164 Proceedings of Royal Society of Edinburgh. [sess. 
vertical ordinates reduced to 1/10, or curve number 10 with its 
vertical ordinates reduced to 1/100. Now by number 1 curve we 
see that at 1/2 centimetre from the initiational surface (supposed 
plane) the amount of the falling off is 16 per cent, of the whole. 
Hence in our iron or steel rod (on the supposition A = 0) the 
current at 1/4300 of a second from the beginning, and at 1/20 of a 
centimetre from the surface, would have fallen off by 16 per cent, 
of its given amount. Thus we judge that during the first 1/4000 of 
a second the effect of the cylindric curvature is but slight, and the 
diffusion follows sensibly the law of plane laminar diffusion. 
The supposition of a circular cylindric sheath of infinite electric 
conductivity, coaxal with the rod considered, and separated from it 
by the insulating material, which we have adopted for the sake of 
simplicity and definiteness, may be departed from, and instead we 
may substitute any conductor parallel to the rod considered, pro- 
vided that the distance between the two is a considerable multiple 
of the greatest diameter of either. In virtue of this proviso, the 
distribution of current-density is necessarily but very little disturbed 
from the equality at equal distances from the axis of the rod, which 
was provided for by the supposition of a cylindric sheath. If the 
second conductor is of the same diameter and of the same material 
as the first, and placed at a distance 2 a from it, the expression for A 
will be the same as that given above. 
Now, instead of the great simplicity of a current, generated (no 
matter how), and given initially as a steady current, through the 
circuit of two long parallel conductors and the end-bridges between 
them ; suppose the conductors and one end-bridge to be given with 
no current, and let a voltaic battery be suddenly applied instead of 
the other end-bridge. If the difference of potentials maintained by 
the latter between the ends to which it is applied be absolutely 
constant, the rise of the current through the parallel conductors 
from its initial zero to its ultimate steady amount will follow nearly 
the same law as the fall from the initial steady current to the final 
zero in our former simple case : exactly the same law if the quantity 
of positive electricity on one conductor, and of negative electricity 
on the other, called forth according to electro-static law, in virtue of 
the gradient of potential, is nothing in comparison with the quantity 
flowing through the circuit. The quantity of electricity required 
