1310 . 
of which was computed to two decimals only, and may thus be 
(0.005 in error. The mean error of the sum can be assumed on 
this account to be about + 0".02. The mean error of the differences 
dé and dQ thus becomes + 0".03. 
2. The terms due to the figure of the earth are, by Brown’s 
theory, the factors being given as logarithms : 
dis — [3.5907] J, 
dj), = — [8.5620] J, 
With e—! = 295.96 + 0.20 (see the preceding paper), we have 
J = 0.0016502, from which 
dw = 6".430 + 0".008, 
dQ, = — 6.019 + 0:007. 
There thus remains for the figure of the moon 
IF do= + 0".16 + 0".03, 
IQ, = — 020° + 0.03 … (1 
II dj = + 0.10 + 0.03, 18 Se 
The values used in Brown’s theory are 
do = +. 0".03, dQ) = — 0".14. 
The contradiction is apparently very great. It will be shown, 
however, that the values (1) can very well be ascribed to the figure 
of the moon. Brown’s values depend only partially on actually 
determined constants, from which they are derived by means of 
En 
) 
G 
the hypothesis that the ratio g==} —— has the same value for the 
Mb? 
moon as for the earth. It will be seen below that the values (1) 
lead to a different value g’. 
Let A’, B’,C’ be the moments of inertia, J/’ the mass, and 6’ 
the largest radius of the moon. Further, in analogy with the notation 
used for the earth 
2C'—A'-- B' B'-A’ 
ale — 5 vie — . Vb? 
2M'b" 
Then the theoretical expressions for the motions of the perigee and 
the node are 
daw = + 390" J'—1027"K’, 
gnl IE TN 
A= ATO EK (2) 
The coefficients are easily derived from Brown’s theory, Chapter 
V, §378 5), where however db, = 6'.57, db, = —6".15, must be 
1) Memoirs R. Astr. Soc, Vol. LEX, Part I, p- 81, 
