Electro-optic Action of a Charged Franklin's Plate. 363 



dimensions of the bars, and even of the difference of tempe- 

 ratures at the junctions. The power is increased by dimi- 

 nishing the length and increasing the sections to a limit not 

 indicated by these expressions (in which the terminal tempe- 

 ratures are regarded as given), and probably determined in 

 practice by the necessity of conveying the heat to the scene 

 of action. 



The resistances being given, the ratio of sections ^/^i *& 

 to be determined so as to make our ratio a minimum. This 

 happens when 



\o-J rvr{* 



and thus we get 



te 2 



To turn this into numbers for the case of German silver 

 and iron, we have the following approximate numbers in C.G.S. 



S(\/^ + \/3) 



r 3 = 2-0xl0 4 , ^ = 1-0 xlO 1 , 



r 2 = l-0xl0 4 , r/=5-0xl0°, 



e = 3>0 xlO 3 . 



The value of J is 4*2 x 10 7 , and for t we will assume 500 

 (absolute measure). The use of these gives, as the ratio of 

 the work that would be obtained by a perfect engine from the 

 conducted heat to that actually obtained from the thermo- 

 electric force, the number 300; from which we may conclude 

 that the steam-engine and dynamo are not likely to be super- 

 seded by a German-silver and iron thermopile, even though 

 considerable allowance be made for the admitted roughness of 

 the numerical estimate. 



As regards other materials, it is interesting to note that the 

 ratio contains as divisor the square of the electromotive force 

 per degree. 



XLIV. Electro-optic Action of a Charged Franklin s Plate. 

 By John Kerb, LL.D., Free Church Training College, 

 Glasgow f . 



I HAVE examined this difficult subject in several sets of 

 experiments, the last of which was finished about three 

 years ago. Having satisfied my own mind, I dropped the 

 subject, thinking that no publication of the results was 



* Everett's i Units and Physical Constants' ; Landolt's Tabellen. 

 t Communicated by the Author. 



