The Vayicit'io}i in Attraction Due to the Attracting Bodies. 237 



prehension than at his surface. Let those believing soUditication com- 

 menced at the center keep these facts in mind while reading tliis chapter. 



27. To find the decrease in attraction on a rotating fluid oblate ellipsoid 

 from the poles to the equator. 



Conception 1st. Such an oblate Ellipsoid can be conceived made up of 

 an infiniie number of oblate Ellipsoids having a common center, and each 

 component Ellipsoid of homogeneous density. 



Conception 2d. The same oblate Ellipsoid can be conceived made up 

 also ia shells or layers with each shell or layer of homogeneous density. 

 The surface of the layers in this case would be at the surface of the com- 

 ponent Ellip-oids of conception iirst. 



The attraction of each component ellipsoid can be computed by formu- 

 lae already developad for homogeaeoas ellipsoids, and the attraction for 

 the heterogeneous mass is equal to the sum of the attractions of the com- 

 ponent parts. 



The attraction of first or largest component ellipsoid at pole is; 



L 5(1— E-)" J A- " " 



B- L 5 (1— E-) 



The attraction at equator of same is: 



^ (1 + A E'^ +„ ) 



Decrease from pole to equator is : 



-5^ (J, E-' +, =^ (i- H-f-J 

 A' A- 



The attraction at the pole of first ellipsoid for the second component 

 ellipsoid is: 



m, r-, _ 3b- E- r " 1_ m r 1 

 B^" L 5B2(1— E^y J A- Ll— E- 



3 a'^ E- 1 m. 



5B2(1— E--^) J A- Ll— E- 5 A^ (1 — E=)- J A- 



in which k-:= 



a 



Fl + E-^4-,, — -^ n- E-+„ Ti 

 The atti'action at equator for same is: 



Decrease is: 



Results are thus obtained for all the component ellipsoids. 

 • The decrease in attraction from pole to equator of the heterogeneous 

 oblate ellipsoid or sum of results for component ellipsoid is: 



2H 9 



— . (m + m -[- m., -j- m.j + etc.) — (m H -f m, u- h -\- m., n '^ 



A- . - . 5 A- 



h -f- m^ ng- h.> -|- etc.). 



