PHYSICS: E. H . HALL 
31 
exceedingly small excess of them along the surface of the colder half of the 
bar, with a corresponding deficiency in the warmer part, is enough to balance 
the mechanical-pressure tendency and maintain equilibrium. Of course this 
equilibrium is a mobile one, individual electrons moving in either direction 
through any cross-section of the bar constantly, but with zero net result so 
long as the bar is isolated and of unchanging temperature-gradient. 
The pressure gradient, and the balancing electric potential, will depend on 
the rate at which n increases with increase of T in this metal a. Let this rate 
be such that the changes of pressure and volume suffered by one gram of elec- 
P 
FIG. 1 
trons in passing, under conditions differing only slightly from those of equi- 
librium, from temperature 7\ to temperature T 2 , or vice versa, through the 
metal a are represented by the curve 2 A D in figure 1 . 
If this curve is steeper than the adiabatic curve of the moving body of elec- 
trons, this body will take up heat from the metal during its progress from Ti 
to T 2 ; that is, the Thomson heat-effect in this metal will be of the same sign 
as that in iron. If the line is less steep than the adiabatic, the Thomson heat- 
effect will be of the same sign as that in copper. In lead the adiabatic line 
would be followed very nearly. 3 
Let the line B C be for the metal 0 what the line A D is for a. 
