24 



PROCEEDINGS OF THE AMERICAN ACADEMY. 



i flowing from E to E 1 ; and let B represent the gradient which would 

 be maintained by an equal current flowing from E' to E. The general 

 disposition of the lines A and B with respect to J in this figure corre- 

 sponds to the phenomena observed in iron, more heat being generated 

 by a given current in this metal when the flow is from cold to hot than 

 when it is from hot to cold. 



If we have two similar cylindrical bars of iron, a and /?, and send the 

 same current from cold to hot in a and from hot to cold in /?, we may have 

 simultaneously gradient A of Figure 1 in bar a and gradient B in bar (3. 

 We shall in the discussion that follows assume this condition of things. 



We shall assume also, 

 for the present, that the 

 bars are so protected that 

 no heat escapes from 

 them laterally. 



In Figure 2 we have 

 parts of the curves A and 

 B, the part a x a 2 belong- 

 ing to any part of the 

 bar a and the part b x b. 2 belonging to the corresponding part of the 

 bar p. Let the length taken on each bar be L cm., and let the area of 

 cross-section of each bar be S sq. cm. 



We shall assume that the specific electric resistance of the iron is a 

 linear function of the temperature, and accordingly shall write 



A(l + yt a ) L — S as the resistance of the L cm. of a 



and A'( 1 -f y t 6 ) L ~ S as the resistance of the L cm. of ft, 



