26 REPORT OF THE SECRETARY. 



ciency of the observations which had been made when the theory was 

 constructed. On account of the extremely slow motion of Neptune, 

 the errors of the observations would be multiplied several hundred 

 times in the final elements of the orbit. 



The second chapter contains the computation of the perturbations 

 of Neptune arising from the attractions of the other planets. This 

 was the most difficult and laborious part of the work, the difficulty 

 being greatly increased by the circumstance that the attraction of 

 Uranus causes the orbit to pass through a regular change of form in 

 a cycle of about 4,300 years. 



The third chapter gives a discussion of the meridian observations 

 of Neptune, made at the observatories of Greenwich, Paris, Wash- 

 ington, Cambridge, Hamburg, and Albany. 



lu the fourth chapter, the positions of the planet given by the ob- 

 servations are compared with a provisional theory, for the purpose of 

 correcting the elements, after which, supposing Neptune to be attracted 

 only by the known planets, its motions, as observed during the nine- 

 teen years since its discovery, are compared with the results of the 

 theory of gravitation, and the greatest difference between the theoreti- 

 cal and observed longitudes is less than a quarter of a second in space, 

 a minuteness so inconsiderable that, if multiplied by 300 times, it would 

 still be too small to be perceptible by the naked eye, and the discre- 

 pancy is as likely to be due to the errors of the observations them- 

 selves as to that of the assumption of no exterior planet. 



It is therefore concluded that there is no evidence of any unknown 

 cause influencing the motions of Neptune, and consequently no evi- 

 dence of the existence of an extra neptunian planet. At the same 

 time, this is only negative evidence; for supposing the extra planet 

 to exist, centuries might be required for its attraction to exert any 

 appreciable influence upon the motions of Neptune. For a similar 

 reason there are no reliable data for correcting the mass of Uranus. 



The fifth chapter is devoted to the tables, which are founded on 

 the theory finally concluded upon, and will probably not be subject 

 to errors of more than a very few seconds during the remainder of 

 the present century. 



The history of the planet Neptune in relation to the perfection of its 

 orbit exhibit a series of facts alike creditable to the science of this 

 country and the policy of the Smithsonian Institution. 



The next paper for the " Contributions" is an exposition of the re- 

 sults of the discussion of the observations made during the expedition 

 under the direction of Dr. I. I. Hayes in the arctic regions, by Chas. 

 A. Schott, of the United States. Coast Survey. 



