520 
MR. G. H. DARWIN ON THE 
for a period of twenty-four times that length.” He evidently places little reliance on 
the observations. 
The Earth. 
I adopt Laplace’s theory of internal density (with Thomson and Tail’s notation), 
and take, according to Colonel Clarke, the ellipticity of surface to be This value 
corresponds with the value 2'057 for the ratio of mean to surface density (theyof 
Thomson and Tait), and to 142° 30' for the auxiliary angle 6. 
The moment of inertia is given by the formula 
_ 
6 (/~ 1) ~ 
_ 
ma 3 . 
These values of 6 and f g ive 
eCZ-if 
fp _ 
= •83595. 
Whence 
C=-33438mcr. 
The numerical coefficient is the same as that already used in the case of the two 
previous planets. 
The moon’s mass being -g^-nd of the earth’s, the earth’s mass is f-f in the chosen unit 
of mass. 
With sun’s parallax 8"’8, and unit of length equal to earth’s mean distance 
8*87t 
° = 648000 
The angular velocity of diurnal rotation, with unit of time equal to the mean solar 
day, 
2rr 
n=- 
•99727 
Combining these values I find for the earth’s rotational momentum 
37-88 
Cn= 
10 10 
Writing in' for the moon’s mass, and neglecting the eccentricity of the lunar orbit, 
the moon’s orbital momentum'"' is 
mm' 
m + m 
-nc- 
* If we determine // from the formula 
and observe that /rM== (2 tt/ 365 , 25) 2 , we obtain 329,000 as the sun’s mass. This disagrees with the value 
315,511 used elsewhere. The discrepancy arises from the neglect of solar perturbation of the moon, and 
of planetary perturbation of the earth. 
