62 PROCEEDINGS OF THE AMERICAN ACADEMY 



Le Verrier. It was during a discussion of this subject by Professor 

 Peirce and Mr. Walker, that the possible omission of some inequality 

 of long period by Le Verrier was suggested by Professor Peirce. On 

 comparing the mean motions of Uranus and Neptune by Elements 

 II., it was found that if the mean distance of Neptune is thirty 

 nearly, such an inequality of great power has been omitted. Thus 

 we have 



For Uranus, fi = 42'.2331 /*' z= 42.2331. 



Elements II., Neptune, fi = 21.3788 2fi = 42.7576. 



2/x — /=: 0.5245. 

 Instead of this, Le Verrier retained only the inequality from (3 /i — 

 fi), which was suited to the mean distance 38, 



" It is impossible to decide, without a revision of the calculations of 

 Le Verrier, substituting the new inequality depending on 2 fx — /, 

 whether the limits would not be so far modified as to include Mr. 

 Walker's Elements II. The inequality of (2/x — fi), if the mean dis- 

 tance is nearly 30, is the most remarkable yet discovered in the pri- 

 mary solar system, and merits a thorough analytical investigation. 



" In conclusion, then, it may be remarked, that the hypothesis of a 

 very small eccentricity is strongly probable by the Elements II., prob- 

 able by Adams's computations from the residual perturbations of Ura- 

 nus, and not necessarily contradicted by Le Verrier's computed limits, 

 unless we admit also that they exclude at the same time the possibility 

 of the semi-axis major which results so directly from Mr. Walker's 

 normal places. 



" It remains to consider the question, whether any light can be 

 thrown on the subject of the orbit of Neptune by the ancient catalogues. 

 On this head it may be remarked that Bradley, Lacaille, and Mayer 

 seldom observed stars of the magnitude 7, 8. In the first three volumes 

 of Piazzi's original observations, now in course of publication by the 

 Vienna Observatory, there is no one of those " not found in the cata- 

 logues," that was near enough to the path of Neptune, on the night 

 of observation, to authorize the supposition of its having been that 

 planet. Bessel, in preparing his zones, never swept so far south as 

 the actual position of Neptune. The Paramatha Catalogue seldom 

 extends north of the 33d parallel of south declination. The Madras 

 observations were generally confined to the stars of Piazzi's or Daily's 

 Catalogues. The only remaining chance at present for finding an 

 ancient observation of Neptune (though doubtless others will be found 



