, is that by which a moving body is perpetually urged towards a centre, and made to revolve in a curve, instead of a right line.

Hence, when a body revolves in a circle, these two forces, viz, the centrifugal and centripetal, are equal and contrary to each other, since neither of them gains upon the other, the body being in a manner equally balanced by them. But when, in revolving, the body recedes sarther from the centre, then the centrifugal exceeds the centripetal force; as in a body revolving from the lower to the higher apsis, in an ellipse, and respecting the focus as the centre. And when the revolving body approaches nearer to the centre, the centrifugal is less than the centripetal force; as while the body moves from the farther to the nearer extremity of the transverse axis of the ellipse: the two forces being equal to each other only at the very extremities of that axis.

It is one of the established laws of nature, that all motion is of itself rectilinear, and that the moving body never recedes from its first right line, till some new impulse be superadded in a different direction: after that new impulse the motion becomes compounded, but it is still rectilinear, though not in the same line or direction as before. To move in a curve, it must receive a new impulse in a different direction every moment; a curve not being reducible to any number of finite right lines. If then a body, continually drawn towards a centre, be projected in a line that does not pass through that centre, it will describe a curve; in each point of which, as A, it will endeavour to recede from the curve, and proceed in the tangent AD; and if nothing hindered, it would actually proceed in it; so as in the same time, in which it describes the arch AE, it would recede the length of the line DE, perpendicular to AD, by its centrifugal force: Or being projected in the direction AD, but being continually drawn out of its direction into a curve by a centripetal | force, so as to fall below the line of direction by the perpendicular space DE: Then the centrifugal or centripetal force is as this line of deviation DE; supposing the arch AE indefinitely small.

The doctrine of centrifugal forces was first mentioned by Huygens, at the end of his Horologium Oscillatorium, published in 1673, and demonstrated in the volume of his Posthumous Works, as also by Guido Grando; where he has given a few easy cases in bodies revolving in the circumference of circles. But Newton, in his Principia, was the first who fully handled this doctrine; at least as far as regards the conic sections. After him there have been several other writers upon this subject; as Leibnitz, Varignon in the Mem. de l'Acad. Keil in the Philos. Trans. and in his Physics, Bernoulli, Herman, Cotes in his Harmonia Mensurarum, Maclaurin in his Geometrica Organica, and in his Fluxions, and Euler in his book de Motu, where he considers the curves described by a body acted on by centripetal forces tending to several fixed points.

See also the art. Central Forces, where this doctrine is more fully explained.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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