﻿24 
  Prof. 
  L. 
  T. 
  More 
  on 
  T7i 
  

  

  leories 
  

  

  and 
  are 
  moving 
  toward 
  each 
  other 
  along 
  their 
  line 
  of 
  centres 
  

   with 
  velocities 
  u 
  and 
  u\ 
  the 
  momentum 
  of 
  each 
  sphere 
  is 
  no 
  

   longer 
  its 
  mass 
  times 
  velocity, 
  but 
  the 
  action 
  takes 
  place 
  as 
  

   if 
  the 
  mnss 
  had 
  been 
  increased. 
  The 
  formula 
  for 
  the 
  kinetic 
  

  

  energy"^ 
  is 
  

   where 
  

  

  in 
  which 
  the 
  /'s 
  are 
  functions 
  of 
  a, 
  5, 
  and 
  c 
  only. 
  

  

  If 
  the 
  spheres 
  are 
  small 
  compared 
  with 
  the 
  distance 
  between 
  

   them 
  

  

  ' 
  3a^/A 
  

  

  

  approximately. 
  

  

  And, 
  lastly, 
  if 
  there 
  is 
  only 
  one 
  sphere 
  moving 
  in 
  an 
  

   infinite 
  fluid 
  

  

  L 
  = 
  2/37rpa3 
  = 
  l/2;?i 
  (A) 
  

  

  M=N=0. 
  

  

  The 
  quantities 
  L, 
  M, 
  and 
  N 
  are 
  the 
  apparent 
  or 
  virtual 
  

   increases 
  in 
  the 
  masses 
  of 
  the 
  spheres, 
  and 
  in 
  the 
  simple 
  case 
  

   of 
  one 
  sphere 
  moving 
  in 
  the 
  fluid 
  reduce 
  to 
  one-half 
  the 
  mass 
  

   of 
  the 
  sphere. 
  In 
  other 
  words, 
  the 
  introduction 
  of 
  a 
  second 
  

   moving 
  sphere 
  in 
  an 
  infinite 
  liquid 
  acts 
  as 
  a 
  constraint, 
  in- 
  

   creasing 
  the 
  kinetic 
  energy 
  lor 
  a 
  given 
  velocity, 
  and 
  so 
  

   virtually 
  increases 
  the 
  inertia 
  of 
  the 
  system. 
  Equation 
  (A) 
  

   should 
  be 
  a 
  satisfactory 
  answer 
  to 
  Dr. 
  Lewis's 
  surprise 
  that 
  

   (17) 
  shows 
  an 
  increase 
  of 
  the 
  energy, 
  E', 
  of 
  a 
  moving 
  

   body. 
  

  

  If 
  we 
  compare 
  these 
  equations 
  with 
  (17) 
  developed 
  by 
  

   Dr. 
  Levels 
  we 
  cannot 
  but 
  be 
  struck 
  with 
  their 
  similarity. 
  

  

  * 
  Lamb, 
  ' 
  Hydrodynamics/ 
  p. 
  139. 
  

  

  