648 BELL SYSTEM TECHNICAL JOURNAL 



about the value of the Thomson coefficient s. In making 4> inde- 

 pendent of temperature we in effect assunud ih.u the Thomson 



coefficient lias the \alue s='~-k (per electron), which iiai)pons to he 



precisely the value demanded (and vainly demanded) by the electron- 

 theory of conduction. If on the other hand we choose to accept 

 from the experiments the fact that 5 is extremeh- small c()m[)ared to 



'-rk, the equation (16) compels us to set 



3 



4> = ^kT:e+<f>o. (22) 



Insertini; this into (111) we obtain 



I=CT-c kf, (23) 



which is conimonK' known as the 7'--law, and is at tlie moment the 

 favorite way of expressing the variation of thermionic current with 

 temperature. As I said earlier, experiment is thus far powerless to 

 distinguish between (8), (20) and (22). 



This brief and superficial sketch of the thcrmocK naniic argument 

 is meant partly to familiarize the reader with the T- formula, and 

 partly to show that the observations upon the dependence of ther- 

 mionic current on temperature do not necessarily sustain the parti- 

 cular type of theor\' which has figured most in these pages, as against 

 its rivals actual or conceivable. Of course it would be unjustifiable 

 to say that any argument of the thermodynamical type is i{>so facto 

 stronger than any argument based on a physical model. It may be 

 true that the laws of thermodynamics are \a\\d ever\ wJHre without 

 exception; but it is certainly true that in an\- particular case it is 

 extremely difficult to feel sure just how tiie\- should be applied to 

 arrive at absolutely binding conclusions. In this case, for instance, 

 we have assumed as both possible and reversible a process which 

 no one has ever carried through, an<l no one, in all likelihood, ever 

 will; and in the course of analyzing tiu' ir.uisfirs of energ\' between 

 the system and the external world in this imagined ]>rocess, we have 

 classified some as transfers of' heat and .some as transfers of mechan- 

 ical work, and possibly ignored yet others, .so that the analysis re- 

 cjuires careful thought and has in fact been made in different ways 

 by different authorities. There is for example the problem of the 

 allowance to be made for work done in transferring the electrons 

 from place to place against eIectromoti\e forces, which might or 

 might not be nil when summed around the complete cycle; H. A. 



