158 PROFESSOR W. THOMSON ON THE 
ture in an infinitely small space dz across the bar in the plane of the diagram, 
and yan unknown element, constant or a function of the temperature, depending 
on the nature of the substance, we may assume 
dt. 
dx 
as the amount of absorption, per unit of the volume of the bar, due to a current of 
intensity 7, by means of the new agency. The whole amount in a lamina of 
thickness dx, length /, and breadth @ perpendicular to the plane of the diagram, 
is therefore 
tx 
ax falda, 
or Y ; xu. 
As there cannot possibly be any other reversible thermal agency to be taken into 
account, we may now assume 
2H=75{[o@-2@]+fo xe } rem 2) 
3 He yh (2G) 2%) fo kay. [= Sey 
The second General Law showing that = = must vanish, gives, by the second 
of these equations, 
a(m)_ a) enna 
a alec gales Aik octal heey he tela 
Substituting, in place of 1, ¢, and differentiating with reference to this variable, 
we have, as an equivalent equation, 
a a 
De OG, A ere: 
aa Ai dt 
and using this in (22), we have 
SH = 75 f Ga - » aise eRe 
Bye t 
This expresses the full amount of heat taken in through the agency of the cur- 
rent y; of which the mechanical equivalent is therefore the work done by the 
current. Hence (according to principles fully explained above) the thermal cir- 
cumstances actually cause an electro-motive force F, of which the amount is given 
by the equation 
lL fta 
Bias 5 th Anmutetia an wit, 21: (27), 
to act along the bar from left to right of the diagram; which will produce a cur- 
rent, unless balanced by an equal and contrary reaction. This result both esta- 
