﻿"©' 
  

  

  the 
  Electrical 
  Resistances 
  of 
  Pure 
  Metals. 
  529 
  

  

  The 
  ratio 
  ~ 
  can 
  be 
  calculated 
  from 
  the 
  increase 
  of 
  volume 
  

  

  A 
  s 
  

  

  that 
  accompanies 
  the 
  fusion. 
  Thus, 
  if 
  d 
  is 
  the 
  average 
  

   distance 
  between 
  the 
  centres 
  of 
  two 
  neighbouring 
  atoms 
  at 
  

   the 
  absolute 
  zero, 
  d 
  + 
  Xe 
  and 
  d 
  + 
  \ 
  s 
  will 
  be 
  its 
  values 
  in 
  the 
  

   liquid 
  and 
  solid 
  states 
  respectively 
  at 
  the 
  temperature 
  ol 
  

   fusion. 
  Also, 
  if 
  p 
  e 
  and 
  p 
  s 
  be 
  the 
  corresponding 
  densities, 
  and 
  

  

  3r 
  7 
  — 
  ~ 
  be 
  denoted 
  bv 
  #, 
  we 
  set 
  

  

  K=(d-\ 
  \s)x—d. 
  

  

  Now 
  the 
  only 
  cases 
  where 
  'reliable 
  information 
  respecting 
  

   fis, 
  Pe 
  9 
  o-g, 
  and 
  a 
  e 
  can 
  at 
  present 
  be 
  obtained, 
  are 
  those 
  of 
  lead, 
  

   cadmium, 
  tin, 
  and 
  zinc, 
  and 
  in 
  the 
  case 
  of 
  these 
  metals, 
  since 
  

   the 
  melting-point 
  is 
  low, 
  the 
  average 
  value 
  of 
  a. 
  between 
  0° 
  

   and 
  100° 
  is 
  probably 
  not 
  far 
  from 
  its 
  value 
  between 
  absolute 
  

   zero 
  and 
  the 
  melting-point 
  T, 
  so 
  that 
  very 
  approximately 
  

   \ 
  s 
  = 
  docY. 
  Hence 
  

  

  X 
  e 
  _ 
  (1 
  + 
  «T 
  )j;-1 
  . 
  

   X 
  *T 
  

  

  the 
  ratio 
  being 
  thus 
  independent 
  of 
  the 
  actual 
  value 
  of 
  d. 
  

   In 
  order, 
  however, 
  to 
  compare 
  the 
  value 
  of 
  X 
  e 
  with 
  the 
  

   constant 
  of 
  Pictet's 
  law, 
  namely 
  "WT, 
  we 
  shall 
  put 
  d 
  = 
  Vi 
  

  

  The 
  increase 
  of 
  volume 
  that 
  accompanies 
  fusion 
  has 
  been 
  

   specially 
  investigated 
  for 
  several 
  metals 
  by 
  Vicentini 
  and 
  

   Omodei. 
  their 
  results 
  being 
  taken 
  in 
  the 
  table 
  that 
  follows 
  

   except 
  in 
  the 
  case 
  of 
  zine. 
  

  

  

  ps. 
  

  

  pe. 
  

  

  Ae- 
  

  

  

  \e 
  

   . 
  \s 
  

  

  ffe 
  

   as 
  

  

  Diff. 
  

  

  Lead 
  

  

  11-005 
  

   8-366 
  

  

  7-183 
  

  

  10645 
  

  

  7-989 
  

   6-988 
  

   6-480 
  

  

  •076 
  

  

  •085 
  

   •054 
  

  

  •087 
  

  

  •046 
  

   •044 
  

   •029 
  

   •042 
  

  

  1-66 
  

   1-93 
  

  

  1-86 
  

   2-07 
  

  

  1*9 
  

  

  2-3 
  

   21 
  

   20 
  

  

  + 
  12 
  p. 
  cent. 
  

   + 
  16 
  „ 
  

   + 
  12 
  „ 
  

   - 
  4 
  „ 
  

  

  Cadmium 
  ... 
  

   Tin 
  

  

  Zinc 
  

  

  

  Vassura's 
  values 
  for 
  — 
  have 
  been 
  taken 
  in 
  the 
  case 
  of 
  

  

  °* 
  

  

  cadmium 
  and 
  tin, 
  and 
  De 
  la 
  Rive's 
  in 
  the 
  case 
  of 
  lead 
  and 
  

  

  zinc. 
  

  

  Omadei 
  gives 
  no 
  values 
  for 
  p 
  s 
  and 
  p 
  e 
  in 
  the 
  case 
  of 
  zinc. 
  

   According 
  to 
  Roberts-Austen, 
  however, 
  the 
  density 
  of 
  zinc 
  

   just 
  when 
  fusion 
  is 
  completed 
  is 
  6*480, 
  from 
  which 
  value 
  

  

  K 
  

  

  - 
  can 
  be 
  calculated. 
  

  

  Taking 
  the 
  results 
  in 
  the 
  table 
  as 
  experimentally 
  valid, 
  it 
  

  

  