PHYSICAL ASTRONOMY. 551 



data ; but that its excellence when established is in the number of ob- 

 servations which it explains. The multiplicity of observations which 

 are explained by astronomy, and which are made because astronomy 

 explains them, is immense, as I have noted in the text. And the mul- 

 titude of observations thus made is employed for the purpose of correct- 

 ing the first adopted elements of the theory. I have mentioned some 

 of the examples of this process : I might mention many others in order 

 to continue the history of this part of Astronomy up to the present 

 time. But I will notice only those which seem to me the most re- 

 markable. 



In 1812, Burckhardt's Tables de la Lune were published by the 

 French Bureau des Longitudes. A comparison of these and Burg's 

 with a considerable number of observations, gave 9-100ths of a second 

 as the mean error of the former in the Moon's longitude, while the 

 mean error of Burg's was 18-100ths. The preference was therefore ac- 

 corded to Burckhardt's. 



Yet the Lunar Tables were still as much as thirty seconds wrong in 

 single observations. This circumstance, and Laplace's expressed wish, 

 induced the French Academy to offer a prize for a complete and pure- 

 ly theoretical determination of the Lunar path, instead of determina- 

 tions resting, as hitherto, partly upon theory and partly upon observa- 

 tions. In 1820, two prize essays appeared, the one by Damoiseau, the 

 other by Plana and Carlini. And some years afterwards (in 1824, and 

 again in 1828), Damoiseau published Tables de la Lune formees sur 

 la seule Theorie d' Attraction. These agree very closely with observa- 

 tion. That we may form some notion of the complexity of the prob- 

 lem, I may state that the longitude of the Moon is in these Tables 

 affected by no fewer than forty-seven equations ; and the other quan- 

 tities which determine her place are subject to inequalities not much 

 less in number. 



Still I had to state in the second Edition, published in 1847, that 

 there remained an unexplained discordance between theory and obser- 

 vation in the motions of the Moon ; an inequality of long period as it 

 seemed, which the theory did not give. 



A careful examination of a long series of the best observations of 

 the Moon, compared throughout with the theory in its most perfect 

 form, would afford the means both of correcting the numerical elements 

 of the theory, and of detecting the nature, and perhaps the law, of any 

 still remaining discrepancies. Such a work, however, required vast 

 labor, as well as great skill and profound mathematical knowledge. 



