PROFESSOR H. LAMB ON ELLIPSOIDAL CURRENT-SHEETS. 
159 
The most important type of induced currents is got by putting n = 2, s = 1 , in (95). 
In this case 
XI oc xz, 
so that the lines of force at the disk are normal to it, but the direction of the force is 
reversed as we cross the axis of y. The current-function relatively to axes displaced 
through the proper angle 17 varies as 
The current-lines for this case are shown in the figure. The signs + and — 
indicate where the normal force due to the field is towards or from the spectator. 
In the next type we have n = 3, s = 2 , so that 
XI OC z ( X 2 — if), 
and the current-function (relatively to displaced axes as before) varies as 
x y Vi 1 ~ <?)• 
* [It may be shown that, referred to the same axes, the potential varies as 
— p 0 x(l — 2r 2 /a 2 ). 
The equipotential lines are not orthogonal to the current-lines, except in the case of the circle r = aj v 2. 
—Note added June 30, 1887.] 
