﻿528 
  Mr. 
  W. 
  Williams 
  on 
  the 
  Temperature 
  Variation 
  of 
  

  

  If 
  € 
  is 
  the 
  average 
  increase 
  of 
  s 
  per 
  unit 
  rise 
  of 
  temperature, 
  

   and 
  if 
  S 
  = 
  J/3, 
  as 
  suggested 
  above, 
  then, 
  approximately, 
  

  

  2*1/3 
  

   e 
  — 
  X(s 
  Q 
  fi) 
  = 
  — 
  — 
  , 
  where 
  iv 
  is 
  the 
  atomic 
  weight. 
  The 
  fol- 
  

   lowing 
  are 
  some 
  of 
  the 
  results 
  obtained 
  for 
  e 
  from 
  this 
  

   relation 
  : 
  — 
  

  

  

  13. 
  

   •00 
  

  

  IV. 
  

  

  e 
  (calc.) 
  

  

  •oooo 
  

  

  e 
  (obs.) 
  

   •0000 
  

  

  950 
  

   1000 
  

   460 
  

   490 
  

   341 
  

   240 
  

   210 
  

   210 
  

   151 
  

   112 
  

  

  

  Aluminium 
  

  

  Conner 
  

  

  1036 
  

  

  1251 
  

  

  1671 
  

   1124 
  

  

  0880 
  

   0806 
  

   1198 
  

   0923 
  

  

  27 
  

  

  633 
  

  

  119 
  

  

  112 
  

  

  106 
  

  

  108 
  

  

  192-5 
  

  

  195 
  

  

  800 
  

  

  410 
  

  

  295 
  

   210 
  

   175 
  

   160 
  

   131 
  

   100 
  

  

  INaccari. 
  

  

  Richards. 
  

  

  Bede. 
  

  

  Trowbridge. 
  

  

  Lorenz. 
  

  

  Naccari. 
  

  

  Violle. 
  

  

  Naccari. 
  

  

  Violle. 
  

  

  Violle. 
  

  

  Tin 
  

  

  Cadmium 
  

  

  Palladium 
  

  

  Silver 
  

  

  Iridium 
  

  

  Platinum 
  

  

  

  The 
  relation 
  does 
  not 
  hold 
  for 
  the 
  metals 
  of 
  the 
  Iron 
  group.. 
  

   Also, 
  for 
  many 
  of 
  the 
  metals 
  experimental 
  results 
  cannot 
  be 
  

   obtained 
  to 
  test 
  the 
  matter, 
  while 
  for 
  metals 
  like 
  lead, 
  mag- 
  

   nesium, 
  and 
  zinc, 
  the 
  results 
  available 
  are 
  not 
  conclusive. 
  

  

  According 
  to 
  the 
  relation 
  <j 
  cc 
  — 
  , 
  since 
  6 
  is 
  constant 
  during 
  

  

  fusion, 
  the 
  change 
  of 
  resistance 
  that 
  accompanies 
  fusion 
  must 
  

   depend 
  upon 
  the 
  change 
  in 
  the 
  value 
  of 
  q 
  *. 
  Hence, 
  if 
  a 
  s 
  is 
  

   the 
  value 
  of 
  a 
  in 
  the 
  solid 
  state 
  just 
  before 
  fusion 
  has 
  begun, 
  

   and 
  a 
  e 
  its 
  value 
  in 
  the 
  liquid 
  state 
  just 
  when 
  fusion 
  is 
  com- 
  

   pleted, 
  and 
  if 
  q 
  s 
  and 
  q 
  e 
  be 
  the 
  corresponding 
  values 
  of 
  q 
  y 
  

  

  — 
  = 
  — 
  . 
  For 
  copper, 
  silver, 
  magnesium, 
  zinc, 
  cadmium, 
  

  

  calcium, 
  thallium, 
  lead, 
  and 
  mercury, 
  qcc 
  — 
  — 
  . 
  If 
  we 
  assume 
  

  

  772 
  A, 
  

  

  that 
  h 
  in 
  this 
  relation 
  is 
  to 
  stand 
  for 
  the 
  internal, 
  and 
  not 
  for 
  the 
  

   total 
  energy 
  of 
  the 
  atom, 
  it 
  will 
  be 
  the 
  same 
  in 
  the 
  solid 
  and 
  

   liquid 
  states 
  at 
  the 
  temperature 
  of 
  fusion. 
  Hence, 
  if 
  \ 
  e 
  , 
  X 
  s 
  be 
  

  

  the 
  values 
  of 
  X 
  corresponding 
  to 
  cr 
  ei 
  <r 
  s 
  — 
  = 
  ~ 
  f. 
  

  

  * 
  Which 
  implies 
  that 
  the 
  average 
  velocity 
  of 
  translation 
  u 
  of 
  the 
  

   moving 
  electrons 
  is 
  not 
  affected 
  by 
  the 
  act 
  of 
  fusion, 
  but 
  remains 
  un- 
  

   altered 
  like 
  the 
  temperature. 
  

  

  t 
  This 
  assumption 
  implies 
  that 
  the 
  electronization 
  per 
  unit 
  volume, 
  so 
  

   far 
  as 
  it 
  depends 
  upon 
  temperature, 
  is 
  determined 
  : 
  — 
  

  

  (1) 
  By 
  the 
  kinetic 
  energy 
  of 
  an 
  atom 
  considered 
  as 
  a 
  system 
  of 
  electrons 
  

   in 
  orbital 
  motion, 
  — 
  this 
  being 
  unaffected 
  by 
  fusion, 
  since 
  the 
  temperature 
  

   of 
  the 
  atom 
  is 
  not 
  altered. 
  

  

  ■ 
  (2) 
  By 
  the 
  average 
  distance 
  apart 
  of 
  the 
  atomic 
  centres, 
  — 
  which 
  is 
  

   directly 
  affected 
  by 
  fusion. 
  

  

  