"In Roger Bacon's works we find a tolerably distinct explanation of the effect of a convex glass; and in the work of Vitellio... the effect of refraction at the two surfaces of a glass globe is clearly traced. ...Vitellio had obtained experimentally a number of measures of the refraction out of air into water and into glass. Out of these facts no rule had yet been collected, when, in 1604 Kepler published his "Supplement to Vitellio." ...Kepler attempted to reduce to law the astronomical observations of Tycho,—devising an almost endless variety of possible formulæ, tracing their consequences with undaunted industry, and relating with a vivacious garrulity, his disappointments and his hopes,— ...he proceeded in the same manner with regard to Vitellio's Tables of Observed Refractions. He tried a variety of constructions by triangles, conic sections, &c., without being able to satisfy himself, and he at last is obliged to content himself with an approximate rule, which makes the refraction partly proportional to the angle of incidence, and partly to the secant of that angle. In this way he satisfies the observed refractions within a difference of less than half a degree each way. When we consider how simple the law of refraction is, (that the ratio of the sines of the angles of incidence and refraction is constant for the same medium,) it appears strange that a person attempting to discover it, and drawing triangles for the purpose, should fail; but this lot of missing what afterwards seems to have been obvious, is a common one in the pursuit of truth."