The London, Edinburgh and Dublin philosophical magazine and journal of science . and for inside points themagnetized line PP having its positive poles at P and ofmagnetic moment Me* /aa2/h2, b being now taken = OB. 7. If a line of poles of strength m suddenly changes positionfrom A to A the effect is equivalent to the superposition of— m at A and^H- m at A, and is thus equivalent to thegeneration of a line of magnets in the direction AA, theimages of which have just been found. Fig. 3 shows the application of this method to constructthe trails of images of a line of poles revolving uniformlyab
The London, Edinburgh and Dublin philosophical magazine and journal of science . and for inside points themagnetized line PP having its positive poles at P and ofmagnetic moment Me* /aa2/h2, b being now taken = OB. 7. If a line of poles of strength m suddenly changes positionfrom A to A the effect is equivalent to the superposition of— m at A and^H- m at A, and is thus equivalent to thegeneration of a line of magnets in the direction AA, theimages of which have just been found. Fig. 3 shows the application of this method to constructthe trails of images of a line of poles revolving uniformlyabout the centre and passing in succession through thepositions Ax, A2, A3, A4, ..., at equal small intervals of time,the actual trails are of course the limits of the series of movingpoles thus plotted out. By supposing the line of poles toremain fixed and the cylinder to rotate, we get a kind of Plane, Cylindrical, and Spherical Current-Sheets. 389 cylindrical two-dimensional Aragos disk, and it is to benoticed that the trails of images lie along equiangular spirals Fiz. (as may readily be verified), the intensity of magnetizationof the trail decreasing toward the centre and increasingoutward and being, in fact, proportional to the distance fromthe centre. Part III. Spherical Sheets. Image due to Generation of a Small Magnet whose Axis isRadial outside a Spherical Sheet. 8. We now consider the problem presented by the currentsinduced in a spherical sheet of radius a when a magnet isgenerated at a distance b from the centre, the axis of themagnet passing through the centre of the sphere. Takingthis axis as the axis of zonal spherical harmonics, and startingin the first instance with a magnet of variable moment f(t),(the positive pole being furthest from the centre), the magneticpotential O0 at a point (r, 6) is given by n° =f{£) db sj(r2 + b2- 2rb cos 6) When r 1bn+2 P • (9) 390 Dr. G. H. Bryan on Electromagnetic Induction inand when r>b we have in like manner ^C?Jp
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