as affected by Induced Currents in an Iron Cylinder. 437 



these experiments have a wider application than to the cylinder 

 experimented upon, Consider two similar homogeneous cylinders 

 having the same magnetic properties and the same specific resistance, 

 and let the ratio of their dimensions be n. As the magnetism pene- 

 trates from the outside into the iron by a diffusion process, and a 

 kinematic coefficient of diffusion is of two dimensions in space and 

 one inversely in time, it follows that if the cylinders be each rotated 

 in a magnetic field of the same intensity, then to induce the same 

 electromotive force at similar points the speed of rotation must vary 

 inversely as ?t' 2 , and the induced currents will be similar in the two 

 cylinders. In (Table I is given the periodic time or frequency at 

 which similar electric and magnetic events will happen in similar 

 cylinders of different diameters. 



I. Madial Variation of Intensity of Magnetic Induction. Five different 

 periodic times have been dealt with, namely, 360, 180, 90, 45, and 

 22 -5 seconds. The collected results for 360, 90, and 45 seconds are 

 given in figs. 2, 4, 6 respectively, and have been taken from Table II 

 which contains the complete data. The curves show approximately 

 how the maximum intensity of induction varies at different depths of 

 the cylinder, and have been obtained by first plotting the maximum 

 average induction per sq. cm. for each coil 1, 2, 3 at its mean radius. 

 We notice at once how marked is the effect of variation of frequency 

 upon the distribution of induction. Moreover, for the smaller periodic 

 times we notice how much more marked are the effects for intermediate 

 values of the external magnetising force. 



The maximum intensity of induction at the surface of the cylinder 

 has been taken from curves, and in each case the corresponding value 

 at the centre has been expressed as a percentage of it. Fig. 7 gives 

 the results so obtained plotted in terms of the maximum intensity of 

 induction at the surface. The curves are numbered 360, 180, 90, 45, 

 22'5 to correspond with the periodic time in each case. AVe see that as 

 the frequency is increased the centre is more shielded ; moreover with 

 increase of frequency the range over which the interior of the cylinder 

 is shielded is increased. At 45 seconds periodic time the surface value 

 of the intensity of magnetic induction at which the effects of induced 

 currents begin to rapidly diminish is about 16,000. At 90 seconds it 

 is about 11,000, but the rate is slower. At 180 seconds the change 

 starts at about 7000 and is more gradual. At 360 seconds the dis- 

 turbing effects due to induced currents are probably small. The 

 distribution of intensity of induction when the cylinder is not rota- 

 ting is not known, and probably varies with the intensity of magnetic 

 force. The curves in fig. 2 may perhaps be trusted to give some indi- 

 cation of the distribution if the cylinder was not rotating. The dotted 

 curve in fig. 2, giving B 15,400 at the centre of the cylinder, probably 

 gives this value too low, owing to some unknown error. The curve is 



