PRODUCED BY ALTERNATING ELECTRIC CURRENTS. 
295 
Hence B/C is a function of b, c only. 
Also it was proved that 
Therefore 
_C_ 
AB da \AC/ 
function of a (or constant). 
11 
A 3 a 
function of a (or constant). 
This, as well as the last condition (iii.), is satisfied by A = function of a. 
Geometrically this means that the normal distance between a and a -f- 8ci is every¬ 
where the same, i. e ., that the a surfaces are parallel. 
Now the radius of curvature p a b of the normal section of a constant along the 
normal to b is given by 
1_ _ JL_3B 
pal, AB da ’ 
and so too 
1_ _i_ dC 
p ac AC da 
Hence, if B/C is independent of a, 
Pab — Pac ) 
i.e., the two curvatures at each point of an a surface are equal. 
Thus, the property in question is satisfied by a sphere, and only by a sphere or 
spherical shell, including, as a special case, a plane slab infinite in both directions. 
The Mechanical Effect of Currents set up in a Thin Circular Cylindric Shell of 
Infinite Length. 
3. We consider the case of a periodic field consisting of currents parallel to the 
axis of the shell. 
In this case the surface condition informs us that since there is no normal com¬ 
ponent of electromagnetic momentum, there will be no electrostatic potential; also, 
if the axis of the cylinder be taken as the axis of cylindric coordinates, we have 
<™=-|(H + H 0 ).(iv.), 
where H 0 is the momentum due to the external field and H that due to the induced 
currents, while <r and w represent the resistance and current across unit length of the 
surface. 
