﻿520 
  Mr. 
  W. 
  Williams 
  on 
  the 
  Temperature 
  Variation 
  of 
  

  

  that 
  the 
  deviation 
  of 
  the 
  temperature-coefficients 
  from 
  the 
  

   simple 
  value 
  273 
  may 
  be 
  due 
  to 
  the 
  temperature-variations 
  

   of 
  a 
  and 
  p. 
  

  

  Since 
  the 
  relation 
  a 
  = 
  a 
  (l 
  + 
  et) 
  is 
  true 
  to 
  a 
  first 
  approx- 
  

   imation 
  for 
  all 
  pure 
  metals, 
  we 
  can 
  put 
  

  

  ^ 
  = 
  273^)=( 
  1+e 
  0( 
  1 
  +y^^ 
  24 
  - 
  •••), 
  

  

  which 
  suggests 
  that 
  temperature 
  enters 
  into 
  the 
  relation 
  for 
  

   a 
  in 
  two 
  ways 
  essentially 
  different, 
  namely 
  : 
  

  

  (1) 
  Directly, 
  as 
  an 
  essential 
  factor, 
  and 
  represented 
  above 
  

  

  hj 
  m 
  ; 
  and 
  

  

  (2) 
  Indirectly, 
  and 
  represented 
  above 
  by 
  <j>(8), 
  as 
  the 
  tem- 
  

   perature-variation 
  of 
  one 
  or 
  more 
  of 
  the 
  other 
  essential 
  

   factors. 
  

  

  We 
  have 
  then 
  to 
  inquire 
  whether 
  these 
  essential 
  factors 
  

   can 
  be 
  a 
  and 
  p, 
  and 
  whether 
  <fi(0) 
  can 
  be 
  built 
  up 
  from 
  their 
  

   temperature-variations. 
  

  

  According 
  to 
  Prof. 
  J. 
  J. 
  Thomson 
  (' 
  Nature,' 
  May 
  10th 
  7 
  

   1900), 
  the 
  specific 
  resistance 
  of 
  a 
  metal 
  on 
  the 
  electronic 
  

   theory 
  is 
  given 
  by 
  

  

  _ 
  2fJLU 
  2 
  

  

  <T 
  ~~q~eH^ 
  

   where 
  q 
  is 
  the 
  average 
  number 
  of 
  electrons 
  dissociated 
  in 
  unit 
  

   volume 
  per 
  unit 
  time, 
  jj, 
  is 
  the 
  mass 
  of 
  an 
  electron, 
  e 
  its 
  

   electrical 
  charge, 
  u 
  its 
  average 
  velocity 
  of 
  translation, 
  and 
  I 
  

   the 
  length 
  of 
  its 
  mean 
  free 
  path. 
  Hence^ 
  since 
  /jl, 
  e, 
  and 
  I 
  are 
  

   constant 
  as 
  regards 
  temperature, 
  the 
  temperature-variation 
  of 
  

   a 
  must 
  depend 
  upon 
  the 
  temperature-variations 
  of 
  u 
  and 
  g. 
  

   On 
  this 
  matter, 
  Prof. 
  J. 
  J, 
  Thomson 
  makes 
  the 
  following- 
  

   observation 
  : 
  — 
  " 
  If 
  we 
  suppose 
  that 
  u, 
  the 
  mean 
  velocity 
  of 
  

   translation 
  of 
  the 
  corpuscles, 
  varies 
  with 
  the 
  temperature 
  in 
  

   the 
  same 
  way 
  as 
  the 
  velocity 
  of 
  translation 
  of 
  the 
  molecules 
  

   of 
  a 
  gas, 
  fin 
  2 
  would 
  be 
  proportional 
  to 
  the 
  absolute 
  tem- 
  

   perature, 
  and 
  the 
  specific 
  resistance 
  would, 
  considered 
  as 
  a 
  

  

  f) 
  

   function 
  of 
  the 
  absolute 
  temperature 
  0, 
  vary 
  as 
  - 
  ; 
  if 
  q, 
  the 
  

  

  amount 
  of 
  ionization, 
  increases 
  as 
  the 
  temperature 
  increases, 
  

   the 
  resistance 
  will 
  vary 
  more 
  slowly 
  than 
  the 
  absolute 
  tem- 
  

   perature 
  ; 
  if 
  q 
  diminishes 
  as 
  the 
  temperature 
  increases, 
  the 
  

   resistance 
  will 
  vary 
  more 
  rapidly 
  than 
  the 
  temperature/' 
  

   Hence, 
  according 
  to 
  Prof. 
  J. 
  J. 
  Thomson, 
  in 
  the 
  temperature 
  

  

  relation 
  — 
  = 
  ^ 
  Q 
  <f> 
  {0) 
  , 
  the 
  factor 
  -r=-~ 
  enters 
  in 
  the 
  deter- 
  

   o" 
  27 
  6 
  & 
  l 
  o 
  

  

  urination 
  of 
  the 
  average 
  velocity 
  of 
  translation 
  of 
  the 
  moving 
  

  

  