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Rh sphere of fire encircling the earth. He had in his correspondence with Rothmann several times discussed questions connected with refraction, not only because the observer at Cassel only made the quantity of refraction about half as great as Tycho did, but also because Rothmann thought that there was no difference between the celestial ether and the air except density.

Tycho recognised as an effect of neglected refraction various discrepancies between the elements of the solar orbit determined by Copernicus and his own results. We have already mentioned that he sent one of his pupils to Frauenburg, and found that the latitude had been assumed 2$3⁄4$′ too small, which, together with the neglect of refraction, accounted for the errors in Copernicus' determination of the obliquity and the other elements of the solar orbit, as the longitude concluded from the erroneous declinations would be as much as 13′ in error at 45° from the equinox.

Among Tycho's "puerile and juvenile" observations there are very few indeed of the moon; only now and then the approach of the moon to some bright star is mentioned, and the distance measured with the "radius" or sextant. At Hveen he gradually came to devote more attention to the moon, and from 1582 his lunar observations are very regular, and become year by year more numerous. They include distances from fixed stars, altitudes, declinations, and differences of right ascension from fixed stars, and as often as practicable the moon was observed in the nonagesimal or that point of her daily course in which the effect of parallax took place only in latitude. Eclipses were carefully attended to whenever they occurred; but, unlike the ancient astronomers, Tycho did not confine himself to observing the moon