RECENT PROGRESS IN THEORETICAL 
ASTRONOMY. 
BY 
Thomas Jefferson Jackson See. 
[Read before the Society February 17, 1900.] 
The year 1899 witnessed the completion of M. Poincare’s 
Methodes Nouvelles de la Mecanique Celeste, the third volume 
of which has recently appeared. In this great work the 
problems of celestial mechanics are treated mainly from the 
theoretical point of view, along the line of the periodic 
solutions, first brought to light by Hill in his researches on 
the moon in 1877; and though the methods developed will 
certainly have important bearings on future tables of the 
planets, it is to be anticipated that the chief use of such 
methods will be in finding the limits of the secular and 
long-period inequalities of the planets and satellites and in 
researches upon the stability of their motions. Some of the 
motions of the planets and satellites are approximately 
periodic, and in such cases the theory will probably be found 
to have important practical applications, since it will be 
simpler and easier to reduce the perturbations to the appro¬ 
priate periodic orbit than to the Keplerian ellipse. The 
point of departure will be similar to that proposed by Hill 
in substituting the variation curve for the Keplerian ellipse 
previously used in all the theories of the moon’s motion. 
Among known bodies probably the system of Jupiter’s satel¬ 
lites offers the best illustration of an approximation to 
periodic orbits, since observation proves that the laws of 
Laplace have been followed with the greatest rigor for 
nearly three hundred years. 
3—Bull. Phil. Soc., Wash., Vol. 14. 
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