1319 
homogeneity indicates that in the moon the density wcreases from 
the centre outwards. A small excess could of course be due to 
irregularities in the distribution of the mass. But, unless we are 
prepared to admit a considerable excess of density of the outer 
layers of the moon over the mean density, we are led to the con- 
clusion that the true value of y’ is certainly not larger and probably 
smaller than the value (16). Now this value was determined from 
the observed motion of the node combined with the adopted com- 
pression of the earth e—! = 296.0. For e—! = 297.0 we should have 
found g’ = 0.85, and Hrtmert’s value 298.3 gives y”= 1.02. Thus, 
if the observed motion of the node is accepted, any value of ¢ 
appreciably smaller than '/,,, becomes very improbable. 
7. From (7) and (9), combined with (11), we find easily 
70, + 3%, 506,540, + PL, 
The numerical value is approximately 
0, = *, = 0.0000078. 
Therefore 
0.0000156 < 6, < 0.0000390 
0.0000117 < », < 0.0000292. 
Take e.g. 
6, = 0.0000300, rv, = 0.0000225. 
We then have from (6) 
tgn 0.0000144 EE eh: 0000108 
2 M'b" : 2 M'b* ; 
and consequently 
J 9000028... K' = 0.000081. 
For the limiting case of homogeneity, these values would become 
S= 0.000082 ‚°° K' = 0.000018. 
The values derived from the motions of the perigee and the 
node were 
J' = 0.000422 + .000055 , K'=— 0.000033 + „000032. 
Further we have from (9), with the above value of 0, : 
5 C a 1 4 
7, = 3| 1 — — — | = 9.60. 
2 MO B, 
Then from (15) taking #,=1, we find 7 =0.494 and conse- 
quently : 
