754 
MR. A. McAULAY ON THE MATHEMATICAL 
Theory of Reversibility. 
Hence for a steady field 
B g = 4tt (YBC0 — 2CHSC0) . (16). 
and if this is the only part of B for a steady field, 
we have 
Theory of Irreversibility. 
For any field, steady or otherwise, 
b (/ = 4 tt (VBKO - 2CHSK0) . (16a) 
and if g is the only term in x containing H, we 
have 
0 = SYB y = 4 ttSV (YBC0 — 2CHSC0) . . (17). 
0 = [SUrB y ] a+ j = 4 tt [SUr (YBC0 
— 2CHSC0)]« + j . . . (18). 
The following equations will be explained 
below :— 
a = o (dP/do - dP;do) . . (19). 
n = 0 [P] a _i .(20). 
dfUjG) , [> - 0P fl ] a _ 4 _ A _ 
do 
+ 
= o 
E = - S E (/ = (n/6>) do 
= n — n 0 + [<r — op g] a -i> do 
I • (22). 
Contributed to equation (27) § 55 we have 
0/ = 2to- 1 SI)st 1 0. x (I iX ' . . (23). 
Hence, for a steady field, 
0/ = 2m -1 SCw' 1 0. x Q lX ' . . (24). 
0 = SVh y = 4 ttSV (YBK0 — 2CHSK0) . (17a). 
0 = [SOVb*], +i = 4:tt [SU v (YBK0 
- 2CHSK0)] a + j . . . (18 a). 
The following equations will be explained 
below :— 
G 
= — (2 A -f 9 tZA/ dO) 
(19a). 
n 
— 0 [A] a _ b ... . 
(20a). 
d 
! Y ) + (, w*-*= 0 • 
(21a). 
~ — 
s dp E, - - p (n /<9 
dO J 
r e 
h 
(22a). 
= II - 
~ H 0 + 1 [cr] «-i dO 
J 
1 
J 
83. Before discussing these equations in detail, it will be shown how in the theory 
of reversibility certain very important restrictions must be imposed on the generality 
of nr as a function of 9, "4-q and H, in order that known experimental facts shall not be 
contradicted. These restrictions seem, for the most part, to depend on the particular 
form of theory adopted in this paper; but as the particular features of the theory 
which are thus involved are held by many physicists, it is of interest to notice exactly 
what part of our fundamental assumptions causes the restrictions. The direct cause 
of the trouble is the equation B = 47t h V/. Now, it will be remembered (§16 above) 
that this equation flows from the assumptions (l) that l contains H and not B 
explicitly, and (2) that = YVH. If, then, it can be proved experimentally that 
the consequences of the restrictions developed below (the chief of which is that 
thermomagnetic phenomena involve dissipation of energy, and that a part of the 
thermoelectric phenomena do the same), are contrary to fact; one or both of these 
assumptions must be relinquished. Thus, perhaps, in this unexpected quarter, will be 
found a practical test of the truth of Maxwell’s fundamental assumption 47 tC = YVH. 
The consequences of relinquishing either of the above assumptions would probably be 
much the same, since it would lead to the physicist being compelled to recognise with 
