TRANSACTIONS OF SECTION A. 737 
indifferently, all that is essential being that the total quantity of current be given 
at each instant, and be uniform throughout the whole length of the coiled con- 
ductor. 
8. This last condition is secured by perfectness of insulation between all con- 
tiguous turns of the coil, unless we were considering so enormously long a coil that. 
Fie. 1. 
the quantity of electricity required for the essential changes of static electrification 
would be sensible as constituting drafts from, or contributions to, the current in 
the coil. The consideration of static electrification, involved in the maintenance 
of alternate currents through acoil such as that represented in Fig. 1, is exceed- 
ingly curious and interesting ; but we do not enter on it at present at all, as in all 
practical cases the quantities concerned are quite infinitesimal in comparison with 
the whole quantity flowing in one direction or the other in the half period. 
4, In the drawing the section of the wires is represented as square; but this: 
is not essential, and in practice a flat rectangular ribbon would, no doubt, for some: 
dimensions of coils, be preferable. I assume the thickness of the insulation 
between the successive squares or rectangles in each layer to be infinitely small in 
comparison with the breadth of the rectangle ; but the thickness of the insulation 
between successive layers, which is a matter of indifference to my calculations, 
may be anything ; and would, in practice, naturally be, as shown in the diagram, 
considerably greater than the thickness of the insulation between the contiguous. 
portions of the coil in each layer. 
5. The full mathematical work which I hope to communicate to the ‘ Philo- 
sophical Magazine’ for publication in an early number includes an investigation of 
the self-induction of the coil with or without anything in its interior (such as core 
or primary wire of a transformer) ; but at present I merely give results, so far as: 
effective ohmic resistance, or generation of heat in the interior of the wire of the coil 
A A A A itself, is concerned, which, as said above, is independent of everything 
in the interior, and of the mode in which the alternating current is produced, 
provided only that the total amount of electricity crossing the section of the wire 
per unit of time be given at each instant. 
6. Asa preliminary to facilitate the expression of these results, it is convenient. 
first to give a general statement of the solution of the problem of laminar diffusion 
of a simple harmonic variation, applied to the case of electric currents in a homo- 
geneous conductor. Let the periodically varying magnetic force in the air or other 
insulating material in the neighbourhood of so small a portion, S, of the surface of 
a conductor that we may regard it as plane, be given. Resolve this magnetic 
