The Variation in Attraction Due to the Attracting Bodies. 343 



The numbers in column 6, divided by 55745 are the masses of the homo- 

 geneous ellipsoids, having radi, 31, 30, 28, etc., composing also the ellipsoid, 

 and these n-jmbersare found by multiplying the cubes of the nu.ubers of 

 column first by those of column third, excepting the first number, vp-hicli 

 is 31 cubed The numbars in column 7 are explained in connection with 

 table 4. 



The formulae already developed for the attraction of a heterogeneous 

 oblate ellipsoid at the pole less that at the equator, is: 



Diff. of Att. = ^^ ( m + m, + m., -f etc )- A. 



A--' ~ 2A^ 



+ iLo n - h, 4- etc ) 



(m H + m, n- h 



For the purpose of this computation ^, and m + m, + nio + etc., or M, 

 can each be made unity, and the formula? put in form as foUovrs: 



Diff Att, = 2H 



mH 



m n^ h — ? m., n ,'- li 



etc. 



The numbers in column 8 are the computed results of — t m H, — f m ^ 

 n- h — etc 



TABLE II. 



4-. 



.11867 



.1261 



.1326 



.1378 



.1415 



. 1435 



.1436 



.1418 



.1379 



.1322 



.1248 



.1160 



.1060 



.0953 



.0842 



.0730 



.0622 



.0519 



.0423 



.0338 



.0-262 



.0197 



1.0000 

 1.1187 

 1.2448 

 1.3774 

 1.5152 

 1.6567 

 1.8002 

 1.9438 

 2.0856 

 2.2235 

 2.3557 

 2.4805 

 2.5965 

 2.7025 

 2.7978 

 2.8820 

 2.9550 

 3.0172 

 3.0691 

 3.1114 

 3.14.52 

 3.1714 

 3.1911 





2791 

 2921 

 3033 

 3125 

 3192 

 3232 

 3242 

 3220 

 3I6S 

 3084 

 2970 

 2830 

 2666 

 2483 

 2285 

 2077 

 1864 

 1650 

 1439 

 1235 

 1041 

 859 

 692 





29791 



3202 



3075 



2910 



2712 



2487 



2242 



1985 



1725 



1468 



1224 



998 



795 



618 



468 



344 



246 



170 



114 



73 



51 



26 



14 



..ft 



aif 



1 

 1 _ 



3^5.8 



■S7ff 

 1 



8. 



.0032143 



3190 



2827 



2464 



2113 



1779 



1469 



1190 



942 



729 



551 



406 



290 



202 



136 



88 



55 



33 



19 



10 



6 



3 



