314 



The solution by least squares gives, — 



= 118.879 X a; 



+ 7.477 X y 



+ 30.443 X z 



— 45.629 



= 7.477 



+ 85.149 



+ 0.250 



-J- 1.687 



= 30.443 



-f- 0.250 



+ 8.111 



— 8.627 



Whence S se = 4 '.21 



X = 3.255712 

 y = —0.272963 

 z =— 11".1475 



r = 29.939950 + rr, = 30.00506 



n = J359— ^2 7 corrected for ab. = 21 ".65789 



^359 ^2 7 



1 



a = 



2 _ /r_rt>^2 = 30.20058 

 r \x. V 



» = Gauss' constant of earth's velocity. 



l^=y.a~"^' =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 variations of the 

 radius vector, would give an ephemeris following the planet's path 

 for a period of 5-2- months, with a sum of the squares of nine discre- 

 pancies = 4". 21, or a probable error of ± 0".48 for any compa- 

 rison. 



This residual error might perhaps have been still further reduced 

 by inserting a term of the form d X u, where u is the daily variation 



of the radius vector, and d = a A r -\- i — j ^ ^ , — being the time 



variation of the daily motion in true longitude, on the principle of 

 conservation of areas. Inasmuch as these terms become more sensi- 

 ble in the course of a few additional months, it was thought better to 

 postpone the research after the final values of e and tt; and by as- 

 signing to them suitable limits of e < 0.06, and to tt its correspond- 



, ~ , . a (I — c2) — r , 

 ing value from the equation, cos v = , then to compute 



the locus of Leverrier for any given date, and search for it as a 

 missing star observed that night in some of the ancient cata- 

 logues. 



The fact of (n — f^) = 0".28, shows that the limit oCv is ± 90% 

 thus, — 



