18 
SEE. 
In this connection it may be pointed out that the theories 
of the celestial motions hitherto used have comprised four 
great stages: 
I. The theory of circular motion proposed by the Greeks, 
and perfected by the addition of eccentrics and epicycles, as 
illustrated in the Almagest of Ptolemy. 
II. The theory of elliptical motion discovered by Kepler 
and placed upon a physical basis by Newton’s discovery of 
the law of universal gravitation. 
III. The reduction of the irregularities of the planetary 
motions to elliptical motion by means of the theory of per¬ 
turbations begun by Newton and since developed by Clairaut, 
Euler, Lagrange, and Laplace and their successors during 
the present century. 
IV. The discovery of periodic orbits by Hill in 1877 and 
the subsequent extension of their theory by Poincare and 
Darwin, the variation curve being used as the intermediary 
orbit instead of the Keplerian ellipse, which departs unduly 
from the actual motions of the heavenly bodies. 
In the lunar theory notable progress continues to be made 
by Professor E. W. Brown, of Haverford College, who is bas¬ 
ing his researches on the methods of Hill, as generalized 
and extended by himself. His investigations promise great 
improvements from a theoretical point of view, and hence 
a practical test in the construction of tables will become a 
desideratum of science. The tables of the moon, which will 
command acceptance in the future, must be adequate to 
represent satisfactorily all the observations, ancient and 
modern, though of course only the best modern observa¬ 
tions can be employed in determining the constants and 
principal coefficients which enter into the theory. 
In the line of planetary perturbations little of strict 
novelty has been produced, though the researches of Pro¬ 
fessor Eichelberger,' of the Naval Observatory, have fur¬ 
nished important tables of some of the Watson asteroids. 1 
1 Memoirs of the National Academy of Sciences, 1899. 
