145 



constant or slowly varying parts and for tlie theoretical perturbations 

 and on the other hand for the empirical ter in also. The mean 

 discordance decreased, in the mean for h and k, from ± 0"605 

 to ±0"389, and the decrease was about the same for // and k, and 

 about equally great for the earlier and the later years. It did not 

 appear, however, to be so certain that the term deduced from tiie 

 investigation of the tabular errors in Right-ascension really represented 

 an inequality in the longitude of the moon. 



Originally de Vos van Steenwijk found the term in the form 

 + 0".66 sin \g + 244°.4 + 40°.35 («— 1900.0) | 



ft soon struck me that the annual variation of the argument x is 

 almost equal to the annual motion of the perigee 40°.6S, so that, 

 as the argument is found most accurately for the mean epoch of 

 the observations used, 1886, the term can be written : 



+ 0'.66 sill [g + 249°.0 + 40°.68 {t — 1900.0) |. 

 — _j_ 0".66sm|/— 85°.3| 

 in w^hich / represents the mean longitude in the orbit or approxi- 

 mately the ecliptical longitude. 

 Now it is possible : 



1. That the approximate agreement of the two rates of motion 

 is merely accidental, and that the original form found for the term 

 is the true one, so that we might probably have to deal with 

 a still unknown inequality caused by the planets. 



2. That the transformation gives us the true formula. 



Taking the tirst supposition, the difficulty remains, which de Vos 

 pointed out in his first paper, that such a considerable term should 

 have escaped both Brown and Radau, and that while all terms with 

 at all considerable co-efficients have been found nearly equal by both. 



Taking the second supposition, if we look upon the term in its 

 altered form as a perturbation-term, this would lead to a very 

 improbable form for such a term, as it would depend upon the 

 absolute longitude of the moon, i.e. of a difference in longitude with 

 a fixed direction in the sidereal system or with the aequinox. 



There is however a third possibility, viz. that the second form is 

 the true one, but that we are not dealing with an inequality in the 

 ongitude, but with one in the right ascension, proceeding from the 

 Iparticular parts of the limb, which are used in the transit-observa- 

 tions, and their different distances from the centre of gravity of the 

 moon. In de Vos's researches, following New comb, the immediately 

 observed errors in R.A. were used, and in the last part of his 

 second paper he discusses the infiuence of this method. He shows 



10 



Proceedins^s Royal Acad. Amsterdam. Vol. XVI. 



