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282 improvements in methods of calculation and of utilising observations.

In estimating the immense mass of work which Lacaille accomplished during an astronomical career of about 22 years, it has also to be borne in mind that he had only moderately good instruments at his observatory, and no assistant, and that a considerable part of his time had to be spent in earning the means of living and of working.

225. During the period under consideration Germany also produced one astronomer, primarily an observer, of great merit, Tobias Mayer (1723–1762). He was appointed professor of mathematics and political economy at Göttingen in 1751, apparently on the understanding that he need not lecture on the latter subject, of which indeed he seems to have professed no knowledge; three years later he was put in charge of the observatory, which had been erected 20 years before. He had at least one fine instrument, and following the example of Tycho, Flamsteed, and Bradley, he made a careful study of its defects, and carried further than any of his predecessors the theory of correcting observations for instrumental errors.

He improved Lacaille's tables of the sun, and made a catalogue of 998 zodiacal stars, published posthumously in 1775; by a comparison of star places recorded by Roemer (1706) with his own and Lacaille's observations he obtained evidence of a considerable number of proper motions (§ 203); and he made a number of other less interesting additions to astronomical knowledge.

226. But Mayer's most important work was on the moon. At the beginning of his career he made a careful study of the position of the craters and other markings, and was thereby able to get a complete geometrical explanation of the various librations of the moon (chapter, § 133), and to fix with accuracy the position of the axis about which the moon rotates. A map of the moon based on his observations was published with other posthumous works in 1775.