﻿466 
  

  

  Mr. 
  D. 
  Macfarlane 
  on 
  

  

  [June 
  10, 
  

  

  taining 
  the 
  mercury 
  in 
  a 
  thermometer-bulb 
  of 
  ordinary 
  dimensions 
  pro- 
  

   duces 
  a 
  sensible 
  difference 
  of 
  temperature 
  between 
  the 
  outer 
  surface 
  of 
  

   the 
  glass 
  exposed 
  to 
  the 
  external 
  medium 
  and 
  the 
  surface 
  of 
  the 
  mercury. 
  

   For 
  let 
  b 
  be 
  the 
  thickness 
  of 
  the 
  glass, 
  E 
  the 
  " 
  emissivity 
  " 
  of 
  its 
  outer 
  

   surface, 
  and 
  h 
  the 
  conductivity 
  of 
  its 
  substance 
  ; 
  let 
  the 
  excess 
  of 
  tem- 
  

   perature 
  of 
  the 
  outer 
  surface 
  of 
  the 
  glass 
  above 
  that 
  of 
  the 
  surrounding 
  

   medium 
  be 
  v, 
  and 
  the 
  excess 
  of 
  temperature 
  of 
  the 
  inner 
  surface 
  of 
  the 
  

   glass 
  above 
  the 
  outer 
  Sv 
  ; 
  we 
  have 
  

  

  Now 
  by 
  the 
  Glasgow 
  experiments 
  it 
  has 
  been 
  found 
  that 
  E 
  is 
  approxi- 
  

   mately 
  j^Vu 
  °f 
  a 
  gramme-water 
  thermal 
  unit 
  per 
  square 
  centimetre 
  per 
  

   second 
  ; 
  and 
  by 
  the 
  determinations 
  of 
  conductivities 
  of 
  stones 
  and 
  

   underground 
  strata 
  in 
  absolute 
  measure 
  by 
  Peclet 
  and 
  Forbes 
  the 
  value 
  

   of 
  Jc 
  for 
  glass 
  may 
  be 
  roughly 
  estimated 
  at 
  in 
  terms 
  of 
  centimetre, 
  

   second, 
  and 
  gramme- 
  water 
  thermal 
  unit. 
  Hence 
  

  

  Thus, 
  if 
  the 
  thickness 
  of 
  the 
  glass 
  be 
  half 
  a 
  millimetre 
  (i. 
  e. 
  2>=-^ 
  cr 
  ), 
  we 
  

   have 
  

  

  This 
  is 
  a 
  small 
  difference, 
  but 
  by 
  no 
  means 
  imperceptible 
  in 
  the 
  delicate 
  

   experiments 
  of 
  Dulong 
  and 
  Petit 
  ; 
  and 
  it 
  is 
  twenty 
  times 
  the 
  difference 
  

   of 
  temperature 
  between 
  the 
  centre 
  and 
  surface 
  of 
  the 
  cooling 
  copper 
  

   globe 
  of 
  4 
  centimetres 
  diameter. 
  

  

  Appendix. 
  

  

  Distribution 
  of 
  temperature 
  in 
  a 
  cooling 
  copper 
  globe 
  of 
  4 
  centimetres 
  

   diameter, 
  calculated 
  from 
  Fourier's 
  formula 
  

  

  Sv 
  1 
  

  

  (1) 
  

  

  where 
  

  

  Pi 
  

  

  art 
  roots 
  of 
  the 
  transcendental 
  equation 
  

  

  tan 
  >m 
  

  

  (2) 
  

  

  and 
  Pj 
  coefficients 
  determined 
  to 
  give 
  (according 
  to 
  Fourier's 
  method) 
  

  

  