The Variation in Attraction Due to the Attracting Bodies. 215 



VI. 



OUTSIDE ELIPSOIDAL ATTRACTION IN ANY DIRECTION. 



First. — An oblate ellipsoid and any outside partiele attract each other 

 directly as product of mass of particle into mass of ellipsoid 

 multiplied by [1-| n« E'^ (1— | sin^ 0)-fE^ (a'-f n^ + f sin'^ O 

 -I sm^O-4n2 siii^Q +3n2 sin40 + V/ ^* sin^O-ff n* sin"©) +„] 

 and inversely as square of distance from center of ellipsoid. 



Second — The sine of the angle made by the direction of the resultant at- 

 traction, and the direction from the particle to the center of the 

 ellipsoid equals | n' E'^ sinO cos O [l+E'^ (|-2 sin= 0-f n^ + ff 

 n'^sin-O) +„J. 



Third — The increase in attraction on an oblate ellipsoid from the equator 

 to the'j)oles true to the fourth power of eccentricilty varies as the 

 square of the sine of the elliptic angle. 



In the above enunciations, n equals B, divided by D (distance), and O 

 represents the elliptic angle used to find B,. 



18, To find an expression for the attraction on any outside particle, of 

 any two opposite infinitesimal wedges of an ellipsoid with the edges in 

 the diameter extending in direction to the particle. 



Diagram 7. 

 In diagram 7 let B, B, be the diameter of the ellipsoid extending in di- 

 rection to the outside particle (P), A A and B B being the priucipaJ axes of 

 the ellipsoid. This elliptic section rotated on axis B, B, through an in- 



