2 n - r = 2 n - m / 2 m - 2 n r = f , wherefore a Sphere of Glass collects the Sun-Beams at half the Semi-diameter of the Sphere without it, and a Sphere of Water at a whole Semi-diameter. But if the Ratio of Refraction m to n be as 2 to 1, the Focus falls on the opposite Surface of the Sphere; but if it be of greater Inequality it falls within.
Another Example shall be when a Hemisphere is exposed to parallel Rays, that is, d and ρ being infinite, and t = r , and after due Reduction the Theorem results nn / mm