801 



We a[»i)i'oacIi, lliei-efoi-c, llic limils williiii wliicli (liis (lifrerenco 

 iiiiglit be ascribed to llie errors ol' obsorvulioii. However, I now 

 tliiiik, that (lie difrereiice which was foiiiid, small as it is, still 

 deserves closer consideration, and this especially with regard to 

 the xalne which Nkwcomb has dednced for this motion from the 

 long series of observed occnltations discussed by him in his lately 

 published posthumous paper Researches on the mution, of tJie moon. 

 He found (p. 225) 146435"29 ± 0"02, a result which appears 

 to be very accurate and which agrees almost exactly with mine. 



This induced me to consider in how far the small difTerence 

 might be ascribed to imicctiracies in the values, deduced from 

 observations, on which the theoretical calculations are founded. Such 

 inaccuracies might occur in those parts of the motion of the perigee 

 which depend upon the figure of the earth and of the moon. The 

 latter part is very small, but probably also very uncertain. It must 

 be calculated from the libration-phenomena and Brown deduced 

 foi" it, from Hayn's results, 0"03. 



Much greater (6"4) is the influence of the ellipticity of the earth, or 

 more exactly of the difFei-ence between its [)olar and equatorial 

 moment of inertia, which can be deduced both from the results of 

 gravity determinations and from measured teri-estrial arcs, by means 

 of relations that are connected with Olairaut's theorem. However, 

 these deductions are open to criticism, as Battermann also pointed 

 out. Still we see that, when the ellipticity of the earth is calculated 

 from the most reliable results, recently deduced from both classes 

 of observations the results agree well with each other, and this 

 makes it appear probable, that also the values deduced for the 

 difference of the moments of inertia and thereby for the constant 

 of the lunar perturbations would be fairly accurate. 



From the graxity determinations Helmert deduced 1 : 298.3 a 

 few yeai-s ago, and recently Hayford and Bowie deduced fi-om deter- 

 minations in the United States 1 : 298.4 ^). On the other hand, 

 Hayford, from his discussion of all the measured arcs in the united 

 States found 1 : 297.0, while in Europe, from the Russio-Scandi- 

 luivian arc of meridian, 1 : 298.6 was deduced. In the American 

 calculations reductions for isostatic compensation were applied. 



According to these results the value adopted by me 1 : 297.5 

 would a|)pear to l)e too large rather than too small. But now it 

 is remarkable, that all lunar perturbations which are caused by the 



1) A divi;5ion of the 8^) stations into 2 groups, an eastern and a western, led 

 to 1 : 297.8 and 1 : 299.6 respectively ; the addition to llie 89 stations of 10 stations 

 in Alaska gave, liowever, as the result from ail I : 3UU.4. 



