24 SECTIONAL ADDRESSES. 



One might precipitately come to the conchision that the events at either 



of the junctions were influenced by the events at all other points of the 



circuit. 



It is, however, only the rate of change of E due to changing the 



temperature T., with which we are concerned, and it might more logically 



/'dJ^ \ 

 be written ( — ) because T, must be left unchanged. 



\'^,'T2/Tl 



In the same way, by changing T, instead of T^ we may obtain 



in which everything refers to the lower temperature T,. 



Sir Oliver Lodge has always insisted that E is invariably the e.m.f. 

 round a complete circuit. This is perfectly correct, but we are only 

 concerned with the contribution to its value arising infinitesimally near 



to either of the extreme temperatures of the circuit, and p. „- is thus 



seen to be identical with ^ where V., is the potential-difference at the 



junction whose temperature is T.^. 



We can obtain further information from considerations of entropj'. 

 Strictly speaking we are entitled to use the principle of entropy only for 

 reversible cycles, while in several respects the circuits we are using may 

 be irreversible. Several ways are known by which the irreversibility 

 may be diminished to zero in the limit, but no change is thereby made in 

 the conclusions which we come to by ignoring the irreversibility altogether 

 — which we accordingly do.' 



The entropy change at any part of a cycle is obtained by dividing any 

 heat entry by the absolute temperature at which it enters. The sum of 

 all the changes must be zero for a complete cycle. 



The two circuits give 



^ T, 



T, + d% T, 



f 



^ -^dT=0 



Ti 



whence ^ f^A+^^-^^- = 

 0T2VT2/ T, 



' By increasing the lengths of the wires the conduction of heat along each may be 

 indefinitely diminished. By surrounding them with conductors having the same 

 temperature as the wire near to it the loss by radiation, &c., can be diminished. A 

 reverse e.m.f. can be superimposed (by electromagnetic induction or otherwise) so 

 as to reduce the current to zero and thereby diminish the value of the ohmic heat; 

 and so on. Ignoring the irreversibility is equivalent to taking for granted that such 

 precautions have been taken. 



