WITH A STAR OBSERVED BY LALANDE. I \\) 



The question of their identity will be decided in due course of time, [f confirmed, this 

 observation of Lalande will be exceedingly precious to the astronomer in discussing the 

 question of the existence of other planets superior to Leverrier. 



I have remarked, that the above estimate of the limits of the Leverrier region for Mn\ 

 10th, 1795, was based on only approximate computations. I expected to examine all the 

 stars in this region with the Equatorial, and if any were missing that were seen by 

 Lalande, then to investigate the question of their identity with Leverrier. The coincidence 

 in place with the Lalande star which induced me to believe beforehand that on examining 

 the heavens it would be missing, was quite unexpected. I have stated the particulars 

 that led to this singular coincidence. Now that the star is known to be missing, 1 will 

 proceed to examine the plausibility of the hypothesis of their identity. 



The first objection to this hypothesis is, the shortness of the period compared with the 

 hypothetical periods obtained by Adams and Leverrier (first published by the latter,) from 

 the equations of condition derived from the residuary perturbations of llerschcl. To this 

 objection it may be answered, that both of those analytical discoverers of Leverrier 

 assumed as the basis of their research a mean distance double that of Uranus, and then 

 only diminished its value as the distortion of the other resulting elements compelled them 

 to do so. Hence the extraordinary eccentricity in their first results, ,V by Adams, and 

 tVV hy Leverrier. Had they allowed free scope to the variations of the mean distances 

 instead of forcing the other elements to conform to the preconceived value, I doubt not 

 that a shorter period and more nearly circular orbit would have resulted. In proof of 

 this remark I will quote from Mr. Adams's letter of September 2d, 184G, to the Astrono- 

 mer Royal, (see pages 529 and 530 of the London and Edinburgh and Dublin Philosophi- 

 cal Journal, No. 197, for December, 1810.) 



" St. John's College, Cambridge, September 2il, 1840. 



'•In the investigation, the results of which I communicated to you last October, the 

 mean distance of the supposed disturbing planet is assumed to be twice that of Uranus. 

 Some assumption is necessary in the first instance, and Bode'e law renders it probable 

 that the above distance is not very remote from the truth: but the investigation could 

 scarcely be considered satisfactory while based on any thing arbitrary; and I therefore 

 determined to repeal the calculation, making a different hypothesis as to the mean dis- 

 tance. The eccentricity also resulting from my former calculations was far too large to 

 be probable; and I found that although the agreement between theory and observation 

 continued very satisfactory down to 18 10, the difference in Bubsequenl years was becoming 

 very sensible, and I hoped that these errors, as well as the eccentricity might be dimi- 

 nished by taking a different mem distance. Not to make too violent a change, I assumed 

 this distance to be less than the former value l>\ about one-thirtieth part of the whole. 

 The result is very satisfactory, and appears to Bhow that by still farther diminishing the 

 distance, tht agreement between theory and iht later observations mm/ bt rendered complete, and 

 the eccentru ity reduced »/ ///' some timt to a rrr>i small Quantity, The mass and the elements 

 of the orbit of the supposed planet, which result from the two hypotheses, are a~ follows 

 vol. x. 



