803.] We have to remark in the first place, that in this problem the thermal conductivity of Fourier's medium is to be taken inversely proportional to the electric conductivity of our medium, so that the time required in order to reach an assigned stage in the process of diffusion is greater the higher the electric conductivity. This statement will not appear paradoxical if we remember the result of Art. 655, that a medium of infinite conductivity forms a complete barrier to the process of diffusion of magnetic force.
In the next place, the time requisite for the production of an assigned stage in the process of diffusion is proportional to the square of the linear dimensions of the system.
There is no determinate velocity which can be defined as the velocity of diffusion. If we attempt to measure this velocity by ascertaining the time requisite for the production of a given amount of disturbance at a given distance from the origin of disturbance, we find that the smaller the selected value of the disturbance the greater the velocity will appear to be, for however great the distance, and however small the time, the value of the disturbance will differ mathematically from zero.
This peculiarity of diffusion distinguishes it from wave-propagation, which takes place with a definite velocity. No disturbance takes place at a given point till the wave reaches that point, and when the wave has passed, the disturbance ceases for ever.
804.] Let us now investigate the process which takes place when an electric current begins and continues to flow through a linear circuit, the medium surrounding the circuit being of finite electric conductivity. (Compare with Art. 660).
When the current begins, its first effect is to produce a current of induction in the parts of the medium close to the wire. The direction of this current is opposite to that of the original current, and in the first instant its total quantity is equal to that of the original current, so that the electromagnetic effect on more distant parts of the medium is initially zero, and only rises to its final value as the induction-current dies away on account of the electric resistance of the medium.
But as the induction-current close to the wire dies away, a new induction-current is generated in the medium beyond, so that the space occupied by the induction-current is continually becoming wider, while its intensity is continually diminishing.
This diffusion and decay of the induction-current is a phenomenon precisely analogous to the diffusion of heat from a part of
