298 A Short History of Astronomy [CH. XL 



published in 1752, with the title Ti.corie de la Lune. Two 

 years later he published a set of lunar tables, and just before 

 his death (1765) he brought out a revised edition of the 

 Theorie de la Lune in which he embodied a new set of 

 tables. 



D'Alembert followed his paper of 1747 by a complete 

 lunar theory (with a moderately good set of tables), which, 

 though substantially finished in 1751, was only published 

 in 1754 as the first volume of his Recherches sur differens 

 points importans du systeme du Monde. In 1756 he pub- 

 lished an improved set cf tables, and a few months afterward 

 a third volume of Recherches with some fresh developments 

 of the theory. The second volume of his Opuscules 

 Mathematiques (1762) contained another memoir on the 

 subject with a third set of tables, which were a slight 

 improvement on the earlier ones. 



Euler's first lunar theory (Theorla Motuum Lunae) was 

 published in 1753, though it had been sent to the St. 

 Petersburg Academy a year or two earlier. In an appendix * 

 he points out with characteristic frankness the defects from 

 which his treatment seems to him to suffer, and suggests 

 a new method of dealing with the subject. It was on this 

 theory that Tobias Mayer based his tables, referred to in 

 the preceding chapter ( 226). Many years later Euler 

 devised an entirely new way of attacking the subject, and 

 after some preliminary papers dealing generally with the 

 method and with special parts of the problem, he worked 

 out -the lunar theory in great detail, with the help of one 

 of his sons and two other assistants, and published the 

 whole, together with tables, in 1772. He attempted, but 

 without success, to deal in this theory with the secular 

 acceleration of the mean motion which Halley had detected 

 (chapter x., 201). 



In any mathematical treatment of an astronomical problem 

 some data have to be borrowed from observation, and of 

 the three astronomers Clairaut seems to have been the most 

 skilful in utilising observations, many of which he obtained 

 from Lacaille. Hence his tables represented the actual 



* This appendix is memorable as giving for the first time the 

 method of variation of parameters which Lagrange afterwards 

 developed and used with such success. 



