240 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1909. 
Four Inner Planets and the Fundamental Constants of Astronomy.” 
All known meridian observations of the sun and of the planets 
Mercury, Venus, and Mars were reduced to a uniform equinox and 
system of declinations and compared with Leverrier’s tables. A 
similar exhaustive comparison was made for the transits of Venus 
and Mercury. The results of these comparisons were then combined 
and upon them was based a new determination of the orbits of the 
four inner planets, including a more accurate determination of the 
deviation of the observed values of the motions of the perihelion of 
Mercury and of the node of Venus from the values computed in 
accordance with the law of gravitation. It was found that the 
observed discrepancies could be accounted for by assuming a ring 
of matter lying between the orbits of Mercury and Venus. Professor 
Newcomb’s conclusion was, however, for reasons which he gave, that 
we can not, in the present condition of knowledge, regard this hy- 
pothesis as more than a curiosity. 
Tt is true the discussion of theoretic methods of celestial mechanics 
was carefully subordinated by Professor Newcomb to the practical 
purposes kept steadily in view. Only in this way was it possible to 
accomplish such monumental practical results. Nevertheless, his 
work did not consist merely in applying the methods of others to the 
determination of the actual motions of the planets under considera- 
tion; his own contributions to planetary theory were important. In 
1874 his paper “On the General Integrals of Planetary Motion ” 
appeared in the Smithsonian Contributions to Knowledge. Assum- 
ing that the differential equations of motion can be satisfied approxi- 
mately by infinite series containing only terms of the forms 
p=c cos (a+bdt) and g=a-+bt 
where ¢# is the time, and a, 6, ¢ are arbitrary constants, he showed 
that these series could be replaced by similar ones having a higher 
degree of approximation, and thus the problem of three bodies could 
be solved formally by series containing no terms except of the given 
form. Poincaré devotes a large part of the second volume of “ Les 
méthodes nouvelles de la mécanique céleste ” to applications of Lind- 
stedt’s method, which he shows is essentially that of Newcomb just 
mentioned. 
Professor Newcomb’s researches on the motions of the moon be- 
gan with a paper read before the American Association for the Ad- 
vancement of Science at its meeting in 1868 and written to show that 
there is no good reason to suppose that there is any want of coinci- 
dence between the center of figure and the center of gravity of the 
moon as maintained by Hansen. Next followed various papers call- 
ing attention to the extraordinary differences existing between the 
positions of the moon as given in Hansen’s tables and as obtained 
