Now by what has been said, it's certain that the Rays which differ in Refrangibility do not converge to the same Focus; but if they flow from a lucid Point, as far from the Lens on one side as their Foci are on the other, the Focus of the most refrangible Rays shall be nearer to the Lens than that of the least refrangible, by above the fourteenth Part of the whole distance; and if they flow from a lucid Point, so very remote from the Lens, that before their Incidence they may be accounted parallel, the Focus of the most refrangible Rays shall be nearer to the Lens than the Focus of the least refrangible, by about the 27th or 28th Part of their whole distance from it. And the Diameter of the Circle in the middle Space between those two Foci which they illuminate, when they fall there on any Plane, perpendicular to the Axis (which Circle is the least into which they can all be gathered) is about the 55th Part of the Diameter of the Aperture of the Glass. So that 'tis a wonder, that Telescopes represent Objects so distinct as they do. But were all the Rays of Light equally refrangible, the Error arising only from the Sphericalness of the Figures of Glasses would be many hundred times less. For, if the Object-glass of a Telescope be Plano-convex, and the Plane side be turned towards the Object, and the Diameter of the Sphere, whereof this Glass is a Segment, be called D, and the Semi-diameter of the Aperture of the Glass be called S, and the Sine of Incidence out of Glass into Air, be to the Sine of Refraction as I to R; the Rays which come parallel to the Axis of the Glass, shall in the Place where the Image of the Object is most distinctly made, be scattered all over a little Circle, whose Diameter is _(Rq/Iq) x (S cub./D quad.)_ very nearly,[H] as I gather by computing the Errors of the Rays by the Method of infinite Series, and rejecting the Terms, whose Quantities are inconsiderable. As for instance, if the Sine of Incidence I, be to the Sine of Refraction R, as 20 to 31, and if D the Diameter of the Sphere, to which the Convex-side of the Glass is ground, be 100 Feet or 1200 Inches, and S the Semi-diameter of the Aperture be two Inches, the Diameter of the little Circle, (that is (_Rq x S cub.)/(Iq x D quad._)) will be (31 x 31 x 8)/(20 x 20 x 1200 x 1200) (or 961/72000000) Parts of an Inch. But the Diameter of the little Circle, through which these Rays are scattered by unequal Refrangibility, will be about the 55th Part of the Aperture of the Object-glass, which here is four Inches. And therefore, the Error arising from the Spherical Figure of the Glass, is to the Error arising from the different Refrangibility of the Rays, as 961/72000000 to 4/55, that is as 1 to 5449; and therefore being in comparison so very little, deserves not to be considered. [Illustration: FIG. 27.]