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336 though the observations "pro refractionibus fixarum indagandis" are numerous, particularly in the year 1589, and are similar to those of the sun.

Imperfect though Tycho's researches on refraction were, they represent a great step forward, as he was the first to determine from observations the actual amount of refraction, and to correct his results for it. This was among the earlier achievements at Uraniborg, and showed the great superiority of the new instruments over the earlier ones. Though not unknown to the ancients, and theoretically examined to some extent by Alhazen and Vitello (whom Tycho quotes, though he doubts whether they really carried out the experiments mentioned by them, as their armillæ could not have been large or accurate), the only astronomer who had practically noticed the effect of refraction was Walther. He found, by observing the sun when setting, by means of his zodiacal armillæ, that the sun seemed to be outside the ecliptic, and explained this as being caused by refraction; but he thought this could only be appreciable very near the horizon, and did not attempt to investigate its laws, for which his instruments would hardly have been accurate enough.

As to the cause of refraction, Tycho did not think that the difference of density of the ether and the atmosphere was of much importance, as he points out that in that case refraction should not disappear except at the zenith, while he imagined it to become insensible half-way towards the zenith. He therefore ascribed refraction chiefly to atmospheric vapours, though he believed that the atmosphere gradually decreased in density and was essentially different from the ether, and he naturally rejected as absurd the Aristotelean idea of a