1300 
and the uncertainty in the numerical part is no more than a few 
units in the last decimal place given. 
We also need the ratio 
2C—A—B 
= one 
For the ideal surface we have A, = B, and consequently 
‘ C ET A, H CA, 
1 
4 f == — Ee EE — - 
PN C, 
The true moments of inertia A and B may however be unequal. 
The ratio H can be determined with great accuracy from the 
constant of precession. The best modern determinations of this 
constant are (for 1850): 
NewcomB (with corrections by Hoven and Harm) *) p,=50".2486 
Boss *) 50°.2511 
Dyson and THACKERAY“) 50 .2503 
We can thus take 
p, = 50".2500 + 0".0010. 
The lunisolar precession then becomes 
p= 90.378. 
If now we take for the mass of the moon 
p= Slot 6.07, 
we find 
H = 0.0032775 + 0.0000022. 
The uncertainty is almost entirely due to w and not to p. 
So far no assumptions have been made regarding the constitution 
of the earth. The theory of Crarraur now leads to a determination 
of the ratio of J and H. We are thus able from H to compute 
J, and then ¢ from (1). Rapav’s transformation of CLAIRAUT’s 
differential equation gives, to the first order of « *), 
i= ae = hee de ee . Vai 
J 
where, also to the first order, 1 = 3 — 5 —, and /\, is a certain 
& 
1) Monthly Notices, Vol. LXX, p. 587. See also: The Observatory, July 1913, 
p. 299. 
2) Astronomical Journal, Vol. XXVI. p. 118. 
3) Monthly Notices, Vol. LXV, p. 443. 
4) This and other formulas of the theory of GrLATRAUT will be collected in the 
following paper. 
