Conductivity of Metals with Temperature. 257 



is constant all down the rod, and equal to eP* + e~^ } or that 



El—Ei = const*=2rsay, . . (25) 



F 2 +X 



and that the value of the constant r is 



r— cosh //.£ (26) 



Hence to find fi we must know r, and to find r we must 

 know X. 



24. Now the only way to determine \ accurately is by a 

 system of trial and error, choosing it so that the expression 

 (25) shall be as constant as possible all down the rod ; but a 

 good approximation to its value can be obtained thus. Let 

 ^i> @2> ®i be three equidistant temperatures near the hot end of 

 the rod, and # 4 , 5 , 6 three equidistant temperatures near the 

 cool end ; then of course 



£l #3 04 ■ 06 • 



and therefore 



e 2 +x e, +x > 



A + I + I_A._I_JL' ' ' 



#2 #4 #6 #1 #3 #5 



an expression which is rather long, but with the aid of a table 

 of reciprocals can be evaluated without difficulty. The value 

 of X so obtained may be introduced into (25) and improved 

 by successive approximations ; after which it is to be intro- 

 duced into (24) and the number m obtained, which, when in- 

 serted in equation (9), expresses the rate of variation of 

 conductivity with temperature for the metal experimented 

 upon. 



Calculation of the Constant fi. 



25. The above process, however, not only determines X, but 

 also gives us a number of values for r; and from the mean of 

 these we must proceed to obtain /*. 



* This equation becomes identical with the one hitherto used, viz. 

 6 A-6 

 -^-ja — - = 2coshju£, as soon as one puts X = 0, and assumes 6 2 to be a geo- 



metric mean between 6 X and d 3 . 



Phil. Mag. S. 5. Vol. 7. No. 43. April 1879. X 



