THEORY OP ELECTROMAGNETISM. 
709 
+ 0 / ) + 00 \ ^ -Q ” 0 • • . . (24), 
where now S only implies such variations as are the consequences of varying the 
velocities of the dynamical system and the temperature, and where of course 2Q 8q is 
given in our case by 
2Q 8q = | | f {- SF S P ' cW + (SE SC + Se Sc) t U} 
+ j j { - SF, df els' + (SE, SC + Se, Sc) ds] . (25). 
This last equation would have to be modified if we contemplated finite sliding of one 
surface over another. In this paper, as already stated, we simplify by supposing this 
never to take place (except in § 64 below). 
Equation (24) is more general than in this paper is required. Throughout this 
paper x s , and therefore will be assumed zero. 
37. The truth of the principle can be verified (as, admitting the restrictions just 
mentioned, will be shown directly) by proving that its consequences are in complete 
harmony with three recognised principles :—(1) that frictional forces can be explained 
by what Lord Rayleigh (‘Sound,’ 1st eel., vol. I., § 81) calls a dissipation function ; 
(2) that the heat which is created by the destruction of energy in other forms, 
appears, in the first instance, at the elements of matter where the destruction takes 
place; (3) the fundamental principle of conduction of heat, that the rate of flow of 
heat out of any region across the element c/2' of its boundary = S c/2'y'®' where y is 
a self-conjugate linear vector function, which is itself a function of the state of the 
medium at the point. 
38. To show the truth of these statements in the limited circumstances mentioned, 
viz., when x s is zero and there is no slipping, notice first what the effects of varying 
0 and c only are. A variation in C will cause a variation in H, since IwC = WH 
and [VUVH] a+ i = 0. The device used in the calculus of variations to take account 
function L. When there are heat sources not included in our system (L and X) we ought to put 
/— h and/, — h s instead of / and/, in eq. (24), hO and h s 0 being the rate of supply of external heat per 
unit volume and surface respectively. The form of eq. (24) would perhaps he made more instructive by 
grouping together the terms 
| j j*/ c0 ds + || f s cO ds + XQ cq. 
If H be the rate of “absorption of heat” by a body (ds or ds) of the system, this expression 
transforms into 2 (H d6/0 + Q 8q). 
