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 on periodic time is a curious foreshadowing of one of the great discoveries of Newton.

The general explanation of light on these principles was amplified by a more particular discussion of reflexion and refraction. The law of reflexion—that the angles of incidence and refraction are equal—had been known to the Greeks; but the law of refraction—that the sines of the angles of incidence and refraction are to each other in a ratio depending on the media—was now published for the first time. Descartes gave it as his own; but he seems to have been under considerable obligations to Willebrord Snell (b. 1591, d. 1626), Professor of Mathematics at Leyden, who had discovered it experimentally (though not in the form in which Descartes gave it) about 1621. Snell did not publish his result, but communicated it in manuscript to several persons, and Huygens affirms that this manuscript had been seen by Descartes.

Descartes presents the law as a deduction from theory. This, however, he is able to do only by the aid of analogy; when rays meet ponderable bodies, "they are liable to be deflected or stopped in the same way as the notion of a ball or a stone impinging on a body"; for "it is easy to believe that the action or inclination to move, which I have said must be taken for light, ought to follow in this the same laws as motion." Thus he replaces light, whose velocity of propagation he believes to be always infinite, by a projectile whose velocity varies from one medium to another. The law of refraction is then proved as follows :—

Let a ball thrown from A meet at B a cloth CBE, so weak that the ball is able to break through it and pass beyond, but with its resultant velocity reduced in some definite proportion, say 1 : k.

Then if BI be a length measured on the refracted ray equal to AB, the projectile will take k times as long to describe BI as it took to describe AB. But the component