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SCIENCE 



[N. S. Vol. XXX. No. 768 



of the U. S. Naval Observatory, chiefly the 

 Pistor and Martin's transit circle, but 

 found time to investigate the distance of 

 the sun, concluded from all the methods. 

 His result for the constant of solar paral- 

 lax was 8".848, a value adopted in nearly 

 all the ephemerides for quite a lengthy 

 period. It is too large chiefly on account 

 of the large weight attributed to the de- 

 termination from Mars, whose observation 

 is subject to systematic errors, at that time 

 unsuspected. 



About the same time Professor Newcomb 

 undertook the investigation of the orbit of 

 Neptune and constructed general tables of 

 its motion. As material he had the two 

 observations of Lalande and those of eight- 

 een years following the discovery of the 

 planet. This investigation, published in 

 the Smithsonian Contributions to Knowl- 

 edge, met an urgent need of practical as- 

 tronomy at that time. 



As the secure reduction of astronomical 

 observations is a matter of prime impor- 

 tance, Professor Newcomb contributed to 

 the Washington Observations for 1870 an 

 appendix dealing with the right ascensions 

 of the equatorial fundamental stars. His 

 aim was to eliminate as far as possible 

 systematic errors of a personal or local 

 nature and thus obtain a homogeneous 

 system. This is an admirably conducted 

 investigation and has served as a founda- 

 tion for whatever has been since accom- 

 plished in this subject. 



The elegant method of treating the mo- 

 tion of the moon by Delaunay, published in 

 1860, led Professor Newcomb to consider 

 this subject; thus we have his memoir in 

 Liouville 's Journal for 1871 on the planet- 

 ary perturbations of the moon. The in- 

 vestigation is very neat, regard being had 

 to the early epoch of its composition, but 

 the final equations derived are precisely 

 those which result from Delaunay 's 

 method. 



Having treated Neptune Professor New- 

 comb next undertook a similar piece of 

 work for the adjacent planet Uranus. This 

 was a heavier task than its predecessor on 

 account of the longer period covered by the 

 observations. These theories of the two 

 planets have been superseded by the in- 

 vestigations of Professor Newcomb while 

 director of the American Ephemeris, but 

 that of Uranus was welcomed by astrono- 

 mers as a great improvement on the discus- 

 sion of Bouvard. As in the case of Nep- 

 tune, the investigation of Uranus appears 

 in the Smithsonian Contributions to 

 Knowledge. 



In the same collection for the following 

 year Professor Newcomb has a memoir on 

 the general integrals of planetary motion. 

 The aim of this paper is to show how to 

 avoid powers of the time as multipliers of 

 the different portions of the algebraic ex- 

 pressions arrived at. The thus modified ex- 

 pressions have since received the name of 

 Lindstedt's series and are the chief subject 

 of investigation in M. Poineare's work in 

 the line of celestial mechanics. This paper 

 is a worthy beginning for what was to 

 follow. 



Only a few years after the introduction 

 of Hansen 's lunar tables for computing the 

 places for the ephemerides it was seen that 

 observation was marching away from them. 

 From the character of the deviation they 

 could only be attributed to an imperfect 

 determination by Hansen of the secular 

 and long-period terms. Always interested 

 in the theory of the moon. Professor New- 

 comb undertook to see what light could be 

 thrown on the matter by observations made 

 before the epoch 1750, chiefly in the form 

 of times of beginning or ending of solar 

 and lunar eclipses and oecultations. This 

 involved a heavy load of numerical com- 

 putation and a careful research for ma- 

 terial in the libraries and observatories of 

 Europe. The results of this labor appear 



