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§§ 223, 224] those made by him at the Cape formed an important part, led, after an elaborate discussion in which the spheroidal form of the earth was taken into account, to an improved value of the moon's distance, first published in 1761.

Lacaille also used his observations of fixed stars to improve our knowledge of refraction, and obtained a number of observations of the sun in that part of its orbit which it traverses in our winter months (the summer of the southern hemisphere), and in which it is therefore too near the horizon to be observed satisfactorily in Europe.

The results of this—one of the most fruitful scientific expeditions ever undertaken—were published in separate memoirs or embodied in various books published after his return to Paris.

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, not- withstanding 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