96 PROCEEDINGS OF THE AMERICAN ACADEMY. 



apart at every temperature, which is equivalent to saying that the 

 Thomson effect coefficients, <xi and a- 2 , of the two metals must be equal 

 at every temperature. 



Examination of equations (15) and (15') shows directly that the 

 conditions just imagined, with respect to R and v, would make <x the 

 same for both metals. This agreement is important only in so far as 

 it gives evidence that the argument carried through in this paper is 

 self-consistent. 



Inspection of equation (34), which expresses the net or total e.m.f. 

 of the circuit, answers in some measure the question raised on p. 72; 

 namely, what conditions of the thermo-electric circuit furnish the 

 mechanism for the production of electric energy at the expense of 

 heat. It is to be noted that this equation makes no reference to the 

 possible tendency of either metal to draw electrons to itself from the 

 other metal, or the possible tendency of hot metal to draw electrons 

 from cold metal, or vice versa. The absence of any such reference is 

 rational; for the net amount of work done on any electron in passing 

 completely around the circuit must be independent of any such 

 attraction. It is to be observed also that equation (34) does not 

 contain x, which indicates the relative importance of the (B) electrons 

 and the (A) electrons in conduction. This omission results from my 

 assumption that the (A) electrons have the same value of R, at any 

 given temperature, that the (B) electrons have. Further considera- 

 tion may show this assumption to be unjustifiable, in which case more 

 complicated formulae must replace some of the equations of this 

 paper. 



On the other hand, it may appear later that I have made too sharp a 

 distinction between the (A) electrons and the (B) electrons. 



Although the theory set forth in this paper has been formed with 

 no regard to the transverse electromagnetic effects observed in a con- 

 ductor carrying a current across a magnetic field, it nevertheless, 

 taken in connection with the idea that the free electrons may have 

 something like the Maxwellian distribution of heat velocities, seems 

 to offer some hope of light in these dark places. I must, however, 

 defer discussion of this matter. 



