108 MESSRS. J. HOPKINSON AND HE. WILSON ON THE 
at the different radii for different epochs, and in each case, by drawing a curve fairly 
through them, we were able to produce areas in fair correspondence with areas as 
got by means of the given cyclic curve. The comparative areas are tabulated in 
Table IIT. 
In fig. 9 the maximum current in the copper coils due to the 54 cells is 
1°8 amperes, corresponding with a force of 20°7 in C.G.S. units. In this case the 
current had passed through zero and attained a maximum at 6 seconds after reversal; 
the change of induction being zero also at this time. We have worked out the 
current per sq. centim. for the different radii at different epochs, as before, and have 
plotted them in fig. 94. Fig 98 gives the relation of B to H, found from the curves, 
and it also shows a fair approximation to the cyclic curve for soft iron, although in 
this case the points are fewer in number and were more difficult to obtain, owing to 
the greater rapidity with which the D’Arsonval needle moved as compared with the 
earlier curves. 
With a reversal of 2°3 amperes the whole induction effects had died out at 
5 seconds after reversal. Coil No. 1 showed a maximum electromotive force at about 
34 seconds. Coil No. 2 gave a dwell, and attained a maximum at 2 seconds, and 
then died rapidly away. Coil No. 3 attained an immediate maximum and died 
rapidly to zero at 5 seconds. 
With a reversal of 65 amperes the whole inductive effects had died out at about 
3 seconds after reversal. No. 1 coil showed a maximum electromotive force at about 
1? seconds. No. 2 gave a dwell and attained a maximum at about 14 seconds and 
rapidly died away to zero at about 2 seconds. No. 3 attained an immediate maximum 
and died rapidly to zero at about 2 seconds. 
The variations in form of these curves and of the times the electromotive forces 
take to die away are intimately connected with the curve of magnetization of the 
material. When the magnetizing force is small (1°7) the maxima occur early because 
the ratio induction to magnetizing force is small. As the magnetizing force increases 
to 3 and 4°96 the maxima occur later because this ratio has increased, whilst when 
the force is further increased to 16 and 37:2, as shown in figs. 13 and 9, the maxima 
occur earlier because the ratio has again diminished. 
The results, both of these experiments and of those which follow, have a more 
general application than to bars of the particular size used. From the dimensions 
of the partial differential equation which expresses the propagation of induction in 
the bar, one sees at once that if the external magnetizing forces are the same in two 
bars differing in diameter, then similar magnetic events will occur in the two bars, 
but at times varying as the square of the diameters of the bars. But one may see 
this equally without referring to the differential equation. Suppose two bars, one 
n times the diameter of the other, in which there are equal variations of the 
magnetizing forces ; consider the annulus between radii 7), 7, and n7,, nr, in the two, 
the resistance per centimetre length of the rods of these annuli will be the same for 

