60 PROCEEDINGS OF THE AMERICAN ACADEMY 



r = 29.939950 -f- ^^ = 30.00506. 



n =z ^i35_9^7j^7o ^ corrected for aber. = 2r'.65789. 



^359 ^2 70 



k r= Gauss's constant of the earth's velocity. 



ij.=zka~^ =21 ".37881. 

 Period =T— 165.97030 tropical years. 



"Thus it appeared that Elements II., assuming the eccentricity and 

 perihelion point unknown, and neglecting the daily variation of the ra- 

 dius vector, would give an ephemeris following the planet's path for five 

 months so closely, that the sum of the squares of 9 comparisons of 

 theory with observation was only 4" .21. This residual quantity might 

 have been still further reduced by inserting a fourth term of the form 

 d M, in which u is the daily increase of rjoo, and d^ a coefficient of the 

 form 



rf =. a A r + ( j-l) A ^ 



where a is the former coefficient of a?, and (^) is the daily variation 

 of X for conservation of areas. Since these terms become sensible in 

 the course of a few additional months, it was thought preferable to 

 postpone the research after the final values of e and tt, and by assign- 

 ing them suitable limits, that of e <^ 0.06, and to tt its corresponding 



value from the equation, cos. v = - — jf—--, then to compute the locus 

 of Neptune's orbit for these limits for any given date, and search for 

 an observation of a missing star in Neptune's path on the same night 

 in some of the ancient catalogues. The fact that {n — /x) is at this 

 time only 0".28, shows the limit of y <^ ± 90*^. The following table 

 of limits of V was computed. 



Assumed val- 

 ues of e. 



1.00 

 0.06 

 0.05 

 0.04 

 0.03 

 0.02 

 0.01 

 Minimum limit, 0.006474 



