NOTES TO BOOK VII. 305 



partly upon observations. In 1820, two prize essays 

 appeared, the one by Damoiseau, the other by Plana and 

 Carlini. And some time afterwards (in 1824, and again, 

 in 1828) Damoiseau published Tables de la Lune formees 

 sur la seule Theorie d 1 Attraction. These agree very 

 closely with observation. That we may form some notion 

 of the complexity of the problem, I may state that the 

 longitude of the Moon is in these Tables affected by no 

 fewer than 47 equations ; and the other quantities which 

 determine her place are subject to inequalities not much 

 less in number. 



It is proper to mention, distinctly, however, that there 

 remain one, perhaps two, unexplained discordances between 

 the theory of universal gravitation and the observed 

 motions of the Sun, Moon and Planets. 



The doubtful unexplained phenomena is a supposed 

 Equation of the Moon of long period. It had been sup- 

 posed by Burg, that in order to make the Tables of the 

 Moon agree with the observations, it was necessary to 

 recognize an equation of which the period was about 

 180 years, and the maximum 15 seconds. It had been 

 imagined also that this inequality in the Moon's motion 

 might be explained by the unequal attraction of the 

 Northern and Southern hemispheres of the earth, arising 

 from its irregular form. But Poisson shewed that accord- 

 ing to theory, the coefficient of such an inequality could 

 not amount to a hundredth of a second. This explanation 

 of the supposed inequality therefore fails ; and the same 

 is the case with other explanations which have been 

 attempted. But new light may be expected to be thrown 

 upon the question of the existence of this inequality, when 

 the reduction of the Lunar Observations and their com- 

 VOL. II. X 



