THE ORBIT OF NEPTUNE. 7 



3. To inquire whether those motions indicate the action 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 formulas by which the theoretical place of 

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

 the years 1COO and 2000. 



In giving the steps of an investigation like this, the true end should be to furnish 

 the means whereby every step can be corrected, or verified if already correct, and 

 to start only from admitted data. Sometimes a result will necessarily depend, to 

 a certain extent, on an act of judgment, as in assigning relative values to different 

 determinations of the same element. In this case data should be given for a 

 revision of the judgment, as far as this may be thought desirable. 



Such, with very few exceptions, is the rule adhered to in the present paper. 

 The data are the published volumes of astronomical observations, and the funda- 

 jnental formulae of celestial mechanics. The steps will nearly or quite always 

 be so short that any one may be verified from the preceding one without much 

 labor. 



The author is indebted to the courtesy of the Astronomer Royal, of the late 

 Captain James M. Gilliss, and of Professor G. W. Hough, for the observations made 

 at Greenwich, Washington, and Albany in the years 1863 and 1864, which have 

 added greatly to the reliableness of the results of his investigation. 



WASHINGTON, April, 1805. 



