ASTRONOMY OF EIGHTEENTH CENTURY. 273 



The labours of other eminent mathematicians contributed to esta- 

 blish the grand result of the stability of the solar system. CLAIRAUT 

 (1713 1765), in 1758 undertook to calculate the period when Hal- 

 ley's comet, that had appeared in 1682, would again be seen. After 

 a long and intricate calculation of the disturbing actions on the comet 

 of Jupiter and Saturn, he found that the attraction of those planets 

 would so retard the comet that its period of revolution would be length- 

 ened by more than a year and eight months. The constellation in 

 which the comet would first appear was named, and the stars among 

 which it would seem to pursue its course were indicated. These pre- 

 dictions were completely verified, and for the first time the movement 

 of a comet was calculated beforehand with the same precision as the 

 planetary orbits. 



Another illustrious mathematician who was deeply engaged in work- 

 ing out the problem of the stability of the solar system was LAGRANGE 

 (1736 1813), a native of Turin, at the Military College of which city 

 he was appointed to the professorship of mathematics before he had 

 completed his twentieth year. But he soon left Turin to enter upon 

 an appointment at Berlin, where he lived twenty years, and where he 

 worked out many of his most remarkable investigations. In 1787 he 

 removed to Paris, where he lived for twenty-six years, and died in 1813 

 a.t the age of seventy-seven. An explanation of the mathematical treat- 

 ment of the problems which Lagrange worked out would be foreign to 

 the design of this work, but the reader has probably already gained some 

 idea of the nature of questions which engaged the attention of the great 

 French mathematicians of the eighteenth century. 



The moon has ever attracted the closest attention of astronomers, 

 and its complicated motions have presented some of the most difficult 

 problems, so that it is only within a recent period that these motions 

 have been completely mastered. As nearer the earth than any other 

 celestial body, the physical structure of the moon has admitted of more 

 immediate observation, from the period when Galileo's telescope first 

 revealed the irregular nature of its surface. The earlier observers 

 considered the diversities of the appearance presented by the moon's 

 surface as partly due to the distribution of land and water, and Milton's 

 reference to Galileo's discovery (p. 109) embodies this view. The 

 appearance presented by the moon, when viewed by a common spy- 

 glass, is rudely represented in Fig. 128. But when a good telescope 

 is directed to the face of our satellite, the forms of mountains and 

 plains are distinctly discernible. The most curious objects, however, 

 are the crater-like formations, which are undoubtedly of volcanic 

 origin, and indicate that at some period the moon was in a semi-fluid 

 state. They are precisely such openings as would be formed by the 

 passage of gases from the interior. The passage of bubbles of air 

 through a semi-fluid mass of slaked lime has been observed to produce 

 appearances exactly similar to many of the lunar craters. Fig. 129 re- 



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