206 Selenography : its Past, Present, and Future. [April, 
About the commencement of the present century, the 
theoretical results obtained by Lagrange, with respect to 
the lunar librations, were confirmed by a full investiga- 
tion of Laplace, who showed, moreover, that the lunar secu- 
lar inequalities were without influence on the relation 
between the periods of rotation and orbital revolu- 
tion, and the nodes of the lunar equator and orbit. Later, 
the theoretical investigation of this question was completed 
by Poisson, who showed that some minor inequalities of the 
second order, affecting the lunar elements neglected by 
Lagrange, were likewise without influence on the above 
relations. 
As already mentioned, owing to the ellipsoidal form of the 
moon, a real libration must ensue from the vibratory motion 
of the longer axis of the moon, due to the endeavour of the 
earth’s attraction to keep it directed towards the earth’s 
centre; whilst the causes producing the moon’s optical 
libration carried it on alternate sides of this direction. 
Laplace and Poisson both investigated the condition of this 
real libration, whose amount depended on the mutual rela- 
tions existing between the lunar axes, and from which it 
appeared that, though all the inequalities in the true 
longitude and latitude of the moon must produce an effect 
on the moon, yet all these would be insensible, except in the 
case of those inequalities known as the annual equation and 
the equation of the centre, both of whom might be expected 
from the probably theoretical form of the moon to produce 
perhaps sensible real librations in longitude, though the 
latter could not amount to one-fifth of the former. 
At the desire of Laplace, Bouvard and Arago, in 1806, 
undertook the investigation of this point, to detect, if pos- 
sible, this theoretical real libration, and made during that 
year 18 observations of the position of the lunar spot Ma- 
nilius, but their plans were interrupted by other work. 
Bouvard, two years after, renewed his work, and between 
September, 1808, and October, 1810, obtained 124. measures 
of the position of Manilius. Employing these observations 
as a basis, Nicollet, in 1816-18, undertook the investi- 
gation of the lunar libration, with the view of confirming 
by observation the theory of libration, and dete¢ting any 
sensible real libration, from whose amount the form of the 
moon might be determined. As a result from the 124 ob- 
servations made by Bouvard during 1808-10, Nicollet 
showed the distance between the nodes of the lunar equator 
and orbit on the ecliptic could not exceed g’ 19’, a quantity 
so far within the errors of observation as to show its origin 
