PHYSICS: E. H. HALL 
35 
So far as mere expansions and contractions are concerned, we may ignore the 
electrical property of the circulating fluid; for the mutual electrical self-repul- 
sion of its particles is balanced by the action of the equally numerous positive 
ions. 
It is to be noted that no necessity has appeared in this discussion for any 
'specific attraction' of either metal for electrons. Ordinary electro-static at- 
traction and repulsion, together with the mechanical, expansive, heat-pressure 
of the electrons, is apparently enough to account for all that is known to occur 
in thermo-electric action confined to a metallic circuit. All the evidence 
we have to show the existence of the so-called 'specific,' or 'essential,' attrac- 
tion comes from other regions of phenomena, especially from studies of ther- 
mionic emission and the Volta contact potential-difference. If such an at- 
traction exists and is active within metals, we need not change the discussion 
above given except in the interpretation of P. This has here been taken as 
ordinary electrostatic potential. If there is an 'essential attraction' between 
electrons and matter having no electric charge, P will appear in the formulas 
just as it appears now, but it will be interpreted as what I have called in a 
previous paper 1 virtual potential, potential due to all attractions and repul- 
sions acting on the progressive electrons. 
It is of interest to observe that the e.m.f . along any part of the circuit does 
not, under either hypothesis (A) or hypothesis (B), necessarily correspond to 
the amount of heat absorbed in this part. For example, the Thomson heat 
absorbed along the line A D may be positive, negative, or zero, according to 
the inclination of the line, while the e.m.f. of this part, represented by the 
area E A DG, remains always of the same sign. 
The preceding discussion expressly assumes that the free electrons are the 
only ones which move through a metal. This is a provisional assumption 
only. If the associated electrons also move progressively, as I have in cer- 
tain previous papers supposed them to do, the conditions of equilibrium in a 
detached metal bar, having a temperature-gradient, are different from those 
indicated in this paper. This matter I hope to discuss at another time. 
1 Boston, Proc. Amer. Acad. Arts ScL, 50, 4 July, 1914. 
2 Great steepness of this curve does not, as one might at first suppose, indicate a very 
rapid increase of n with increase of T, but the contrary. 
3 That is, if the moving body of electrons that constitute an electric current obeyed the 
laws of a perfect manotomic gas, we should have in lead n oc T 1 ' 5 , very nearly. 
