"I tried another way of measuring the refraction, which should include the density of the medium and the incidence: for, since a denser medium is the cause of refraction, it seems to be the same thing as if we were to prolong the depth of the medium in which the rays are refracted into as much space as would be filled by the denser medium under the force of the rarer one. "Let A be the place of the light, BC the surface of the denser medium, DE its bottom. Let AB, AG, AF be rays falling obliquely, which would arrive at D, I, H, if the medium were uniform. But because it is denser, suppose the bottom to be depressed to KL, determined by this that there is as much of the denser matter contained in the space DC as of the rarer in LC: and thus, on the sinking of the whole bottom DE, the points D, I, H, E will descend vertically to L, M, N, K. Join the points BL, GM, FN, cutting DE in O, P, Q; the refracted rays will be ABO, AGP, AFQ."—"This method is refuted by experiment; it gives the refractions near the perpendicular AC too great in respect of those near the horizon. Whoever has leisure may verify this, either by calculation or compasses. It may be added that the reasoning itself is not very sure-footed, and, whilst seeking to measure other things, scarcely takes in and comprehends itself." This reflection must not be mistaken for the dawn of suspicion that his examination of philosophical questions began not altogether at the right end: it is merely an acknowledgment that he had not yet contrived a theory with which he was quite satisfied before it was disproved by experiment. After some experience of Kepler's miraculous good fortune in seizing truths across the wildest and most absurd theories, it is not easy to keep clear of the opposite feeling of surprise whenever any of his extravagancies fail to discover to him some beautiful law of nature. But we must follow him as he plunges deeper in this unsuccessful inquiry; and the reader must remember, in order fully to appreciate this method of philosophizing, that it is almost certain that Kepler laboured upon every one of the gratuitous suppositions that he makes, until positive experiment satisfied him of their incorrectness.