548 MR A. CRICHTON MITCHELL ON THE THERMAL CONDUCTIVITY 



III. (M). 







v by formula 





x, in feet. 



v by experimental 

 curve. 



log v = log A - , 



° ° 1+cx 



Difference. 



00 



247-2 



245-4 



-1-8 



025 



1721 



1721 



00 



05 



125-25 



12545 



+ 02 



075 



92-3 



923 



00 



1-25 



520 



520 



00 



1-75 



3035 



306 



+025 



2-25 



18-2 



18-72 



+052 



2-75 



1115 



11-65 



+ 0-5 



3-75 



4-3 



435 



+ 0-05 



4-75 



1-85 



253 



+ 0-68 



5-75 



0-7 



1-34 



+ 064 



The next table shows how far the formula (A), on the other hand, suits the 

 case of the iron bar cooled midway. 



x, in feet. 



v by experimental 

 curve. 



v by formula 



logi^log A- — — . 

 1+cx 



Difference. 



00 



0-25 



05 



075 



1-25 



1-75 



2-25 



206-35 

 15085 

 111-4 



83-45 

 47-7 

 28-15 

 165 



20635 

 15075 

 111-2 

 8285 

 47-25 

 27-9 

 16-95 



00 

 -01 

 -0-2 

 -0-6 

 -0-45 

 -025 

 + 045 



The agreement shown here, though not so close as that shown in II. above, 

 was much closer than that which the use of formula (B) gave. 



Lambert {Pyrometrie, Berlin, 1779) showed, from experiment, that the 

 curve of stationary temperature along a bar could be represented by an 

 equation of the form 



v = Ae- px - 

 whence 



log v = log A — px . 



So that the curve representing, at each point of the bar, the logarithms of the 

 temperature excesses should be a straight line. 



This result was shown to hold for the case of copper (C) by Prof. Tait 

 ( Trans. R. S. K, 1878). 



