Proposition XCI. Problem XLV.
To find the attraction of a corpuſcle ſituate in the axis of a round ſolid, to whoſe ſeveral points there tend equal centripetal forces decreaſing in any ratio of the diſŧances whatſover.
Let the corpuſcle P (Pl. 24. Fig. 2.) ſituate in the axis AB of the ſolid DECG, be attracted towards that ſolid. Let the ſolid be cut by any circle as RFS, perpendicular to the axis; and in its ſemi-diameter FS, in any plane PALKB paſſing through the axis. Let there be taken (by prop. 90.) the length FK proportional to the force with which the corpuſcle P is attracted towards that circle. Let the locus of the point K be the curve line LKI, meeting the planes of the outermoſt circles AL and BI in L and I; and the attraction of the corpuſcle P towards the ſolid will be as the area LABI. Q. E. I.
Cor. 1 Hence if the ſolid be a cylinder deſcribed by the parallelogram ADEB (Pl. 24. Fig. 3.) revolved about the axis AB, and the centripetal forces tending to the ſeveral points be reciprocally as the ſquares of the diſtances from the points; the attraction of the corpuſcle P towards this cylinder will be as AB - PE + PD. For the ordinate FK (by cor. 1. prop. 90.) will be as
