  Researches.') 
  

  

  23. 
  To 
  show 
  this, 
  let 
  the 
  electric 
  displacement 
  across 
  any 
  

   surface 
  be 
  equal 
  to 
  the 
  difference 
  in 
  the 
  number 
  of 
  tubes 
  

   that 
  enter 
  and 
  leave 
  the 
  surface 
  and/, 
  g, 
  h 
  their 
  components 
  

  

  