By the ſame method one may determine the attraction of a corpuſcle ſituate within the ſphere, but more expeditiouſly by the following theorem.
Proposition LXXXII. Theorem XLI.
In a ſphere deſcribed about the centre S (Pl. 23. Fig. 4.) with the interval SA, if there be taken SI, SA, SP continually proportional; I ſay that the attraction of a corpuſcle that the attraction of a corpuſcle within the ſphere in any place I, is to its attraction without the ſphere in the place P, in a ratio compounded of the ſubduplicate ratio of IS, PS the diſtances from the centre, and the ſubduplicate ratio of the centripetal forces tending to the centre in the places P and I.
As if the centripetal forces of the particles of the ſphere be reciprocally as the diſtances of the corpuſcle attracted by them; the force with which the corpuſcle ſituate in I is attracted by the entire ſphere, will be to the force with which it is attracted in P, in a ratio compounded of the ſubduplicate ratio of the diſtance SI to the diſtance SP, and the ſubduplicate ratio of the centripetal force in the place I ariſing from any particle in the centre, to the centripetal force in the place P
