Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/392

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To find the attraction of a corpucle ituate in the axis of a round olid, to whoe everal points there tend equal centripetal forces decreaing in any ratio of the diŧances whatover.

Let the corpucle P (Pl. 24. Fig. 2.) ituate in the axis AB of the olid DECG, be attracted towards that olid. Let the olid be cut by any circle as RFS, perpendicular to the axis; and in its emi-diameter FS, in any plane PALKB paing through the axis. Let there be taken (by prop. 90.) the length FK proportional to the force with which the corpucle P is attracted towards that circle. Let the locus of the point K be the curve line LKI, meeting the planes of the outermot circles AL and BI in L and I; and the attraction of the corpucle P towards the olid will be as the area LABI. Q. E. I.

Hence if the olid be a cylinder decribed by the parallelogram ADEB (Pl. 24. Fig. 3.) revolved about the axis AB, and the centripetal forces tending to the everal points be reciprocally as the quares of the ditances from the points; the attraction of the corpucle P towards this cylinder will be as AB - PE + PD. For the ordinate FK (by cor. 1. prop. 90.) will be as