﻿240 
  Dr. 
  J. 
  Buchanan 
  on 
  a 
  Model 
  which 
  

  

  its 
  course, 
  executing 
  in 
  the 
  reverse 
  direction 
  all 
  the 
  changes 
  

   through 
  which 
  it 
  has 
  passed. 
  In 
  this 
  respect 
  Planck's 
  problem 
  

   differs 
  toto 
  cwlo 
  from 
  that 
  of 
  Boltzmann's 
  H 
  theorem, 
  where 
  

   we 
  have 
  a 
  process, 
  consisting 
  of 
  a 
  number 
  of 
  separately 
  

   reversible 
  processes, 
  supposed 
  to 
  be 
  irreversible 
  in 
  the 
  

   aggregate. 
  

  

  XXIV. 
  Note 
  on 
  a 
  Paper 
  by 
  Prof. 
  Fleming, 
  F.R.S., 
  and 
  

   Mr. 
  Ashton, 
  entitled 
  il 
  On 
  a 
  Model 
  which 
  Imitates 
  the 
  

   Behaviour 
  of 
  Dielectrics" 
  By 
  John 
  Buchanan, 
  JJ.Sc. 
  

   (Lond.)*. 
  

  

  UNDER 
  the 
  above 
  title 
  there 
  has 
  appeared 
  in 
  the 
  Phil. 
  

   Mag. 
  for 
  August 
  1901 
  a 
  description 
  of 
  a 
  very 
  ingenious 
  

   model 
  invented 
  by 
  the 
  authors 
  of 
  the 
  paper. 
  The 
  diagrams, 
  

   obtained 
  by 
  help 
  of 
  the 
  model, 
  which 
  illustrate 
  the 
  paper 
  are 
  

   exceedingly 
  interesting 
  and 
  suggestive. 
  

  

  There 
  are 
  some 
  points 
  in 
  the 
  theory 
  of 
  the 
  action 
  of 
  the 
  

   model, 
  and 
  of 
  the 
  behaviour 
  of 
  the 
  dielectric 
  in 
  a 
  condenser, 
  

   w 
  T 
  hich 
  may 
  be 
  deemed 
  worth 
  attention. 
  

  

  1. 
  The 
  action 
  of 
  the 
  model 
  clearly 
  depends 
  on 
  the 
  viscosity 
  

   of 
  a 
  liquid. 
  The 
  diagrams 
  show 
  by 
  their 
  form 
  the 
  very 
  

   interesting 
  fact 
  that 
  the 
  motion 
  of 
  the 
  pencil 
  which 
  traced 
  

   them 
  approximated 
  closely 
  to 
  what 
  may 
  be 
  expressed 
  by 
  the 
  

   term 
  " 
  motion 
  of 
  a 
  viscous 
  fluid 
  by 
  diffusion"!. 
  

  

  In 
  other 
  words, 
  the 
  displacement 
  curves 
  obtained 
  from 
  the 
  

   model, 
  and 
  their 
  derived 
  velocity 
  curves, 
  are 
  of 
  the 
  same 
  form 
  

   as 
  the 
  graphs 
  of 
  certain 
  solutions 
  of 
  Fourier's 
  well-known 
  

   equation 
  

  

  dt 
  ^dx> 
  [l) 
  

  

  For 
  comparison 
  with 
  figs. 
  I. 
  & 
  III. 
  (PL 
  Y.) 
  respectively, 
  

   of 
  Prof. 
  Fleming 
  and 
  Mr. 
  Ashton's 
  paper, 
  I 
  give 
  here 
  figs. 
  1 
  

   and 
  2, 
  which 
  are 
  the 
  respective 
  graphs 
  of 
  equations 
  (2) 
  

   and 
  (3) 
  below. 
  In 
  these 
  solutions 
  of 
  (1) 
  v 
  denotes 
  the 
  dis- 
  

   placement, 
  t 
  the 
  time, 
  x 
  the 
  distance 
  from 
  the 
  origin 
  at 
  which 
  

   exists 
  the 
  motion 
  under 
  consideration, 
  and 
  K 
  denotes 
  the 
  

   " 
  diffusivity." 
  

  

  Without 
  the 
  guidance 
  afforded 
  by 
  some 
  such 
  theory 
  as 
  is 
  

   here 
  given, 
  it 
  would 
  be 
  quite 
  impossible 
  to 
  discover 
  from 
  

   experiment 
  such 
  a 
  law 
  of 
  displacement 
  as 
  is 
  expressed 
  by 
  (2) 
  

   for 
  instance, 
  or 
  of 
  velocity 
  as 
  expressed 
  by 
  (3). 
  Thus, 
  the 
  

  

  * 
  Communicated 
  by 
  the 
  Physical 
  Society 
  : 
  read 
  November 
  8, 
  1901. 
  

   t 
  Of. 
  Lord 
  Kelvin's 
  Math, 
  and 
  Phys. 
  Papers, 
  vol. 
  iii. 
  art. 
  xcviii. 
  

   p. 
  433. 
  

  

  