298 



PROCEEDINGS OP THE AMERICAN ACADEMY. 



"yafues oj r ^ 



as it is from thirteen well distributed pairs of junctions, represents 

 with considerable accuracy the mean difference of potential between 



the two faces of the steel disk ; 

 4 but is this mean difference of 



potential proportional to the 

 mean difference of tempera- 

 ture between these two faces ? 

 This question would be at 

 once answered in the affirma- 

 tive if the disk, instead of being 

 metallically continuous, were 

 made up of little columns of 

 steel, in length equal to the 

 thickness of the disk, tipped 

 at both ends with copper, each 

 column being insulated from 

 its neighbors. For in such an 

 aggregation there would be no short-circuiting, and the difference of 

 potential at the two ends of any steel column would depend merely 

 upon the difference of temperature at these ends ; and, with the very 

 small difference of temperature existing, only a fraction of one degree, 

 the potential difference would be very strictly proportional to the tem- 

 perature difference. 



But the disk is continuous, and there must be short-circuiting cur- 

 rents within it. IIow will these currents affect the mean difference 

 of potential of the two faces ? These currents in the steel will be 

 partly vertical and partly horizontal. "We will consider, first, the 



vertical components. Let Figure 11 

 represent any two equal vertical ele- 

 ments, S-^ and /So, of the disk, connected 

 by the copper strips Ci and Co. Let 

 the e. m. f of element *S'i be E^, directed 

 upward, and the e. m. f. of S^ be ^j) 

 also directed upward, and let ^i > E^. If connection between ele- 

 ments were broken, the difference of potential betweeen the top and 

 bottom of Si would be E^, and that between top and bottom of tS'2 

 would be E^. The mean difference of potential would be \ (Ei -f E2). 

 Let the resistance of *S'i, equal to that of S2, be called r. When 

 connection exists, as in the figure, we have a short-circuiting current, 

 C, passing up through Si and down through S^. With this current, 

 the difference of potential between top and bottom of Si is Ei — rC, 



c 



c. 



Fig. 11. 



.5, 



