Page:The Mathematical Principles of Natural Philosophy - 1729 - Volume 1.djvu/398

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If the more ditrant part of this olid be rejected, becaue its attraction compared with the attraction of the nearer part is inconiderable; the attraction of that nearer part will, as the ditance increaes, decreae nearly in the ratio of the power $$\scriptstyle CG^{n-3}$$

And hence if an finite body, plane on one ide, attract a corpucle ituate over-againt the middle of that plane, and the ditance between the corpucle and the plane compared with the dimensions of the attracting body be extremely mall; and the attracting body conit of homogeneous particles, whoe attractive forces decreae in the ratio of any power of the ditances greater than the quadruplicate; the attractive force of the whole body will decreae very nearly in the ratio of a power whoe ide is that very mall ditance, and the index les by 3 than the index of the former power. This aertion does not hold good however of a body coniting of particles whoe attractive forces decreae in the ratio of the triplicate power of the ditances; becaue in that caes the attraction of the remoter part of the infinite body in the econd corollary is always infinitely greater than the attraction of the nearer part.

If a body is attracted perpendicularly towards a given plane, and from the law of attraction given the motion of the body be required; the problem will be olved by eeking (by prop. 39.) the motion of the body decending in a right line towards that plane, and (by cor. 2. of the laws) compounding that motion with an uniform motion, performed in