on certain Equations in the Analytical Theory of Heat. 441 



We have then in (7) the solution of the problem of deter- 

 mination of conductivity by the bar method, free from the 

 most serious of the errors involved in the usual assumptions. 

 The outstanding assumption is that of plane isothermal surfaces. 



To confirm the deductions made in this paper, from the fact 

 that the loss of heat from a heated bar is proportional to a 

 power of the temperature-excess, I proceed to apply them to 

 the observations of Mitchell*, who has repeated Forbes's 

 experiments on conductivity, after having the bars used by 



Forbes nickel-plated. He gives the values of — ^- : for dif- 

 ferent temperature-excesses for an iron bar ; and from this the 

 following Table is calculated : — 



Temp. 





\ 







<b<& 



excess in 



d" 



specific 



„„d u 



v 1 ' 26 . 



& 



degrees 



Cent. 



d*" 



heat. 

 c = l. 







V V26 



10 



•11 



101 



•1111 



18-19 



•0611 



20 



•26 



1021 



•2655 



43-56 



10 



30 



•43 



1-031 



•4433 



72-61 



10 



40 



•61 



1041 



•635 



104-5 



10 



50 



•807 



1052 



•849 



138-4 



14 



60 



1-00 



1062 



1-062 



173-9 



07 



70 



119 



1-072 



1-276 



211-2 



05 



80 



1-405 



1082 



1-521 



248-9 



11 



90 



1-605 



1092 



1-755 



289-8 



06 



100 



1-83 



1-103 



2-018 



331 



10 



110 



2-04 



1-113 



2-270 



373-4 



08 



120 



2-28 



1-124 



2-563 



4176 



14 



200 



4-4 



1-206 



5-307 



792-5 



•0670 



250 



612 



1-258 



7-699 



1051 



•0733 



The constancy of the quotient c^ ^— 



,1-26 



up to a tempera- 



ture-excess of over' 100° C. shows how well the index 1*26 

 represents the cooling in this case. Above 100° C. n appears 

 to increase. 



Putting n = 1*26 in (7), the equation determining k from 

 the observation of temperatures along such a bar heated at 

 one end is 



Mitchell gives v and — =^at different points along the bar, and 



from these we have the following Table : — 

 * Trans. R. S. E. 4 July, 1887. 



