304 A Short History of Astronomy [CH. xi. 



rates of change of the elements of the varying ellipse 

 could be calculated, and made some progress towards 

 deducing from these data the actual elements ; but he 

 found the mathematical difficulties too great to be over- 

 come except in some of the simpler cases, and it was 

 reserved for the next generation of mathematicians, notably 

 Lagrange, to shew the full power of the method. 



237. Joseph Louis Lagrange was born at Turin in 1736, 

 when Clairaut was just starting for Lapland and D'Alembert 

 was still a child ; he was descended from a French family 

 three generations of which had lived in Italy. He shewed 

 extraordinary mathematical talent, and when still a mere 

 boy was appointed professor at the Artillery School of his 

 native town, his pupils being older than himself. A few 

 years afterwards he was the chief mover in the foundation 

 of a scientific society, afterwards the Turin Academy of 

 Sciences, which published in 1759 its first volume of 

 Transactions, containing several mathematical articles by 

 Lagrange, which had been written during the last few 

 years. One of these * so impressed Euler, who had made 

 a special study of the subject dealt with, that he at once 

 obtained for Lagrange the honour of admission to the 

 Berlin Academy. 



In 1764 Lagrange won the prize offered by the Paris 

 Academy for an essay on the libration of the moon. In 

 this essay he not only gave the first satisfactory, though 

 still incomplete, discussion of the librations (chapter vi., 

 '33) of the moon due to the non-spherical forms of both 

 the earth and moon, but also introduced an extremely 

 general method of treating dynamical problems,! which 

 is the basis of nearly all the higher branches of dynamics 

 which have been developed up to the present day. 



Two years later (1766) Frederick II. , at the suggestion 

 of D'Alembert, asked Lagrange to succeed Euler (who 

 had just returned to St. Petersburg) as the head of the 

 mathematical section of the Berlin Academy, giving as a 

 reason that the greatest king in Europe wished to have 

 the greatest mathematician in Europe at his court. 



* On the Calculus of Variations. 



f The establishment of the gene.-al equations of motion by 

 a combination of virtual velocities and D 1 Alemberf s principle. 



