ON THE ATTRACTION OF AN INDEFINITELY THIN SHELL BOUNDED BY 

 TWO SIMILAR AND SIMILARLY SITUATED CONCENTRIC ELLIPSOIDS. 



WE shall find it convenient to consider the relations between two 

 systems of points. 



A system of points is said to be related to another system of points 

 when if x, y, z and x', y', z' be corresponding points, then 



X II T Z 



= a; - = b; - = c\ 



x, y, z, 



where a, l>, and c are constants. 



If a b c, the systems are similar. 



Volumes bounded by corresponding surfaces are in the ratio of cibc : 1 ; 

 for the ultimate corresponding elements are in this ratio, and therefore, 

 by Newton's fourth Lemma, the whole volumes are in the same ratio. 



The shells will be supposed to be contained between two similar and 

 similarly situated concentric surfaces ; the ratio of similitude between the 

 inner and outer surfaces being 1 : 1 + 1, where t is indefinitely small. 



We may without ambiguity designate any shell by the same symbols 

 which denote its inner bounding surface. 



If the principal sections of two ellipsoids be confocal the ellipsoids 

 themselves will be said to be confocal. 



A. 53 



