148 



results, in the second place the results show distinctly that the smaller 

 co-efficient satisfies the observations less well. From all this it seems 

 to me that the supposition that the new term is due to a deviating form of 

 the limb gains in probability, and we must then conclude that, while the 

 polar arcs require a centre of figure about 0".8 south of the centre 

 of gravity, the aequatorial arcs deviate in the opposite sense and 

 require a centre of figure about 0".9 to the north of the centre of 

 gravity. This is identical with saying that the northern extremities 

 of these arcs lie 0".35 further outside, and the southern 0".35 further 

 inside relatively to the centre of gravity. If we take into account 

 that the term has not exactly tlie form « cos I, the conclusion is but 

 little altered. 



These conclusions now agree with the results found by Battermann 

 from his occultations, who deduced from them on the average a 

 centre of figure coinciding with the centre of gravity. 



Our results can be further tested by the results which Hayn, in 

 his " Selenociimpliuclte Koordinaten" deduced for the form of the lunar 

 limb from his measurements in Leipzig and Hartwig's in Strassburg 

 and also by the results obtained by Przybyllok in his ''Das Profil 

 der Ra?idpartien des M ondes" . (Mitteilungen der Gr. Stern warte zu 

 Heidelberg, XI). 



Hayn gives in his 3"^ paper on p. 77, for a mean libration, the 

 mean radii for arcs of 10° and of 30° counted from the North 

 pole along the limb of the moon (Argument P), and I deduced 

 analogous results from Przybyllok's Tafel der Randkorrektionen. 



In this way I found 



Thus for parts of the limb diametrically opposed to each other 

 Hayn finds deviations in the same sense, which does not agree with 

 the results obtained by de Vos. The agreement with Przybyllok is 

 better, but not yet satisfactory. 



Still I think that the explanation of the results by the form of 

 the lunar limb is the most probable, or, at any rate, the least 

 improbable, and certainly the investigation of de Vos in connection 

 with mine in 1912 confirms Hayn's remarks (I.e. p. 75) with regard 

 to the great imjiortance of the study of the deviations of the moon's 

 limb, also for the determination of the moon's position. 



