1312 
Referring to the definitions given above we havé 
JL PK =9 ig 
Taking now 
B = 0.000626 + .000002, 
we find 
g' = 0.70 + 0.11, 
which differs considerably from the value for the earth (g = 0.502). 
If f is brought into evidence in the expressions for do and df 
we have, 
da = {| — 832" + 1222" f] (J’ + EK), 
ag = — A470" (F' + 4 Ry: 
From ds, we find, of course, the value of /' + 4 K' stated above, 
and then from do: ; 
uf LE (1+ II) m.e. 5 
fz DE 0.87 0.92° a= 0-06" 6) 
Generally f is determined from the coefticients of certain terms 
in the libration in longitude, which depend on y*), and of which 
the largest are, for f= 4, — 156" sin S and + 22" sin M, where 
S and M/ are the mean anomalies of the sun and moon respectively. 
The geocentric amplitudes of these oscillations are 1".4 and 0".2 
respectively. It is hardly surprising that the determinations of such 
small quantities by different observers are not very accordant. The 
results are 
FRANZ F = 048717 2 0027S 
STRATTON 0.50 + 0.03 
HAYN 0.75 + 0.04, 
The results of Franz and Srrarron are both derived from the 
observations by Scurürer. The results of the different observers are 
very discordant amongst themselves as well as with the value (5). 
It seems certain that the mean errors of the values derived from 
the observations of the libration are no true measure of the real 
accuracy. The true value of f is certainly much nearer to unity 
than to 4. The value found by Scurürer and others for the coefficient 
of the principal term of the libration in longitude must then be due 
to systematic errors in the observations with a period of a year’). 
1) [t would thus be more natural to take as unknown 5 1—f. All writers 
have however expressed their results in terms of f. 
2) See also Hayn, Selenographische Koordinaten II, p. 135—136. He there finds 
f = 0,85 + 0.07 and explains how the smaller values found by FRANz and Harr- 
wia (0.47) can be due to errors in the adopted radius-vector of MösrinG A which, 
through optical libration, give rise to a spurious oscillation of yearly period, if the 
observations are made near the time of full moon. 
