

44] ADDRESS ON PRESENTING GOLD MEDAL TO M. DELAUNAY. 329 



Newton in his Principia ; and although his investigations are only fragmentary, 

 being simply intended to shew how some of the leading lunar inequalities 

 may be deduced from theory, yet they form one of the most admirable 

 portions of that immortal work. Towards the middle of the eighteenth 

 century the theory was more systematically entered upon by Clairaut, 

 D'Alembert, and Euler, who severally shewed that the theory was competent 

 to give very approximate values of all the inequalities which were then 

 recognised by observation. 



Still the theory was far from being sufficiently perfect to serve as a 

 foundation for lunar tables accurate enough for the uses of navigation. 

 This degree of accuracy was first attained by the tables of Mayer, who 

 not only carried the approximations to the values of the coefficients of the 

 various lunar inequalities further than his predecessors had done, but also 

 corrected the theoretical coefficients thus obtained by comparison with his 

 own observations. The theory was greatly advanced by Laplace, not only 

 by his more accurate theoretical determination of the coefficients, but also 

 by several important discoveries, especially that of the cause of the Moon's 

 secular acceleration. 



The improvements in the lunar tables, however, which were made 

 successively by Burg and Burckhardt, were founded, not on theory, but on 

 comparison of the former tables with observations ; and the empirical tables 

 thus produced were far more accurate than any that could have been 

 formed at that time by theory alone. Dissatisfied with this state of things, 

 and wishing to see astronomy founded exclusively on the law of attraction, 

 only borrowing from observation the necessary data, Laplace induced the 

 Academy of Sciences to propose for the subject of the mathematical prize 

 which it was to award in 1820 the formation, by theory alone, of lunar 

 tables as exact as those which had been constructed by theory and obser- 

 vation combined. The prize was divided between two memoirs one by 

 M. Damoiseau, the other being the joint production of MM. Plana and 

 Carlini. Damoiseau's memoir is printed in the third volume of the Recueil 

 des Savants Strangers. Plana's great work on the lunar theory, which 

 appeared in 1832, is the development of the joint memoir by himself and 

 Carlini. By these important works an immense advance was made in the 

 theory, the approximations being carried to such an extent that the resulting 

 coefficients were comparable in accuracy with those given by observation. 

 In 1824 Damoiseau published tables founded entirely on his theory, which 

 were found to be quite as exact as those of Burckhardt. 



A. 42 



