380 [470 
470. 
NOTE ON THE ATTRACTION OF ELLIPSOIDS. 
[From the Monthly Notices of the Royal Astronomical Society, vol. xxix. (1868—1869), 
pp. 254—257.] 
If an indefinitely thin shell of uniform density, bounded by two similar and 
similarly-situated ellipsoids, attracts a point P on its outer surface, it has been shown 
geometrically by M. Chasles that the attraction is in the direction of the normal at 
P, and is equal to twice the attraction of an infinite plate, the thickness of which is 
equal to the normal thickness at P. Assuming that the attraction is in the direction 
of the normal, the proof is in fact as follows:—with P as vertex, circumscribe to the 
interior surface a cone; this divides the shell into three parts; the one, D + F + F, 
exterior to the cone, the other two, A + B and G, interior to the cone. It is shown 
that in the direction of the normal the attraction of G is equal to that of A +B; 
and it is assumed that in comparison with these the attraction of D + E + F may be 
neglected; the whole attraction is thus equal to twice that of the portion A + B. At 
the point where the normal at P meets the internal surface draw the tangent plane 
to the internal surface, thus dividing the portion A + B into the solid cone A and