"I go on to other methods. Since density is clearly connected with the cause of the refractions, and refraction itself seems a kind of compression of light, as it were, towards the perpendicular, it occurred to me to examine whether there was the same proportion between the mediums in respect of density and the parts of the bottom illuminated by the light, when let into a vessel, first empty, and afterwards filled with water. This mode branches out into many: for the proportion may be imagined, either in the straight lines, as if one should say that the line EQ, illuminated by refraction, is to EH illuminated directly, as the density of the one medium is to that of the other—Or another may suppose the proportion to be between FC and FH—Or it may be conceived to exist among surfaces, or so that some power of EQ should be to some power of EH in this proportion, or the circles or similar figures described on them. In this manner the proportion of EQ to EP would be double that of EH to EI—Or the proportion may be conceived existing among the solidities of the pyramidal frustums FHEC, FQEC—Or, since the proportion of the mediums involves a threefold consideration, since they have density in length, breadth, and thickness, I proceeded also to examine the cubic proportions among the lines EQ, EH. "I also considered other lines. From any of the points of refraction as G, let a perpendicular GY be dropped upon the bottom. It may become a question whether possibly the triangle IGY, that is, the base IY, is divided by the refracted ray GP, in the proportion of the densities of the mediums. "I have put all these methods here together, because the same remark disproves them all. For, in whatever manner, whether as line, plane, or pyramid, EI observes a given proportion to EP, or the abbreviated line YI to YP, namely, the proportion of the mediums, it is sure that EI, the tangent of the distance of the point A from the vertex, will become infinite, and will, therefore make EP or YP, also infinite. Therefore, IGP, the angle of refraction, will be entirely lost; and, as it approaches the horizon, will gradually become less and less, which is contrary to experiment.