M. Le Chev. Biirg's Improveme^its of the Lunar Tables. 135 



soon, we have no other alternative but by comparison with ob- 

 servations. 



I have succeeded in finding the first coefficient of the varia- 

 tion independently of the radius of the moon, by determining 

 its value from the meridional passages of both kinds observed 

 by Maskelyne at the full moon from 1765 to 1803. In ge- 

 neral the result was not different from that which I had for- 

 merly found, by comparing the observations made at Green- 

 wich between 1765 and 1794 before full moon, with those 

 made after full moon. The result shows, that the radius of 

 the moon adopted in my tables ought on no account to be di- 

 minished, as Burckhardt believes, but, on the contrary, in- 

 creased by 1"4 from 1765 to the 11th July 1772, and by 

 0"3 after this period, in order to reduce exactly to the moon's 

 centre the observed right ascensions of her limbs. From the 

 first coefficient of the variation found in this manner we de- 

 duce the sun's parallax 8"62, and it appears to me that this 

 value is not less probable than that found by M. Encke from 

 the two transits of Venus in 1761 and 1769. The result given 

 by the two equations, one of which depends on the longitude 

 of the node, and the other on the true longitude of the moon, 

 is equally satisfactory. The first gives for the flattening of 

 the poles of the earth ^ J55 and the second, which is quite in- 

 dependent of the first, gives ^1^. 



With respect to the fundamental epochs, I have found for 

 1779, and for the meridian of Greenwich, 



Mean longitude of the moon, 

 Mean anomaly. 

 Supplement of the node, 



These results include the secular equations. I have found 

 also the 



Annual motion in longitude, 4s 9^ 23' 4".8195 



in anomaly, 2 28 43 18 1737 



Suppl. of node, 19 19 4103 



As the observations on which these mean motions are found- 

 ed embrace a period of only twenty-nine years, they will per- 

 haps require ulterior corrections, but I consider them to be 



