224. In 1757, under the title _Astronomiae Fundamenta_, appeared a catalogue of 400 of the brightest stars, observed and reduced with the most scrupulous care, so that, notwithstanding the poverty of Lacaille’s instrumental outfit, the catalogue was far superior to any of its predecessors, and was only surpassed by Bradley’s observations as they were gradually published. It is characteristic of Lacaille’s unselfish nature that he did not have the _Fundamenta_ sold in the ordinary way, but distributed copies gratuitously to those interested in the subject, and earned the money necessary to pay the expenses of publication by calculating some astronomical almanacks. Another catalogue, of rather more than 500 stars situated in the zodiac, was published posthumously. In the following year (1758) he published an excellent set of Solar Tables, based on an immense series of observations and calculations. These were remarkable as the first in which planetary perturbations were taken into account. Among Lacaille’s minor contributions to astronomy may be mentioned: improved methods of calculating cometary orbits and the actual calculation of the orbits of a large number of recorded comets, the calculation of all eclipses visible in Europe since the year 1, a warning that the transit of Venus would be capable of far less accurate observation than Halley had expected (§ 202), observations of the actual transit of 1761 (§ 227), and a number of 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,[126] 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.[127] 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.