220 Selenography : tts Past, Present, and Future. (April, 
admits without difficulty of being computed for any given 
time, and may be held to include the paralla¢ctic or diurnal 
libration due to the same cause as the lunar parallax, and 
depending on the position of the observer with relation to the 
earth’s centre. ‘This libration, therefore, presents no diffi- 
culty: but with regard to the real libration of the moon, 
this is not the case, for there exists no trustworthy deter- 
mination of its amount; and this introduces some uncer- 
tainty into observation depending on the true lunar libration 
being known, which it is desirable should not be allowed to 
remain. ‘The existing uncertainty on this point lends addi- 
tional advantage to the employment of positions on the 
moon itself, rather than its limb, to measure points on the 
surface from, as under these conditions a small variation of 
the true lunar libration from the assumed produces no sen- 
sible error. As measured from the limb, the libration must 
be known corre¢tly, as any error produces a corresponding 
error in the resulting place; whilst this error cannot be 
eliminated by increasing the number of observations, but 
only by spreading them over a very considerable period of 
time, naturally a highly inconvenient condition for many 
reasons. 
It has been already mentioned, that from the mathe- 
matical investigation of Lagrange, Laplace, and Poisson, 
the complete theoretical conditions of this real libration in 
so far as results from the theoretical ellipsoidal form of the 
moon, is known. Its amount depends primarily upon the 
relation holding between the axes of the lunar ellipsoid, and 
on this point theory can afford little trustworthy data, con- 
sidering the imperfect condition of our present knowledge; 
while they depend in part upon the condition of the initial 
motions of the moon, which is at present unknown. The 
amount of the real libration must therefore be deduced from 
observation, or at least one of the principal periodical ine- 
qualities of the moon’s axial rotation constituting the real 
libration must be so found, and from that, by theoretical 
consideraticns, the others found. Mention has already 
been made of the observations commenced by Arago and 
Bouvard, and finished by Nicollet, with the view of deter- 
mining directly the amount of this real libration if sensible, 
and of the success attending Nicollet’s research based on 
these observations, resulting in the deduction of a value of 
4’ 49” for the maximum value of the periodical real libration 
in longitude corresponding to the annual equation. The 
results of this investigation are, however, unsatisfactory, 
the value deduced being very uncertain, owing to~the 
