4'68 Astronomical Society. 



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 Mccaniqne 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 Meca- 

 nique 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 necessary ; but the progress of late made in the theory of 

 perturbations having enabled him to treat certain particular 

 questions more generally, and with more symmetry than here- 

 tofore, it is not to be wondered at if he has been led to re- 

 sults which surpass 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 arithmetical calculations on which these conclusions have 

 been founded. 



The 1st chapter is devoted to the consideration of that ar- 

 tifice in the Meccmique 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. 1\I. Plana de- 

 votes this chapter to the elucidation of tliis artifice, and shows 

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

 conclusion by another, and direct method. He then applies 

 his I'easoning to numerical examples, and computes the quan- 

 tity by which the moon's mean distance from the earth is pet- 

 manentli/ altered by the sun's action, which he finds to be 

 about 1-lOOdth of the radius of the globe of the moon, in auff- 

 mentation, the corresj^ondmg nicrease of the periodic time 

 being about 1-tth of a day. The excentricity too undergoes 

 an alteration in its mean quantity from the same cause, equal 

 to about 0-0007 of its actual amount. 



A similar artifice in the use of an arbitrary constant added 

 in one of the necessary integrations for arriving at the first 

 term of the motion of the moon's perigee, M. Plana observes, 



'' has 



