12 EEPOET OF THE SECEETAEY. 



of the greatest tides in the Atlantic one or two days after the time of 

 the greatest force. A correct tidal theory should furnish the data for 

 a determination of the moon's mass ; and this determination should be 

 the same for every port. Considering this as one of the best tests 

 of any tidal theory, the author has given much attention to framing 

 various equations from theory for this purpose, and to their application 

 to the results of tidal observations at various ports. The comparisons 

 are made with the extended series of observations of the United States 

 Coast Survey and with the results obtained by the Tidal Committee of 

 the British Association from the analysis of tidal observations of various 

 ports by means of the harmonic method of analysis. The memoir also 

 contains the discussion of the published series of observations of the 

 French government at Brest, with a comparison of the results with 

 theory, and a chapter on the retardation of the earth's rotation on 

 account of the tides, and its effect upon the apparent secular variation of 

 the moon's motion in its orbit. 



Beside the labor expended on this memoir in the line of higher mathe- 

 matics, it involves arithmetical computations of a very laborious charac- 

 ter, the expense of which will be defrayed by the Institution. 



The investigation of the orbit of Uranus, by Prof. S. Newcomb, of 

 the National Observatory, was substantially completed in October last, 

 and has since been entirely prepared for the press, with the exception 

 of some final revision. Considerable additions and alterations are, 

 however, still required in the appended tables, to be used for comput- 

 ing ephemerides of the planet; but these the author hopes to complete 

 in a few months, so that the work may be put in the hands of the 

 printer early in 1873. 



This work, on which the author has been engaged for thirteen years, 

 has absorbed the greater part of his leisure time from his duties in the 

 National Observatory during the last five years. Its preparation not 

 only involved abstruse mathematical discussions, but also arithmetical 

 calculations of very great extent. The latter were made at the expense 

 of the Institution ; and through the assistance thus rendered, Professor 

 Newcornb has been enabled to complete his important investigations 

 without devoting his energies to labors which could be well performed 

 by intelligence of a less valuable character. 



The following remarks by the author of this work may here be con- 

 sidered in place : 



"It will perhaps surprise those not especially devoted to astronomy 

 to learn that, although the planet Neptune has been known for a 

 quarter of a century, the positions of Uranus in all the astronomical 

 ephemerides of Europe are still computed, without regard to the action 

 of that body, from the old tables of Bouvard, dating back as far as 1820, 

 the errors of which led to the discovery of Neptune in 1846. A result 

 of this was that an occultation of Uranus by the moon, which occurred 



