736 
MR. A. McAULAY ON THE MATHEMATICAL 
PQ. Hence, if at pq p is small enough to be neglected in the above expression, 
the whole current which on the present theory would be flowing through the strip 
VQqp is the same as the current due to surface charge, which on the convection 
current theory would be flowing in the same direction across the element PQ. The 
extension to the case when slipping is allowed and the dielectric is at rest is obvious. 
With regard to the plausibility of this explanation, it must be remembered that in 
this paper we admittedly do not take account of the independent motion in the very 
same space of two mediums such as air and ether. Now, probably,* the ether is at 
rest relative to the conductor, and it is reasonable to suppose that the relative motion 
of the conductor and the ether is of more importance in connection with the part 
W'V dp' of c' than the relative motion of the air and the conductor. On the other 
hand, as the air carries about with it any charge it possesses, it is the motion of the 
air we must consider in interpreting the term — p'SV'd'. Indeed, if we suppose the 
ether only to bound the conductor and the molecules of air, and that the ether is 
mainly at rest (i.e., acts to the conductor and the molecules of air much as an ocean 
of perfect fluid, which could slide over surfaces, and was originally at rest, would act 
to the conductor and molecules supposed immersed in it) the explanation is complete. 
[I do not wish to imply that I endorse this theory of the relative behaviour of the 
ether and matter]. 
On the whole, I think it may be said that this test of the correctness of eq. (23) is 
fairly well met. 
65. Before comparing eq. (12) with the corresponding results of the present theory, 
it is necessary to make one or two remarks on passages from Maxwell’s ‘ Electricity 
and Magnetism.’ In the quotations I am about to make I have in every case changed 
Maxwell’s notation to the notation used above, as leading to a clearer comparison of 
results. Consistently with this, I have always substituted Quaternion language for 
the corresponding Cartesian. 
In the first placet I wish to discuss Maxwell’s views concerning the scalar he calls 
■'b, and which has been above denoted by z [equations (6) (12) (22)]. In his second 
volume he seems to intend the symbol always to have the same meaning. The first 
place in which it occurs in this volume is in § 598, where he is investigating the 
expression for E' 0 . After proving that 
E' 0 = Vp B' - dA'/dt - Vz, 
he proceeds : “ The terms involving the new quantity 2 are introduced for the sake of 
giving generality to the expression for E' 0 . They disappear from the integral when 
* According to a report in ‘ Nature,’ September, 1891, p. 454, Professor Lodge described to the 
British Association experiments which go to prove this. I have not yet seen details of the experiments. 
t Before going further, attention may be recalled to the footnote of § 38 abova 
