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Rh a quantity which Tycho's instruments could not possibly measure, this looks a surprising statement, particularly when it is remembered that Tycho, like his predecessors, assumed the solar parallax equal to 3′. This mystery was believed to have been solved by Kepler, who states that he examined the observations of 1582–83, and found little or no parallax from them; but, to his surprise, he found among Tycho's manuscripts one written by one of his disciples, in which the observed places were compared with the orbit of Mars according to the planetary theory and numerical data of Copernicus, and a most laborious calculation of triangles ended in the result that the parallax of Mars was greater than that of the sun. Kepler suggests that Tycho meant his pupil to calculate the parallax from the observations, but that the pupil, by a misunderstanding, worked out the distance of Mars from the diameters of the excentrics and epicycles of Copernicus. The subject of the parallax of Mars is alluded to by Tycho in a letter to Brucæus, written in 1584. Here he does not hint at having already constructed a new system himself, but merely tries to disprove that of Copernicus, and among his arguments is, that, according to Copernicus, Mars should in 1582 have been at a distance equal to two-thirds of that of the sun, and consequently have had a greater parallax, whereas he found by very frequent and most exquisite observations that Mars had a far smaller parallax, and therefore was much farther from us than the sun. In other words, Tycho could not find any parallax of Mars from his observations, but somehow he afterwards imagined that he had found Mars to be nearer