[ *3 ] 
91. and the fecond has been fupplied by feveral. 
authors. But Sir Ifaac, who feldom does any thing 
in vain, found, that he could, by one of his artifices, 
make that 91ft propofition ferve like wile to determine 
the attraction at the equator, by the following argu- 
ment : 
Let G be the attraction of the exterior fphere at A' y 
and let the decrement of that attraction, when the 
fphere is diminifhed into the oblate fpheroid ApBq, 
be d ; and S' the decrement of this laft attraction, 
when the oblate fpheroid is diminifhed into the pro- 
late, whofe poles ar t AB : then, I fay, d is nearly 
equal to S' 3 the difference of the axes of the gene- 
rating ellipfe being fmall. 
For the attractive matter, that is taken away, has, 
in both cafes, the fame ratio to the matter, that is 
left 3 and its pofition, with refpeCt to that which is 
left, is, in both cafes, nearly the fame : And there- 
fore the fuccefiive attractions will be nearly in con- 
tinued proportion, G : G — d : : G — d S Of 
multiplying and rejecting d z as inconfiderable, G d— 
G S', and d=S. 
Thus, if the attractions of the fphere APBQ^, and 
of the prolate fpheroid, at its pole A , be 126 and 
125 refpeCtively 3 the attraction 'of the intermediate 
oblate fpheroid at its equator will be 12 f{ : and how 
nearly this approaches to the truth, may be feen from 
an exaCt computation of thofe attractions. For, if the 
axes of the generating ellipfe be 101 and too, and the 
attractive force at the furface of the fphere 1263 the 
attraction at the pole of the prolate fpheroid will be 
124.98383 and that at the equator of the oblate 
I 2 c.f 077 ; which exceeds the arithmetical mean 
between 
