﻿t/ie 
  Electrical 
  Resistances 
  of 
  Pure 
  Metals. 
  519 
  

  

  The 
  metals 
  of 
  the 
  platinum 
  and 
  palladium 
  groups 
  have 
  a 
  

   valency 
  of 
  4 
  in 
  their 
  sesqui- 
  and 
  tetra-chlorides. 
  Ruthenium 
  

   and 
  osmium, 
  however, 
  form 
  potassium 
  compounds 
  analogous 
  

   to 
  chromates, 
  manganates, 
  and 
  ferrates, 
  in 
  which 
  the 
  valency 
  

   must 
  be 
  6. 
  In 
  addition, 
  they 
  form 
  tetroxides 
  Ru0 
  4 
  and 
  

   Gs0 
  4 
  , 
  indicating 
  a 
  valency 
  of 
  8 
  in 
  accordance 
  with 
  the 
  

   Periodic 
  Law, 
  a 
  valency 
  that 
  also 
  accords 
  with 
  the 
  potassium 
  

   compounds 
  K 
  2 
  Pt01 
  6 
  , 
  and 
  K 
  2 
  PdCl 
  6 
  . 
  It 
  therefore 
  appears 
  

   that 
  a 
  maximum 
  valency 
  of 
  8 
  is 
  not 
  incompatible 
  with 
  the 
  

   chemical 
  characteristics 
  of 
  the 
  metals. 
  

  

  The 
  metals 
  of 
  the 
  Iron 
  Group 
  do 
  not 
  conform 
  with 
  the 
  

   relation 
  for 
  a, 
  a 
  matter 
  to 
  he 
  fully 
  dealt 
  with 
  on 
  a 
  future 
  

   occasion. 
  

  

  According 
  to 
  the 
  law 
  of 
  Dulong 
  and 
  Petit, 
  s 
  is 
  approxi- 
  

   mately 
  — 
  , 
  where 
  s 
  is 
  the 
  specific 
  heat 
  and 
  w 
  the 
  atomic 
  

  

  weight. 
  Also, 
  V= 
  - 
  where 
  d 
  is 
  the 
  density. 
  Hence 
  

  

  6*3 
  .... 
  

  

  V= 
  -j-. 
  Again, 
  if 
  a 
  is 
  the 
  coefficient 
  of 
  thermal 
  expansi- 
  

   bility, 
  supposed 
  to 
  be 
  constant, 
  and 
  if 
  \ 
  = 
  Vscc6 
  and 
  c 
  = 
  Vf«T, 
  

  

  we 
  get 
  

  

  - 
  A 
  mYd 
  _ 
  5^ 
  _ 
  BmX 
  - 
  BmX0 
  

  

  273* 
  cT 
  ~ 
  c 
  2 
  scl 
  ~~ 
  c 
  2 
  np 
  c 
  2 
  nli 
  

  

  where 
  B 
  is 
  a 
  constant, 
  n 
  the 
  average 
  number 
  of 
  atoms 
  per 
  

   unit 
  volume, 
  p 
  the 
  atomic 
  specific 
  heat, 
  and 
  li 
  or 
  (p6) 
  the 
  

   average 
  thermal 
  energy 
  of 
  an 
  atom 
  at 
  temperature 
  6. 
  Now. 
  V 
  

   is 
  proportional 
  to 
  the 
  average 
  space 
  assigned 
  to 
  an 
  atom 
  at 
  the 
  

   absolute 
  zero. 
  Hence 
  X 
  or 
  Yjotf) 
  will 
  be 
  proportional 
  to 
  the 
  

   average 
  relative 
  displacement 
  of 
  the 
  centres 
  of 
  two 
  neigh- 
  

   bouring 
  atoms 
  between 
  absolute 
  1 
  zero 
  and 
  the 
  temperature 
  #, 
  

   which 
  we 
  may 
  call 
  the 
  average 
  atomic 
  displacement 
  at 
  

   temperature 
  6. 
  

  

  If 
  a. 
  is 
  constant, 
  so 
  that 
  X 
  for 
  any 
  metal 
  is 
  proportional 
  

   to 
  0, 
  and 
  if 
  p 
  is 
  also 
  constant, 
  a 
  must 
  be 
  proportional 
  to 
  #, 
  so 
  

  

  that 
  = 
  .^-y 
  = 
  l-\-et, 
  where 
  a 
  and 
  <r 
  are 
  the 
  values 
  at 
  t° 
  C. 
  

  

  cr 
  z.7 
  o 
  

  

  and 
  0° 
  C. 
  respectively, 
  and 
  € 
  = 
  '003665. 
  According 
  to 
  this, 
  

   the 
  temperature 
  resistance-coefficients 
  of 
  all 
  pure 
  metals 
  must 
  

   be 
  the 
  same, 
  namely 
  ^73? 
  and 
  the 
  resistance 
  must 
  vanish 
  at 
  

   the 
  absolute 
  zero. 
  The 
  investigations 
  of 
  Fleming 
  and 
  Dewar, 
  

   however, 
  have 
  shown 
  that 
  while 
  the 
  resistance 
  tends 
  to 
  vanish 
  

   at 
  the 
  absolute 
  zero, 
  the 
  temperature-coefficient 
  is 
  usually 
  

   higher 
  than 
  . 
  2 
  ^~. 
  its 
  average 
  value 
  being 
  about 
  *004. 
  Now 
  

   we 
  know 
  that 
  a 
  and 
  p 
  are 
  not 
  constant, 
  but 
  slowly 
  increase 
  

   with 
  rise 
  of 
  temperature. 
  Hence 
  the 
  view 
  suggests 
  itself 
  

  

  