840 LAPLACE. 
The admirable memoir of Lagrange upon the libra- 
tion of the moon seemed to have exhausted the subject. 
This, however, was not the case. 
The motion of revolution of our satellite around the 
earth is subject to perturbations, technically termed secu- 
lar, which were either unknown to Lagrange or which 
he neglected. These inequalities eventually place the 
body, not to speak of entire circumferences, at angular 
distances of a semi-circle, a circle and a half, &c., from. 
the position which it would otherwise occupy. If the 
movement of rotation did not participate in such pertur- 
bations, the moon in the lapse of ages would present in 
succession all the parts of its surface to the earth. 
- This event will not occur. The hemisphere of the 
moon which is actually invisible, will remain invisible 
for ever. Laplace, in fact, has shown that the attraction 
of the earth introduces into the rotatory motion of the 
lunar spheroid the secular inequalities which exist in the 
movement of revolution. 
Researches of this nature exhibit in full relief the 
power of mathematical analysis. It would have been | 
very difficult to have discovered by synthesis truths so 
profoundly enveloped in the complex action of a multi- 
tude of forces. 
We should be inexcusable if we omitted to notice the 
high importance of the labours of Laplace on the im- 
provement of the lunar tables. The immediate object of 
this improvement was, in effect, the promotion of mari- 
time intercourse between distant countries, and, what 
was indeed far superior to all considerations of mercan- 
tile interest, the preservation of the lives of mariners. 
Thanks to a sagacity without parallel, to a_perse- 
verance which knew no limits, to an ardour always 
