ON THE OEBIT OF NEPTUNE. 



CHAPTER I. 



INTRODUCTION. 



The errors of the published ephemerides of Neptune are now increasing very 

 rapidly. In 1S63, Walker's ephemeris was in error by 33", and Kowalski's by 

 22". Both ephemerides may be 5' in error before the end of the present century. 

 The orbit of this planet is, therefore, more uncertain than that of any other of 

 the larger members of our system. The uncertainty arises from the insufficiency 

 of the data at the command of those astronomers who have hitherto investigated 

 the motions of this planet. These motions are so slow that it is impossible to 

 determine the elements of the orbit with accuracy from observations extending 

 through only a few years. In Walker's investigations the errors of observation 

 are multiplied more than a hundred times in the elements deduced from them, on 

 account of the smallness of the arc through which the planet had moved. 



The time has now come when the orbit can be determined with some approach 

 to accuracy. The planet has moved through an arc of nearly 40° since its dis- 

 covery, and the errors of observation will be multiplied only ten or twelve times 

 in the errors of the elements. In commencing the work of a revision of the theory 

 of Neptune, it will be well to glance at the past and present state of our know- 

 ledge on this subject. 



Approximate elements of this planet, neglecting the effect of perturbations, 

 were computed by several astronomers within a year or two after its discovery. 

 But the work of preparing a theory which should include the perturbations 

 produced by all the other planets seems to have been left entirely in the hands, 

 of Professor Peirce and Mr. Sears C. Walker. 



§ 2. All the first approximations to the elements showed that the mean motion 

 was very nearly half that of Uranus. It was, therefore, for some time doubtful 

 whether the mutual action of the two planets might not be such as to render the 

 period of Neptune exactly double that of Uranus, and thus present us, on a much 

 grander scale, with a phenomenon similar to that exhibited by the satellites of 

 Jupiter. Professor Peirce's first perturbations of Neptune were computed on this 

 hypothesis, and published in the Monthly Notices of the Koyal Astronomical 

 Society, Vol. VIII, p. 40. The eccentricity of Neptune was neglected, but that 

 of the disturbing planets was included in the perturbations. 



With these perturbations, the ancient observations of Lalande, and the vast 

 number of modern observations made in nearly every active observatory in the 

 world during 1846 and 1847, Mr. Walker computed his "Elliptic Elements I." of 



1 May, 1865. 1 



