The Variation in Attraction Due to the Attracting Bodies. 22& 



VII. 



The gravity and the Fi/,iire of a body, due to its Rotation and the attrac- 

 tion of its Component Particles. 



First. — The oblate ellipsoid is the figure of ecpiilibriuvi due to tlie rotation 

 and attraction of the component particles of a fluid body. 



Second. — The increase in gravity from the equator tothe poles uariesas the 

 square of the sine of the elliptic angle, or the angle with vertex at 

 center of figure, and not as the square of the sine of latitude. 



24. To find the combined effect of attraction and rotation on any par- 

 ticle in the plane of the equator of an oblate ellipsoid. 



Case 1st. When the velocity of rotation is just sufficient to counter- 

 balance the attraction of the ellipsoid on the particle. 



/ Diagram 10. 



In Dia. 10 let a be the particle and let arc a b be the distance of ro- 

 tation fur an infinitesimal unite of time (t) or velocity of rotation. Let a f 

 the versed sine of arc a b in direction A C represent the unite of attraction, 

 also let f a in direction C A represent the repulsive effect of rotation. As 

 attraction just couuter-balances repulsion the particle must revolve in the 

 circumference of a circle of radius a C. As attraction and repulsion act 

 at a right angle to an infinitesimal portion of the circumference these 

 forces can neither increase or diminish the velocity (v) of rotation. 



Let af, ag, ah, etc., to aC represent the attraction of the ellipsoid for 

 one. two, three, etc., units of time acting on a particle with a constant 

 force equal to the attraction of the ellipsoid at distance a C. On the cir- 

 cumference lay off arcs ab, be. c d, etc., to s, each equal to ab; and con- 



