Temperatures of a Thin Rod, 237 



(AS or — ), and the length o£ the bar /. Similar state- 

 ments as to their ratios must hold as in the first approxi- 

 mation. 



The lines of flow (shown in the diagram) are given by the 

 conjugate family of logarithmic curves 



y = A exp (\ 2 x/2) . 



(28) 



where A is a parameter. 



The following table gives numerical values for the tem- 

 peratures at the axis and at the surface for bismuth rods of 

 radii 4 cms. and 1 cm. respectively. For calculation the 

 formula 



9 *> 



is employed, and the results of the preceding table may be 

 used. It will be seen that even for the rod of smaller radius 

 the difference between the surface and axial values is quite 

 appreciable, although the curvature of the isothermals would 

 not show in a diagram of the same scale as that given for the 

 larger radius. The rod is supposed to have its hot end kept 

 at 100°. 









Axial 



Fourier 



Surface 







v 



*. 



value. 



value. 



vame. 





( 



1 



92-8 



91-3 



89-8 



L=60.... 



1 



::1 



•• i 



5 



646 



63-4 



62-5 



a=4. .... 

 V=100 . 



10 



411 



40-1 



39-8 





i 



20 



166 



16-1 



16-1 





i 



1 



837 



83-3 



830 



L=60.... 



'• i 



5 



40-4 



40-1 



40-0 



a = l .... 

 V=100 . 



..< 



10 



162 



16-1 



161 





{ 



20 



26 



,6 



2-6 



The only other conductivity measurement of interest in 

 this connexion (beyond these of Despretz and Wiedemann and 

 Franz) is that of Angstrom ; for in the Forbes and Tait 

 method, though bars are used, yet the calculation goes direct 

 to the fundamental definitions, and does not employ the 

 Fourier formula, while in the Berget method and several 

 others radiation is avoided altogether. In the periodic method 



