722 
MR. A. McAULAY ON THE MATHEMATICAL 
We collect here, partly for reference, partly to show more clearly the actual stage 
we have now reached, the other chief equations of the field. 
(f> = — 20.1 .(32). 
<E>/= .(33). 
477 H VZ = B = 
YVA, 
[VUvA] b + * = 
°1 
SVB = 
0 , 
[SU^B] a + l = 
47 t h Vx = b = 
VVa, 
[ Y UTa] re + i, = 
o] 
SVb = 
0 , 
[SUvb]„ + 6 = 
°i 
4 ttC = VVH, 
[VUj'H] u + 6 = 
cr 
SVC = 
0 , 
[SUvC ] 0 + t = 
o l 
SVD = 
0, 
[SUM)] a+i = 
0 
D = d q- 
k, C 
= c + Kl 
c = d, 
K = k 
, C = DJ 
(34) . 
(35) . 
(36) . 
(37). 
c' = i' + vv'Wdy, = sd'/a t + wvay - ,/sv'd' 
c' = d' + y v, VDp'i = aD'/a t + wtd>' 
(38). 
[The last set has not yet been proved, as it is more convenient to discuss it along 
with the detailed results, though clearly itself a general result.] Roughly speaking, 
of these equations [(25) to (38)], it may be said that (36) and (37) contain the 
assumptions of the present theory, and the rest the consequences of those assump¬ 
tions. 
Two remarks may be made here. It is clear that, since in the equations (25) to 
(38), y and Y occur only under the form y -f- Y, there is nothing by means of which 
we could experimentally distinguish them. Putting, then, 
y -f Y = v.(39), 
we shall generally in the future speak only of v. It may be conveniently called the 
potential, though, as we shall see later, this is not in accordance with Maxwell’s 
usage of the term ; and, what is perhaps of more importance, there is something 
arbitrary about it apart from the arbitrary additive constant which every potential 
involves. 
