29. 



NOTE ON THE INEQUALITY IN THE MOON'S LATITUDE WHICH IS DUE 

 TO THE SECULAR CHANGE OF THE PLANE OF THE ECLIPTIC. 



[From the Monthly Notices of the Royal Astronomical Society, Vol. XLI. (1881).] 



THE first theoretical explanation of this inequality was given by Hansen 

 in the year 1849, in No. 685 of the Astronomische Nachrichten, just a year 

 after the Astronomer Royal had pointed out, in a letter published in the 

 same journal Beilage zu No. 648 that such an inequality was clearly indi- 

 cated by the observations. In the same paper Hansen shews that there is 

 a small term in the Moon's longitude depending on the same cause, the 

 coefficient of which amounts to about 0"'5, the inequality being proportional 

 to the cosine of the longitude of the Moon's node. The existence of this 

 inequality also had been indicated by the Astronomer Royal from the 

 observations, though he assigns to it a somewhat larger coefficient. 



The calculation of both these inequalities is given by Hansen somewhat 

 more fully in p. 491, Art. 176 of his Darlegung. 



In 1853 I communicated to Mr Godfray a simple theoretical explanation 

 of the inequality in latitude, which he inserted in his Elementary Treatise, 

 on the Lunar Theory. This explanation is there given in rather too 

 compendious a form, and I propose in the course of this paper to present 

 to the Society the same investigation, with some slight modification, together 

 with some additional remarks, which will, I hope, render it clearer than 

 before. 



