Vol.. 7, 1921 
PHYSICS: E. H. HALL 
63 
From my paper in these Proceedings for April, 1918, we get, by inte- 
gration of equation (5) there given, 
(Pe - P a ) = - (P 0 - p„) e . (2) 
Integrating equation (6) of the same paper, we get 
CP, - Pa) + (P, - PJf -f^--Hr*- ^.l0g e £. (3) 
a a * 
From (1), (2) and (3) we get 
If we had used at the beginning the hypothesis that the ionization oc- 
curred in a, just before the crossing, we should have obtained the expres- 
sion 
(5) 
The total change of state being the same in the process which gives equa- 
tion (5) as in that which gives equation (4), the total heat absorbed must 
be the same in both cases — that is, the II of (5) is the same as the II of (4) . 
Subtracting (5) from (4) we get 
m.-cm^ s +[&).- (?)>-».)-*«> 
whence 
X,-X«=;^.log e g, (7) 
or 
?5 = e RT ■ (8) 
Up 
Equation (8) has a familiar form, and in fact it might have been written 
down at once without circumlocation as soon as the fact was recognized, 
as it was in my paper of April, 1918, that the free electrons in the one 
metal are in equilibrium with those in the other, there being no circulatory 
motion of the electrons at the junction if the metals are at one temperature. 
Making use of equation (7) we can change (4) to the form 
and so 
It is now in order to see how well values of II calculated by means of 
