Septembek 18, 1914] 



SCIENCE 



395 



it actually represents the deviations from a 

 plane 0".5 below the ecliptic. A similar 

 deviation was found by Newcomb. Certain 

 periodic terms have also been taken out. 

 The explanation of these terms will be re- 

 ferred to directly. 



The net result of this work is a deter- 

 mination of the constants of eccentricity, 

 inclination, and of the positions of the peri- 

 gee and node with practical certainty. The 

 motions of the perigee and node here agree 

 with their theoretical values when the new 

 value of the earth's ellipticity is used. The 

 only outstanding parts requiring explana- 

 tion are the deviations in the mean longi- 

 tude. If inquiry is made as to the degree 

 of accuracy which the usual statement of 

 the gravitation law involves, it may be 

 said that the index which the inverse square 

 law contains does not differ from 2 by a 

 fraction greater than 1/400,000,000. This 

 is deduced from the agreement between the 

 observed and theoretical motions of the 

 perigee when we attribute the mean of the 

 differences found for this motion and for 

 that of the node to a defective value of the 

 ellipticity of the earth. 



I have mentioned the mean deviation of 

 the latitude of the moon from the ecliptic. 

 There are also periodic terms with the mean 

 longitude as argument occurring both in the 

 latitude and the longitude. My explana- 

 tion of these was anticipated by Professor 

 Bakhuysen by a few weeks. The term in 

 longitude had been found from two series 

 of Greenwich observations, one of 28 and 

 the other of 21 years, by van Steenwijk, 

 and Professor Bakhuysen, putting this with 

 the deviations of the mean latitude found 

 by Hansen and himself, attributed them to 

 systematic irregularities of the moon's 

 limbs. 



"What I have done is to find (1) the devi- 

 ation of the mean latitude for 64 years, (2) 

 a periodic term in latitude from observa- 



tions covering 55 years, and (3) a periodic 

 term in longitude from observations cover- 

 ing 150 years, the period being that of the 

 mean longitude. Further, if to these be 

 added Newcomb 's deviations of the mean 

 latitude derived (a) from immersions and 

 (6) from emersions, we have a series of five 

 separate determinations — separate because 

 the occupations are derived from parts of 

 the limb not wholly the same as those used 

 in meridian observations. Now all these 

 give a consistent shape to the moon's limb 

 referred to its center of mass. This shape 

 agrees qualitatively with that which may 

 be deduced from Franz's figure. 



I throw on the screen two diagrammatic 

 representations" of these irregularities ob- 

 tained by Dr. F. Hayn from a long series 

 of actual measures of the heights and 

 depths of the lunar formations. The next 

 slide shows the systematic character more 

 clearly. It is from a paper by Franz.* It 

 does not show the character of the heights 

 and depths at the limb, but we may judge 

 of these from the general character of the 

 high and low areas of the portions which 

 have been measured and which extend near 

 to the limbs. I think there can be little 

 doubt that this explanation of these small 

 terms is correct, and if so it supplies a satis- 

 factory cause for a number of puzzling in- 

 equalities. 



The most interesting feature of this re- 

 sult is the general shape of the moon 's limb 

 relative to the center of mass and its rela- 

 tion to the principle of isostasy. Here we 

 see with some definiteness that the edge of 

 the southern limb in general is further from 

 the moon's center of mass than the northern. 

 Hence we must conclude that the density 

 at least of the crust of the former is less 

 than that of the latter, in accordance with 



5 Abh. der Math.-Phys. Kl. der Kon. Siidhs. Ges. 

 der Wiss., Vols. XXIX., XXX. 



6 Konigsberger Astr. Beob., Abth. 38. 



