752 
MR. A. McAULAY ON THE MATHEMATICAL 
results. On the theory of this paper the most striking would seem to be that, while 
thermoelectric effects must in the main be explained on the theory of reversibility, 
the explanation of the thermomagnetic effects by this theory is inadmissible by reason 
of certain collateral consequences. 
81. Let c«T—which has no connection with the or of § 54 above—be a linear vector 
function of a vector, itself a function of 6. \E r , and H ; and let 
— [0] + M + [ 2 ] = 2 [n] .(1), 
where [n] is a homogeneous function of degree n in the vector H. 
In particular, let — be given by 
WO = Aco + BYcoH - a>SUCH.(2), 
where A, B, 0 are linear vector functions of a vector, themselves functions of T' and 0 
only. B and C, but not A, may for simplicity be assumed self-conjugate. Notice 
that SH h V. \n\ = — n [«], and therefore 
(1 + SH h V.) rrr = 2 (l — n) [«] = A + SHCH.(3). 
Similarly, 
(SK k V. + SH h V. + S© e V.) SKsr© = - SK (2 [0] + 3 [1] + 4 [2]) © . (4), 
ct and A will be assumed to be of a class given by 
Sttwctc/s = St zs'cr'ds = Stts" a"d<s 
= X~ l ^X’ — \p~ l 
and, of course, exactly similarly for A. It should be noticed that unlike the two 
classes of § 9 above, vr and A have not the property that if trr or A is self-conjugate, 
so also is zo' or A' and ur" or A". But they have another simple property, namely, 
that if tjt is a scalar, 
It may also be noticed that zocr is an intensity, and zs c t a flux where or c stands for 
the conjugate of ct. 
B is assumed to be of Class II. of § 9 above, and C of a class given by 
Scr„Co 7 , = Sov/CV/ = S(T,/ / C"o- 6 " ] 
C' = x cy, c" = xfiCxfi J. (7) ' 
so that it is very closely allied to Class I. of § 9 above. 
