188 The Permanent Temperature of Conductors, $c. [June 19, 



Neglect now the variations of k and * with temperature, and suppose 

 the conductor of uniform material and area and girth of cross-section 

 throughout its length from x=0 to xa. Equation (1) becomes 



d*v ah c 2 * A s R \ 



_ fV-4 --- =U ....... (u) 



dx* fcA 100JA 



and its integral, fulfilling the end conditions, is 



v = 



lOOJgh 



e 



1 



-] 



where m= '/T~r ......... (^)- 



AA 



For round wire or rod of diameter D, we have 



0=>rD, and A^^D 2 . .. ; . . i . (9). 



whence m= v irS ......... (10)- 



ftJ_/ 



For copper we have k '91 (Angstrom). 



Now put It - - 



n x 1UOU 



where n might be about 4 for the ranges of temperature in Mr. 

 Bottomley's experiments, if we could judge from Macfarlane's 

 experiments on the cooling of a globe of copper of 4 centims. 

 diameter; and in the wires experimented on by Mr. Bottomley, 

 D='08. Hence for these wires 



Hence if n=4, j = f . But Mr. Bottomley's experiments show n 



8't) 



to be more nearly 1, and to be actually <1 for wires of somewhat 

 less diameter than '08. Hence we have, as a practical rough approxi- 

 mation, w = |; and (7) becomes 



m jr 



T e~"*+~~l 



ut 1 - 



v = 



1 1 n i 1 1 j, 1 1 



1-M 



In Mr. Bottomley's experiments a =50, and therefore 



