THEORY OF ELECTROMAGNETISM. 
7 57 
in the assigned direction X crdd. Consider an elementary (generally oblique) cylinder 
whose generating lines are parallel to C or K and whose faces are coincident with the 
isothermal surfaces 9 and 6 -j- cW. Let dp be the vector in the direction from the 
section 9 to the section 9 d9, representing a generating line, and d% the vector area 
of either face, drawn inwards at the section 9 and outwards at the section 9 + d9 
(tig. 2). The rate of “ absorption ” of heat means the rate at which energy dis- 
Fig. 2. 
d 22 d 22 
appears as heat (positive when it causes fall of temperature) and appears as some 
other form of energy, in the present case that of “ electrical separation.” Taken per 
unit volume of the standard position of matter this = 9 X what is contributed to 
the left of equation (35), § 40. [The truth of this statement should be clearly 
recognised. The principal term on the left of equation (35), §40, is c9j9 where c is 
the capacity for heat per unit volume. Any other positive term contributed to this 
side will therefore tend to render 9 negative.] Hence the rate of absorption of heat 
per unit volume due to the terms now under consideration will be + the expression 
on the right of equation (L3), § 82, and —■ the expression on the right of equation (13a). 
Putting = the scalar P or A, and noting that SVC = 0, and that for a steady field 
SVK = 0, we see that on the theory of reversibility the rate of absorption of heat 
for our element — S dSdp of volume is 
e (- P e SCVd + SC VP) (- S dtdp) 
and on the theory of irreversibility 
(2ASKV0 + 0SKVA) (— S dtdp). 
Now VP = Vd . dP/d9 and VA = Vd . dk./d9, and since C is parallel to dp, these 
two may be interchanged in the expressions just given. Thus the rates of absorption 
of heat on the theories of reversibility and irreversibility respectively, are 
- 9(- 0P fi9 + dVjd9) Sc/pVdSC dt 
