PHYSICAL AND MATHEMATICAL SCIENCES. 151

Lastly, all the planes of the planetary orbits weresupposed by Ptolemy to pass through the earth. Co-pernicus did not go so far as to reject this notion.Kepler showed that they all passed through the sun,and that the lines of their nodes all intersect in thecentre of that luminary.

In l6’l 1 Kepler published his Dioptrics, in which hemade further efforts to investigate the law of refraction ;but with only a limited degree of success. He was led tosee the importance of it chiefly in connection with thetheory of lenses, then an object of attention with refer-ence to the construction of the telescope. His investi-gations, however, are quite independent of their applica-tion, which must be spoken of in its proper place. Heattempted to deduce the connection between the anglesof incidence and refraction. In the case of glass, hefound by experiment that these angles, when of anysmall value, always preserve very nearly the ratio ofthree to two. This sufficed for the immediate purposeof finding the focal length of a lens, when the angles ofincidence are practically comprised within very smalllimits. Mathematical views were hardly enough ad-vanced to enable him to hazard the conjectural hypo-thesis, which would have instantly occurred to anymodern mathematician in such a case, to pass from thearc to the sine, and try whether that relation held goodin other cases.

Under the same limitation of the angle of incidencebeing small, he made several other useful applicationsof the same approximate law;

Of the astronomical, or atmospheric refraction, hehad a much more correct notion than his predecessors ;he understood that it extended from the horizon to thezenith, and even gave an approximate law to express therate of its decrease.

He incidentally suggests the idea, afterwards so fullyverified, that the air is a substance possessing weight ;and that the refractive power varies with the tempera-ture. He also remarks, that during a lunar eclipse,

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