﻿[ 
  515 
  ] 
  

  

  LX. 
  On 
  the 
  Temperature 
  Variation 
  of 
  the 
  Electrical 
  

   Resistances 
  of 
  Pure 
  Metals, 
  and 
  Allied 
  Matters. 
  By 
  

   W. 
  Williams, 
  B.Sc, 
  Municipal 
  Technical 
  College, 
  

   Swansea*. 
  

  

  MANY 
  of 
  the 
  physical 
  properties 
  of 
  metals 
  are 
  periodic 
  

   functions 
  of 
  their 
  atomic 
  weights. 
  This 
  is 
  especially 
  

   true 
  of 
  the 
  valency 
  and 
  atomic 
  volume. 
  In 
  a 
  lesser 
  degree 
  

   it 
  is 
  also 
  true 
  of 
  the 
  melting-point 
  and 
  electric 
  resistance. 
  

   Now, 
  the 
  periodic 
  variations 
  of 
  these 
  four 
  quantities 
  for 
  most 
  

   of 
  the 
  metals 
  can 
  be 
  very 
  simply 
  related 
  to 
  one 
  another. 
  

   For 
  if 
  a 
  is 
  the 
  specific 
  resistance, 
  at 
  0° 
  C, 
  m 
  the 
  maximum 
  

   chemical 
  valency, 
  V 
  the 
  atomic 
  volume, 
  and 
  T 
  the 
  absolute 
  

  

  KmV 
  

  

  melting-point, 
  to 
  a 
  first 
  approximation 
  a 
  — 
  — 
  ff— 
  , 
  where 
  K 
  

  

  is 
  a 
  quantity 
  which 
  appears 
  to 
  have 
  different 
  values 
  for 
  

   different 
  groups 
  of 
  metals. 
  Dr. 
  Fleming 
  has 
  already 
  pointed 
  

   out 
  that 
  the 
  metals 
  of 
  large 
  specific 
  resistance 
  are 
  those 
  

   having 
  large 
  atomic 
  volumes 
  and 
  large 
  valencies. 
  For 
  

   silver, 
  copper, 
  magnesium, 
  zinc, 
  cadmium, 
  thallium, 
  lead, 
  

   mercury 
  (in 
  the 
  solid 
  state), 
  and 
  probably 
  calcium, 
  K 
  = 
  

   1*72 
  x 
  10 
  ? 
  if 
  or 
  is 
  measured 
  in 
  microhms 
  for 
  a 
  centimetre 
  

   cube, 
  and 
  V 
  is 
  the 
  quotient 
  of 
  the 
  atomic 
  weight 
  by 
  the 
  

   density. 
  For 
  gold, 
  indium, 
  tin, 
  and 
  aluminium, 
  however, 
  K 
  

   has 
  only 
  half 
  this 
  value. 
  For 
  sodium 
  and 
  potassium 
  also 
  its 
  

   value 
  appears 
  to 
  be 
  half 
  that 
  given 
  above 
  ; 
  while 
  for 
  arsenic, 
  

   antimony, 
  and 
  bismuth 
  it 
  is 
  about 
  double. 
  

  

  In 
  the 
  table 
  that 
  follows, 
  a 
  is 
  the 
  value 
  calculated 
  for 
  the 
  

  

  specific 
  resistance 
  at 
  0°C. 
  from 
  tjt- 
  , 
  while 
  a' 
  is 
  the 
  value 
  

  

  obtained 
  by 
  observation. 
  The 
  maximum 
  chemical 
  valency 
  

   is 
  as 
  given 
  by 
  the 
  Periodic 
  Law, 
  except- 
  in 
  the 
  case 
  of 
  gold 
  

   and 
  copper, 
  where 
  the 
  values 
  3 
  and 
  2 
  are 
  taken 
  as 
  being 
  

   more 
  consistent 
  with 
  the 
  chemical 
  characteristics 
  of 
  the 
  

   metals. 
  

  

  

  m. 
  

  

  V. 
  

  

  T. 
  

  

  <r. 
  

  

  <x'. 
  

  

  Diff. 
  

  

  Silver 
  

  

  1 
  

  

  2 
  

   2 
  

  

  2 
  

   2 
  

   3 
  

   4 
  

  

  10-2 
  

   7-1 
  

   13-9 
  

   , 
  9-1 
  

   12-9 
  

   17-2 
  

   181 
  

  

  1173 
  

   1333 
  

   1023 
  

   676 
  

   593 
  

   561 
  

   605 
  

  

  1-5 
  

  

  1-82 
  

   4-6 
  

   4-65 
  

   7-5 
  

   15-9 
  

   20-6 
  

  

  1-5 
  

  

  1-7 
  

   4-1 
  

   5-8 
  

   7-5 
  

   17-6 
  

   20-0 
  

  

  p. 
  cent. 
  

  

  7 
  „ 
  

   12 
  „ 
  

   20 
  „ 
  

  

  „ 
  

  

  9-6 
  „ 
  1 
  

  

  3 
  „ 
  , 
  

  

  

  Magnesium 
  

  

  

  Thallium 
  

  

  

  

  Communicated 
  by 
  the 
  Physical 
  Society 
  : 
  read 
  March 
  14, 
  1902. 
  

  

  