MEAN DISTANCES OF TliE PLANETS. 



241 



In a paper published in the Monthly Notices of the Royal Astro- 

 nomical Society (1910, December, page 127), the writer gave the 

 results of a rough calculation for this case, viz., 

 hLa = —0.0000154 

 or a =: — 0.000 1 00 

 but unfortunately the last number was incorrectly given as 

 — o.ooooio, which is ten times too small. 



Turning now to the planets Uranus and Neptune. In vol. 

 XXVIII. of the Annales of the Observatory of Paris (Memoires) 

 which has just appeared, Monsieur A. Gaillot brings to a con- 

 clusion his researches on the motions of the planets Uranus and 

 Neptune accompanied by tables for the preparation of 

 ephemerides. and in fact his tables are used in the Connaissance 

 des Temps for 1913. Monsieur Gaillot's work is closely 

 modelled on the lines of Le Verrier's theories. We have thus 

 two modern theories with tables for these planets: — (a) Gaillot's 

 based on the method of Lagrange's variation of elements; (b) 

 Newcomb's based on the perturbations of co-ordinates in which 

 Hansen's method appears. Comparisons of the ephemerides for 

 1913 show quite small differences, but one cannot help remark- 

 ing on the shortness of the calculations actually made by New- 

 comb and the brevity of his tables. It is true that Newcomb 

 did not publish his calculations in full, but the criticism seems 

 just; Newcomb avoids some considerable work by not develop- 

 ing the great inequality in the longtitudes of Uranus and Nep- 

 tune, one consequence is that his elements of the two planets' 

 orbits are not the mean elements. Monsieur Gaillot's work puts 

 us in possession of these. 



Tlie great inequality just mentioned is caused by the near 

 commensurability of the mean motions of the two planets, the 

 mean motion of Uranus being nearly twice that of Neptune. 

 This inequality takes 4,230 years to go its course ; it can dis- 

 place Uranus from its mean place in orbit by over 3150" and 

 Neptune by 2150". 



Tables showing the elements according to these two astro- 

 nomers are not without interest. 



