213 
Communications made to the Society: 
On the Attraction of an infinitely thin Shell bounded by 
two similar and similarly situated concentric ellip- 
soids on an external point. By Professor ADAMS. 
No problem has more engaged the attention of mathematicians, 
or has received a greater variety of elegant solutions, than that 
of the determination of the attraction of a homogeneous ellips- 
oid on an external point. 
Poisson’s solution, which was presented to the Academy of 
Sciences in 1833, is founded on the decomposition of the ellip- 
soid into infinitely thin shells bounded by similar surfaces. By 
a theorem of Newton’s, it is known that such a shell exerts no 
attraction on an internal point, and Poisson proves that its 
attraction on an external point is in the direction of the axis of 
the cone which envelopes the shell and has the attracted point 
for vertex, and that the intensity of the force can be expressed 
in a finite form, as a function of the co-ordinates of the attracted 
point. 
In 1834, Steiner gave, in the 12th volume of Crelle’s Jour- 
nal, a very elegant geometrical proof of Poisson’s theorem re- 
specting the direction of the attraction of a shell on an external 
point. He shows that if the shell be supposed to be divided 
into pairs of opposite elements with respect to the point in 
which the axis of the enveloping cone meets the plane of con- 
tact, then the resultant of the attraction of each pair of such 
elements acts in the direction of the axis of the cone, and con- 
sequently the attraction of the whole shell acts in the same 
direction. 
About three years later, M. Chasles showed that Poisson’s 
solution might be greatly simplified by the consideration that 
the axis of the enveloping cone is identical with the normal to 
the ellipsoid which passes through the attracted point and is 
confocal with the exterior surface of the shell. 
