THEORY OF ELECTROMAGNETISM. '699 
F • [J] fck + ((/,*.(2), 
and f and f s will be determined from the values of l and l s in a manner that will he 
described later on. All thermal phenomena not determined by F, and all forces of the 
nature of friction, will be supposed g’iven by a third function X, given by 
X = [j[ xch +- jj x s ds . (3), 
where x, x s , unlike ff s , do not in any way depend upon L. The way in which these 
forces and the thermal phenomena depend upon X will be explained later. We shall 
call X the dissipation function. It is, in fact, a generalisation of Lord Rayleigh’s 
dissipation function (‘Theory of Sound,’ 1st ed., §81). 
24. The absolute temperature of any element of matter will be denoted by 0. The 
vector © (assumed an intensity—§ 7 above) is defined by the equation 
0 = Vd .(4). 
Since both © and V are intensities, we have 
©' = V9 . (5). 
All electric and magnetic phenomena are supposed ultimately to depend upon the 
magnitudes and rates of variation of two fluxes (§ 7), d, k, called respectively the 
dielectric displacement and the conduction displacement. The whole displacement, 
D, is defined as the sum of these two, so that 
D = d + k .(6). 
D must satisfy the two conditions of incompressibility for vectors, i.e ., 
SVD=0, [Sc7SD] a + i := 0.(7), 
the notation [ \ + h being as defined on p. 119 of former paper, i.e. the suffixes a and b 
denote the two regions bounded by a surface of discontinuity, and [ ~] a + 6 stands for 
]« + [ ]&• Since D is a flux, it follows by Prop. IV., § 8, above, that 
SV'D' = 0, [ScZVD']^ =0.(8). 
The dielectric current, c, the conduction current, K, and the whole current, C, all 
assumed to be fluxes, are given by the equations 
c = d, K = k 
C = D — c -f K 
4 U 2 
( 9 ), 
( 10 ). 
