﻿the 
  Electrical 
  Resistances 
  of 
  Pure 
  Metals.- 
  521 
  

  

  electrons, 
  while 
  (f)(6) 
  enters 
  as 
  the 
  temperature-variation 
  of 
  

   the 
  electronization-coefficient 
  q. 
  

  

  -r, 
  , 
  m\0 
  TT 
  <T 
  A/in 
  ^1 
  , 
  //l\ 
  ^""0 
  

  

  But 
  a 
  *^-r. 
  Hence 
  - 
  = 
  _ 
  . 
  ° 
  so 
  that 
  <£(0) 
  = 
  - 
  ° 
  

   and 
  therefore, 
  since 
  according- 
  to 
  Prof. 
  J. 
  J. 
  Thomson 
  (f)(0) 
  = 
  — 
  , 
  

  

  Ji 
  . 
  ' 
  9- 
  

  

  we 
  must 
  have 
  #x 
  -. 
  This 
  result, 
  taken 
  in 
  conjunction 
  with 
  

  

  a-yz—r-, 
  suggests 
  that 
  c/x 
  — 
  r-. 
  That 
  is, 
  that 
  for 
  the 
  metals 
  

  

  that 
  conform 
  with 
  the 
  relation 
  for 
  <r, 
  the 
  electronization 
  per 
  

   unit 
  volume 
  increases 
  with 
  the 
  average 
  thermal 
  energy 
  of 
  the 
  

   atom 
  and 
  the 
  number 
  of 
  atoms 
  per 
  unit 
  volume, 
  and 
  decreases 
  

   with 
  the 
  average 
  relative 
  displacements 
  of 
  the 
  atoms 
  and 
  their 
  

   maximum 
  chemical 
  valency. 
  

  

  The 
  investigations 
  of 
  Fleming- 
  and 
  Dewar 
  have 
  shown 
  that 
  

   4>(6) 
  is 
  not 
  a 
  linear 
  function 
  of 
  6. 
  If, 
  however, 
  we 
  confine 
  

   ourselves 
  to 
  a 
  limited 
  range, 
  say 
  from 
  0° 
  C. 
  to 
  100° 
  0., 
  

   we 
  may 
  consider 
  it 
  to 
  be 
  approximately 
  linear, 
  and 
  so 
  

   considerably 
  simplify 
  the 
  matter. 
  In 
  that 
  case 
  we 
  get 
  

   a 
  = 
  (T 
  Q 
  (l 
  + 
  €t)(l 
  + 
  ^t) 
  = 
  (T 
  () 
  (l-i-at 
  + 
  bt 
  2 
  ), 
  where 
  a 
  = 
  (e 
  + 
  y), 
  and 
  

   b 
  = 
  ey. 
  As 
  might 
  be 
  expected, 
  this 
  temperature-factor 
  fails 
  

   to 
  hold 
  both 
  at 
  very 
  high 
  and 
  at 
  very 
  low 
  temperatures, 
  but 
  

   may 
  be 
  taken 
  to 
  hold 
  with 
  a 
  considerable 
  degree 
  of 
  accuracy 
  

   between 
  0° 
  and 
  100°, 
  the 
  only 
  range 
  within 
  which 
  the 
  tem- 
  

   perature-variations 
  of 
  a. 
  and 
  p 
  can 
  be 
  said 
  to 
  be 
  fairly 
  

   accurately 
  known. 
  

  

  Let 
  a 
  and 
  s 
  be 
  linear 
  functions 
  of 
  the 
  temperature, 
  which 
  

   is 
  sufficiently 
  accurate 
  for 
  our 
  present 
  purpose, 
  and 
  let 
  

   a 
  = 
  a 
  (l 
  + 
  ftt) 
  and 
  s 
  = 
  s 
  (l 
  + 
  8t), 
  where 
  a 
  and 
  s 
  are 
  the 
  values 
  

   at 
  f 
  C., 
  a 
  and 
  s 
  at 
  0° 
  C, 
  and 
  ft 
  and 
  8 
  the 
  temperature- 
  

   variations. 
  Then 
  

  

  &=/K,[(l-^)+4&](273+t)j 
  

  

  and 
  therefore, 
  

  

  /, 
  \ 
  1+jft't 
  

  

  = 
  l 
  + 
  i(/3 
  / 
  -5 
  / 
  )^-^ 
  / 
  (/3 
  / 
  -8')^+ 
  &c, 
  

   where 
  ft' 
  = 
  ^-^, 
  and 
  S'= 
  

  

  273/3' 
  1 
  273S 
  

  

  