The Variation in Attraction Due to the Attracting Bodies. 213 



V. 



COMPARISON OF ATTRACTION AT POLE AND EQUATOR, AND ATTRACTION OP 

 CONFOCAL ELLIPSOIDS. 



First. On an oblate ellipsoid the attraction at the pole exceeds that at the 



equator by -^.(10^^ +280^^+ 560^^+ 4480^'+">) °^' ^^ 

 M/1. 6,,, 4,, 1,4 \ 



Second. On a prolate ellipsoid the atti'action at the equator exceeds that at 

 ., , , M / 1 _, 37^, 229^, \ , M/1, 3,_ \ 

 thepole 62/^(- E^ +^E^ + 1680^^ + ")^^ ''^A:\l''^n^''') 



Third. Confocal ellipsoids having foci at same pomts attract an outside 

 particle in line of poles or plane of the equators directly as their 

 masses. 



A-B 

 In the above enunciations h equals —r — or E" equals h (2 — h). 



16. The expression for the attraction at the pole of an oblate ellipsoid is 



— ^1— - E + ^ E*- ^ E « + etc. ^ By substituting. 

 B" \ 5 7 9 / ^ 



E' 

 ■z — ™ for E," and A" (1 — E-) for B'^, the exi:)ression beconaes, 

 1 — E 



(a) ^. (l+iE' + |4E'+|i,«E.+etc.) 

 A- \ 0.7 5.7.9 / 



The expression for the same oblate ellipsoid at the equator is: 



(b) ^ / 1 + Ly J! E'^ + --X -E^+ -— X- E« + etc. "^ 

 ^ A-^ V ^ 2 ^ 5 ^ 2.4^ 1 ^ 2.4.6 ^ 9 ^ / 



Subtract expression (b) from (a) and the difference is: 



M /1^„ , 19^, , 27^.. 163 „, \ 



— / _ E- -^ E^ A E** H E** + I 



A- VlO ^280 ^560 ^4480 ^" / 



By substituting as above for E'-, and for B-, the expression for the pro- 

 late elli^jsoid at the equator becomes: 



M / , 7 ^„ 157 ^, 263 „. „ \ 



The expression for Pole is: 



(d) ~ (l+^E-^ + fE^+^E«+etc. ) 



equals difference 



VrO^ + 280^ + 1680^ -+■ ) 



