354 



such that 



Prof. 0. Lodge on the Controller 



<r«-<r 6 = T^=T/"(0; 



and the total E.M.F., in addition to the modes of writing- 

 adopted above, may also be represented as, 



since E represents the work done per unit quantity of elec- 

 tricity conveyed. 



The representation of all this in a thermoelectric diagram 

 is neat and convenient, and is sufficiently shown in the figure, 

 without overlapping of areas. 



Ffr. 2. 



Kerne inhering that it is P which is plotted vertically, and 

 that P = II/T everywhere, the whole of the above various 

 expressions for the area E are geometrically represented. 

 The only one needing explanation is the expression f{ti) — f(t 2 \ 

 the difference of two indefinite -integral areas, of which the 

 second limit is incomplete in the figure, because unknown. 

 All that is known about f(t) is that E is the difference between 

 its values at the temperatures t ± and t 2 , that f'(t) = IIab/T 

 everywhere, and that f' / (t)= (cr a — cT b )jT everywhere. But 

 the value of the function /(£). itself is not known; nor is there 

 any means of determining it from observed values of a current 

 in a closed thermoelectric circuit. (I have no reason for de- 

 picting this area in the diagram on the right towards infinity, 

 instead of on the left towards absolute zero, except that 

 thereby overlap is avoided. Otherwise one would naturally 

 draw it so as to be bounded hypotheticaliy by the line of 

 absolute zero. The diagram does not attempt to represent 

 its probable value, but merely to emphasize the fact that its 

 absolute value is not known or needed in ordinary thermo- 

 electricity.) , 



