SEC. XIV.J OF NATURAL PHILOSOPHY. 2M mm — mn m — 2n .... mm — mn m — 2n A — 7, — , or, which is the same thinor, as L> m . nn nn As if the ordinate describe a parabola, m being — 2, and n = 1, the force will be as the given quantity 2B°, and therefore is given. Therefore with a given force the body will move in a parabola, as Galileo has demon strated. If the ordinate describe an hyperbola, m being = 0 — 1, and n — 1, the force will be as 2 A 3 or 2B 3 ; and therefore a force which is as the cube of the ordinate will cause the body to move in an hyperbola. But leaving this kind of propositions, I shall go on to some others relating to motion which I have fiot yet touched upon. SECTION XIV. Of the motion of very small bodies when agitated by centripetal forces tending to the several parts of any very great body. PROPOSITION XCIV. THEOREM XLVIII. If two similar mediums be separated from each other by a space termi nated on both sides by parallel planes, and a body in its passage through that space be attracted or impelled perpendicularly towards either of those mediums, and not agitated or hindered by any other force ; and the attraction be every where the same at equal distances from either plane, taken towards the same hand of the plane ; I say, that the sine of incidence upon either plane will be to the sine of emcr gence from the other plane in a given ratio. CASE 1. Let Aa and B6 be two parallel planes, and let the body light upon the first plane Aa in the direction of the line GH, and in its whole passage through the intermediate space let it be attracted or impelled towards the medium of in cidence, and by that action let it be made to de scribe a curve line HI, and let it emerge in the di rection of the line IK. Let there be erected IM perpendicular to Eb the plane of emergence, and meeting the line of incidence GH prolonged in M, and the plane of inci dence Aa in R ; and let the line of emergence KI be produced and meet HM in L. About the centre L, with the interval LI, let a circle be de scribed cutting both HM in P and Q, and MI produced in N ; and, first, if the attraction or impulse be supposed uniform, the curve HI (by what Galileo has demonstrated) be a parabola, whose property is that of a roc