ATTRACTION'. OBLATE SPHEROID. J7!l 



. V ; and suppose P in the preceding figure to be 

 where the axis of the enveloping cone 



plane of contact of the cone and the ellipsoidal shell. Draw 

 trjutfht line* .\MM'.\" and nmm'n as in the preceding 



figure. Lot p a. mass of the element J/ ai 



the mass of the element .1.' 



n of /* is equal to *J- f and it acts along ' 

 the attraction of p is equal to -fiTf* an ^ li acts a ^ on g C-^'- 



N"*v .A., - 



wn that QM and QM 1 make equal angle* with 

 (see Conic Section*, Chap, xv., last example) ; therefore 



Q 



PM PIT 



Thus tin- ert ^yu/i/ attraction* on Q; and 



us !' ( iii' Attractions make equal angles 

 with v/', tin- r..<>t r t.int attractioo t* these two elements acts 

 \ similar n-sult holds for erery pair oi' 



ellipsoidal shell maj be decomposed ; and thin 

 the proposition follows. It appears from the course < 

 demonstr t any plane through P divides the shell into 



two parts which exercise equal attractions on Q. 



>llows from this result, by proceeding 'rnit, that 



sultant attraction of tl. thin shell on a 



particle in contact with the external surface 



normal to the surface at the point of contact 

 We shall now give in the next two Articles some proposi- 

 rve as exercises; the approximate results 

 ;i wo shall obtain may be subsequent d by an 



exact investigation. (See Art 2*26.) 



>jlnd the attraction of a komogtncou* oblat* iphfroid 

 of small eccentricity on a particle at its pole. 



Let 2c be the length of the minor axis and 2a that of the 

 major axis of the generating ellipse. The spheroid may be 



