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170 that an epicycle might be introduced to account for this, but as the inequality was only 5′, he did not deem it necessary to go so far in refining the theory of a transient body like a comet; and besides, it is probable that comets, which only last a short time, do not move with the same regularity as the planets do. He finds the inclination of the orbit to the ecliptic equal to 29° 15′, and shows how to compute the place of the comet for any given time by means of the table of its orbital motion with which he concludes the first part of the book. The ninth chapter is a very short one, and treats of the actual size of the comet; as the apparent diameter of the head on the 13th November was 7′, the diameter was 368 miles, or $3⁄14$ of the diameter of the earth. Similarly he calculates the length of the tail, and finds it equal to 96 semi-diameters of the earth. This is on the assumption that the tail is really turned away from Venus, and though he adds that he had also found this to be the case with the comet of 1582, he suspects that some optical illusion must be the cause of this, as it would be more natural that the tail should be turned from the sun than from Venus. In a letter to Rothmann in 1589, he expresses the opinion that the tail is not a mere prolongation of the head, for in 1577 head and tail were of a different colour, and stars could be seen through the tail. He apparently thought that the tail was merely an effect of the light from the sun or Venus shining through the head, and referred to the opinion of Benedict of Venice that the illumination of the dark side of the moon was due to Venus, about which he, however, does not express any decided opinion.

The only part of the tables of the comet's motion which requires notice is that relating to the horizontal parallax. This he makes out from his theory to have been nearly 20′