PHYSICS: E. H. HALL 
103 
play in the local virtual e.m.fs. of the circuit, we can, by making a gap in any 
isothermal homogeneous part of this circuit and inserting there an electrometer, 
measure the total e.m.f. as a simple difference of charge-potential. The total, 
or net, amount of work done by or against the specific attractions which 
enter into P a and Pf is zero for any quantity of electricity which goes com- 
pletely through the circuit. 
Under hypothesis (B): If, in place of hypothesis (A), we assume that the 
mechanical tendency of the free electrons is towards the condition of equilib- 
rium which holds for thermal effusion, each local virtual e.m.f. will be rep- 
resented by an area like E' A' D' G f g'e' in figure 4, where E' is the mid- 
point of E A' and G' is the mid-point of G D' . But the combination of four 
such areas, one for each of the lines A' B f , B' C' , A' D f , and D' C f , of figure 
3, will give precisely the same net result that is represented in figure 3 by 
? 
E 
FIG. 4 
A' B' C' D' . The total e.m.f. is, then, precisely the same under hypothesis 
(B) as under hypothesis (A). This is because the fundamental conditions of 
p and v, represented by the lines A B, B C, C D, and D A, in figure 3, remain 
substantially the same under hypothesis (B) as under hypothesis (A). 
1 These Proceedings, 4, 1918, (29-35). 
2 For suggestions see a paper by myself in these Proceedings, March, 1917, and one by 
P. W. Bridgman in the Physical Review, April, 1917, p. 269. 
3 1 am not without hope that the mechanism here suggested will prove to be of great 
service in the theory of heat conduction. It seems probable that the free electrons within 
a metal are quite incapable, acting as a permanent gas, of accounting for the magnitude of 
the metal's heat conductivity. But it is a familiar fact that the heat-carrying power of a 
vapor, involving evaporation and condensation, is vastly greater than that of a permanent 
gas. It appears, from the imperfect data now at my command, that the operation illus- 
trated by figure 1 would give thermal conductivity of the right order of magnitude. 
This conception of thermal conductivity, a conception occurring quite incidentally and 
unexpectedly, has already been communicated to the American Physical Society in a paper 
read at the meeting of December, 1917. 
