REPORT OF THE SECRETARY. 25 



there no other planets in the system, and from this to calculate an 

 ephemeris. 



The motion of Neptune was further investigated by another of our 

 countrymen, Professor Peirce, of Cambridge. He calculated the 

 action of all the other planets on Neptune, and obtained results 

 which enabled Mr. Walker to correct his elliptical orbit, and to com- 

 pare the calculated places of the planet with its actual position in the 

 heavens. This led to a further correction of the orbit, and to a more 

 perfect table of calculated places. The Ephemeris was published 

 annually for several years, until the establishment of the American 

 Nautical Almanac, when, in accordance with the general policy of 

 the Institution, it was transferred to that work. 



During the last nineteen years, which have elapsed since the investi- 

 gation of Professors Peirce and Walker relative to the orbit of this 

 planet, a series of accurate observations have been made upon its mo- 

 tion at the principal observatories of the world, and these have now 

 been discussed by Professor S. Newcomb, of the Washington Observa- 

 tory, a young mathematician in whose progress and advancement this 

 establishment has taken great interest. 



The objects of Mr. Newcomb' s investigations, as stated in the in- 

 troduction of his memoir, are as follows: 



1. To determine the elements of the orbit of Neptune with as 

 much exactness as a series of observations extending through an arc 

 of forty degrees will admit of. 



2. To inquire whether the mass of Uranus can be deduced from 

 the motions of Neptune. 



3. To inquire whether these motions indicate the existence of an 

 extra neptunian planet, or throw any light on the question of the 

 existence of such a planet. 



4. To construct general tables and formulae, by which the place 

 of Neptune may be found at any time, and more particularly between 

 the years 1,600 and 2,000. 



The work is divided into five chapters. 



The first is introductory, giving a brief review of the previous la- 

 bors of astronomers in perfecting the theory of Neptune. The only 

 approximately correct theory which had been published is shown to 

 be that of Professor Sears C. Walker and Professor Benjamin Peirce, 

 whose labors were given to the world in the second and third vol- 

 umes of the Smithsonian Contributions to Knowledge, and in the first 

 volume of the Proceedings of the American Academy. The elements 

 of this theory were, however, far from correct, owing to the insuflS- 



