6i4 
PHYSICS: E. H. HALL 
Proc. N. A. S. 
supposed increase of this quantity with rise of temperature may be due 
to the expansion of the metal. 
The meaning of Pa and Pf, symbols which I have used before and 
shall presently use again, is such that 
Pf - Pa = 1 (X'o + (5 - 2.b)RT), (2) 
e 
where e is the electron charge. 
The revision leaves equations (12), (13), (17) of my previous paper 
unchanged, but in (14) it substitutes (5 + 1 • 5 — g) for (4 — q) in the 
first term of the second member, and in (15) it puts (25 + 1-5 — q) in 
place of (6.5 — q). 
Thermal Conduction.- — In December, 1917, I proposed^ the following 
theory: That thermal conduction in a metal is due to the convective 
action of a circulating electric current, free electrons moving down the 
temperature gradient and associated electrons moving up, with ioniza- 
tion at the hot part of the metal, involving absorption of heat, and re- 
association at the cold end, involving the emission of heat. I now pro- 
pose to go as far as I can at present in the way of submitting this theory 
to a quantitative test. 
As in my previous papers, "hypothesis (A)" will mean the assumption 
that the purely mechanical tendency of the free-electron gas is toward 
equality of pressure throughout the metal. Under this hypothesis the 
condition of equilibrium in a detached metal bar having an established 
and permanent temperature gradient is expressed by the equation 
This comes from equation (1) of my paper in these Proceedings for April, 
1918, by substitution for ^ according to equation (2) of that paper, 
which should he 
The first member of (3) as just given is the strength of the free-electron 
current, down the temperature gradient, and the second member is the 
strength of the associated-electron current, up the temperature gradient, 
per unit cross-section of the bar. We can rewrite (3) as follows,5__taking, 
for simplicity, the case in which {dT dl) = 1: 
The term {dPf dT) expresses a possible differential attraction of 
the unequally heated metal for the free electrons, tending to move them 
down the temperature gradient, something distinct from the force due 
to the gradient of potential {dP dT), which the gas-pressure drift 
