1826.] Astronomical Society/. 65 



place, and vice versa, without any reference to the horizon, the 

 ecHptic, and the equator, which is often useful in computing the 

 occultation of fixed stars by the moon. 



9. A general problem, to find the apparent azimuth and appa- 

 rent altitude, from the true longitude and the true latitude of a 

 star. 



The resulting expressions for these several solutions are 

 analytically simple. Those which are deduced in series are 

 usually of this kind, namely, 



log. c = log. b — {^\ cos. & — i (^y cos. 2 9 



■HI) 



3 



cos. 3 S, &c. 



in which the law is evident. 



M. Littrow concludes his paper by suggesting the applica- 

 tion of his principal formulae to the solution of various other 

 problems. 



Lastly, there was read a paper, entitled " A Memoir on dif- 

 ferent Points relating to the Theory of the Perturbations of the 

 Planets expounded in the Micatiique Celeste;" by M. Plana, 

 Astronomer Royal at Turin, and an Associate of this Society. 



The object of the author in this memoir he states to be an 

 examination of various points in the theory of the planetary 

 perturbations as explained by M. de Laplace in the Mecanique 

 Celeste. In undertaking this labour, he observes, he at first had 

 no expectation of meeting with any instance in which an actual 

 rectification of the results already arrived at would be neces- 

 sary ; but the progress of late made in the theory of perturba- 

 tions having enabled him to treat certain particular questions 

 more generally, and with more symmetry than heretofore, it is 

 not to be wondered at if he has been led to results which sur- 

 pass in exactness those hitherto published. But in all such 

 cases, he adds, where he has arrived at conclusions not in 

 accordance with those of the illustrious author of the Mecanique 

 Celeste, he has thought it incumbent on him to give with the 

 fullest detail, not only the developments, but even the arithme- 

 tical calculations on which these conclusions have been founded. 



The first chapter is devoted to the consideration of that arti- 

 fice in the Mecanique Celeste in which M, Laplace transfers his 

 formulae from the mean motions, axes, &c. of the primitive or 

 undisturbed orbits, which are not given by observation, to those 

 of the disturbed, which are given as they exist in nature. This 

 he does by assuming an arbitrary constant introduced in one of 

 the integrations by which the perturbation in longitude is 

 derived, in such a manner as to make the term in the result 

 which depends on the mean motion vanish. M. IMana devotes 

 this chapter to the elucidation of this artifice, and shows (he 

 correctness of M. Laplace's results by obtaining the same con- 



Nieto Series, vol. xi. f 



