214 Proceedings of Boy al Society of Edinhurgh. [sess. 
From any vector satisfying these equations let us derive (by means 
of the operators dfdt and a V , which are the only ones occurring 
in the equation of motion) the concomitants 
€ = ^, ix= — aV 6 j 
or e = ^, fJi=-aV6, &c., (kc. 
and we have between them Clerk-Maxwell’s equations 
€ = aV fjL, /4=— aVc, 
with the conditions 
SVe = 0, SV/x = 0. 
The extension to dielectrics, whether they he isotropic or not, is 
obtained at once : — and it secures (in the latter case) all the sim- 
plicity which Hamilton’s linear and vector function affords. Thus 
the properties of double refraction, wave-surfaces, &c., follow almost 
intuitively. 
When we come to conducting bodies, we have to introduce 
further conditions. But I do not enter on these at present, as the 
problem is essentially altered in character. FTor do I, for the 
moment, discuss the bearing of the above notions upon the profound 
question of the possible nature of electricity and of magnetism. 
There is a sort of analogy to the above, in the case of sound. 
For it is not the (vector) disturbance of the air which affects the 
sense of hearing, hut the (scalar) concomitant change, or rate of 
change, of density. 
Thus, possibly, the widely different results obtained by observers 
of the alteration of plane of polarisation in diffracted light, may all 
really he in accordance with Stokes’ splendid investigation : — if we 
look upon light as an effect produced by the concomitants of the 
ether disturbance, and not directly by the ether disturbance itself. 
