24 



after a cci-tain law fVoni I lie cent re outwards. Seeligek arrived at 

 the ooncliisioii that two ellipsoids suffice, one of which is wholly 

 coulaiued within the oi-hit of Mercury, the other reachirifji,' outside 

 the orbit of the earth. There appears to exist a certain lilierty in 

 choosing the values of the ellipticities and the quantities determining 

 the position of the second ellipsoid. As quantities to be determined 

 so as to account for the differences which are to be explained 

 Skeliger introduces the densities of both ellipsoids, the inclination 

 and the longitude of the ascending node of the equatorial plane of the 

 first ellipsoid with reference to the ecliptic, and a quantity not con- 

 nected with the attraction of the masses of matter, but relating to 

 the deviation of the system of coordinates used in astronomy from 

 a so called "inertial system". 



Last year Prof, de Sitteij drew my attention to the necessity 

 of testing Seeliger's hypothesis by calculating the influence of the 

 masses admitted by Seeligek on the motion of the moon and the 

 perturbation of the obliquity of the ecliptic, which Seeltger did not 

 consider '). I performed the calculations and arrived at the conclusion 

 that the pertnrl)ation of the ecliptic changes the sign of Newcomb's'') 

 residual and makes its absolute value a little larger ; further that 

 the perturbations of the motion of the moon are insensil)le. I may 

 be allowed to thaidv Prof, de Sitter for the introduction into this 

 sul)ject and the interest shown in its further development. — One could 

 take the formulae required for the last mentioned purpose from 

 Seeliger's publication ; I did not do so, luit developed them anew. 

 I give them here on account of small differences in derivation. First 

 I shall give this derivation and the results ; after that I shall do 

 the same for the motion of the moon. 



I. Perturbations of the ecliptic. 



Let X, y, z be coordinates in a system the origin of which is at 

 the centre of the ellipsoid, while the axis of rotation is the axis of 

 z, k' the constant of attraction, q the density of. the ellipsoid, a, a 

 and 6' its axes, then the potential V at the point x, y, z is given 

 by the expression : 



Vz=k'jrga'c i ~ , ^ ■ ; 



1) See DE Sitter, the secular variations of the elements of the four inner 

 planets, Observatory, July 1913. 



2) Astronomical Constants p. 110. 



