240 MEAN DISTANCES OF THE PLANETS. 



for the eight major planets are given on pages 107 and 108 of 

 this journal for 191 1, January. In the cases of the minor planets 

 Eros and Ceres, such simple formulae cannot be used as 

 an algebraical expansion of the perturbative function is too 

 slowly convergent for practical use, — in fact, for the case Eros 

 disturbed by Mars, the algebraical expansion is divergent. For 

 these two planets we must have recourse to other means, and 

 fortunately Mr. C. J. Mertield has computed the secular pertur- 

 bations of both of these planets by a celebrated method devised 

 by Gauss. 



In the case of the planet Eros, it happens that the correction 

 to the elliptic semi-axis-major is nearly negligible. Using the 

 data provided by Mr. Merfield in Nos. 4178-9 of the Astro- 

 nomischc Nachrichtcn for 1907, ]\Iay, we find 



h La 

 Eros (in units of the 8th decimal). 



Total — 56 

 Hence La = 0.1638127 — ■ .0000006 = 0.1638121. 



In the case of the planet Ceres, using the values of 

 a:t = [-^f-Joo given by Mr. Merfield in the Monthly Notices of 

 the Royal Astronomical Societv LX\"II, p. 560, we have 



BLa 

 Action of for Ceres (Units of 8th decimal). 



Mercury 

 Venus 

 Earth 

 ]\Iars 

 Jupiter 

 Saturn 

 Uranus 

 Neptune 



— 1403 

 The mean distance of Ceres is therefore as follows : — 



Elliptic value using ob- ^^ ^ 



served mean motion . . o .4420738 2 .767412 



True semi-axis-major from 

 whi'ch the planet only 

 departs by periodic per- 

 turbations .4420598 2 .767323 



