Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/375

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By the ame method one may determine the attraction of a corpucle ituate within the phere, but more expeditiouly by the following theorem.

In a phere decribed about the centre S (Pl. 23. Fig. 4.) with the interval SA, if there be taken SI, SA, SP continually proportional; I ay that the attraction of a corpucle that the attraction of a corpucle within the phere in any place I, is to its attraction without the phere in the place P, in a ratio compounded of the ubduplicate ratio of IS, PS the ditances from the centre, and the ubduplicate 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 phere be reciprocally as the ditances of the corpucle attracted by them; the force with which the corpucle ituate in I is attracted by the entire phere, will be to the force with which it is attracted in P, in a ratio compounded of the ubduplicate ratio of the ditance SI to the ditance SP, and the ubduplicate ratio of the centripetal force in the place I ariing from any particle in the centre, to the centripetal force in the place P