S82 Royal Astronomical Society. 



It is remarkable that the missing star, to which allusion has been 

 made, is actually entered as an observed star in the Berlin Star-Map ; 

 and this circumstance prevented Mr. Adams from tracing the new 

 orbit of the planet so soon as he would otherwise have done. This 

 insertion of an unobserved star can be accounted for only on the 

 supposition that the star had been taken by the observer in his work- 

 ing-catalogue as a zero-star, and had then been inserted as a matter 

 of course. 



The mean distance of Neptune from the sun now appears, instead 

 of 38, to be something near 30 ; and its periodic time, instead of 

 220 years, to be nearly 166. It is certainly a most curious thing 

 (in which much is owing to chance) that elements, now known to 

 be extremely erroneous, should have accounted for the perturbations 

 of Uranus through 150 years with such accuracy, and should also 

 have given the planet's place, for the particular year in which the 

 attention of astronomers was first strongly directed to it, with such 

 precision. It remains to be seen whether the new elements of Nep- 

 tune will, with any possible mass, explain the perturbations of 

 Uranus. In any case, Bode's law, on the assumption of which the 

 original investigations of M. Le Verrier and Mr. Adams entirely de- 

 pended, fails completely. 



Calcul detaille d'une In^galit6 Nouvelle a Longue Periode, qui 

 existe dans la Longitude moyenne de la Lune. By M. Hansen. 



The author states that he has lately made known to some astro- 

 nomers a discovery of two inequalities in the motion of the moon, 

 whose periods are respectively nearly 273 and 239 years. Denoting 

 by g, g' , g" the geocentric mean anomaly of the moon, and the helio- 

 centric mean anomalies of the earth and Venus, these inequalities are^— 

 27"-4x sm(-g-l6g'+l8g" + 35° 20'-2) 

 -f-23"-2 X sin (8i^"-13^'-f-315° 30') ; 

 of which the first depends on a new argument, while the second 

 depends on the argument of an equation of long period in the motion 

 of the earth, discovered by Mr. Airy. 



As the calculation of those parts of the coefficients which depend 

 on the product of the square and cube of the sun's disturbing force 

 by the disturbing force of Venus is extremely laborious, and is more- 

 over connected with other unpublished calculations of other inequa- 

 lities of the moon, it does not appear possible to publish it at pre- 

 sent. Indeed M. Hansen does not consider himself able yet to 

 answer for their perfect correctness, though he has the strongest 

 reason to believe that they are very nearly correct. The present 

 paper therefore includes only the calculation of that part of the co- 

 efficient of the first inequality which depends on the first power of 

 the disturbing force. 



It appears difficult to abstract very completely the remaindef of 

 this paper, but the following indications will enable a person ac- 

 quainted with the developments of physical astronomy to follow the 

 whole process. 



The perturbing function CI for the moon as disturbed by Venus 

 being formed, it will be found that it may be expanded in a rapidly 



