﻿152 
  Prof. 
  D. 
  N. 
  Mallik 
  on 
  Fermat's 
  Law. 
  

  

  Therefore 
  from 
  (1) 
  and 
  (3) 
  we 
  get 
  

  

  2T 
  = 
  (y 
  + 
  C 
  

  

  2V 
  = 
  C 
  / 
  

  

  + 
  01 
  

  

  But 
  this 
  is 
  meaningless, 
  since 
  the 
  mean 
  potential 
  energy 
  and 
  

   the 
  mean 
  kinetic 
  energy 
  are 
  alone 
  constant, 
  as 
  these 
  

   quantities 
  are 
  understood 
  to 
  mean 
  in 
  the 
  above 
  equations. 
  

   Accordingly, 
  the 
  only 
  conclusion 
  that 
  seems 
  to 
  be 
  con- 
  

   sistent 
  with 
  all 
  the 
  equations 
  is 
  that 
  the 
  optical 
  energy 
  is 
  

   entirely 
  kinetic. 
  

  

  The 
  equation 
  (1) 
  then 
  becomes 
  T 
  = 
  A, 
  the 
  equation 
  (2) 
  

   disappears 
  and 
  the 
  equation 
  (3) 
  becomes 
  T 
  / 
  = 
  A 
  / 
  , 
  and 
  

   T'— 
  T 
  = 
  A'— 
  A 
  = 
  intrinsic 
  energy. 
  

  

  Again, 
  if 
  the 
  potential 
  energy 
  of 
  deformation 
  of 
  'the 
  

   sethereal 
  medium 
  involved 
  in 
  light 
  propagation 
  is 
  to 
  be 
  

   regarded 
  as 
  essentially 
  kinetic, 
  we 
  are 
  led 
  to 
  conclude 
  that 
  

   all 
  energy 
  is 
  kinetic. 
  

  

  18. 
  This 
  view 
  of 
  the 
  intimate 
  nature 
  of 
  energy 
  intrinsic 
  

   or 
  otherwise 
  is 
  partially 
  accepted 
  in 
  effect, 
  in 
  different 
  

   branches 
  of 
  Physics. 
  Thus, 
  on 
  the 
  kinetic 
  theory 
  of 
  gases, 
  

   the 
  pressure 
  of 
  a 
  gas 
  has 
  a 
  kinetic 
  origin 
  and, 
  in 
  fact, 
  all 
  

   cases 
  of 
  equilibrium 
  in 
  molecular 
  physics 
  are 
  best 
  explained 
  

   as 
  those 
  of 
  mobile 
  or 
  convective 
  equilibrium. 
  

  

  19. 
  But, 
  if 
  the 
  interpretation 
  of 
  Fermat's 
  law, 
  sketched 
  

   above, 
  is 
  admissible, 
  we 
  are 
  led 
  to 
  a 
  further 
  generalization- 
  — 
  

   to 
  regard 
  the 
  energy 
  of 
  mere 
  configuration, 
  also, 
  as 
  kinetic. 
  

   We 
  must, 
  in 
  fact, 
  conceive 
  some 
  subtle 
  sethereal 
  motion, 
  

   being 
  associated 
  with 
  every 
  given 
  configuration 
  of 
  a 
  con- 
  

   servative 
  system, 
  existing 
  in 
  the 
  field 
  ; 
  thus 
  the 
  so-called 
  

   potential 
  energy 
  of 
  a 
  vibrating 
  system 
  at 
  any 
  moment 
  is, 
  in 
  

   reality, 
  kinetic 
  energy 
  of 
  the 
  field. 
  It 
  follows, 
  therefore, 
  

   that 
  the 
  phenomena 
  of 
  elasticity 
  are 
  to 
  be 
  regarded 
  as 
  in- 
  

   trinsically 
  kinetic, 
  and 
  remembering 
  the 
  intimate 
  relation 
  

   between 
  electrostatics 
  and 
  the 
  phenomena 
  of 
  elasticity, 
  

   developed 
  by 
  Maxwell 
  and 
  others, 
  we 
  are 
  led 
  to 
  conclude 
  that 
  

  

  electrostatic 
  phenomena 
  are 
  also 
  kinetic. 
  

  

  20. 
  An 
  indirect 
  verification 
  of 
  the 
  last 
  conclusion 
  may 
  be 
  

   derived 
  from 
  an 
  application 
  of 
  the 
  compatibility 
  equations 
  

   of 
  St. 
  Venant 
  to 
  the 
  theory 
  of 
  electrostatic 
  stress 
  developed 
  

   by 
  Maxwell, 
  at 
  any 
  rate, 
  if 
  we 
  assume 
  that 
  the 
  system 
  of 
  

   stresses 
  in 
  an 
  electrostatic 
  field 
  is 
  that 
  given 
  by 
  Maxwell. 
  

   For 
  this, 
  let 
  e 
  xx 
  , 
  e^, 
  &c. 
  be 
  the 
  strains 
  at 
  any 
  point. 
  Then 
  

   it 
  is 
  easy 
  to 
  show 
  that 
  the 
  above 
  system 
  of 
  strains 
  is 
  

   given 
  by 
  

  

  