ae oad inten Ce he ae gen, - — a! 
- i % ’ 
LIBRATION OF THE MOON. 337 
with a second instrument termed the mural circle. These 
two inequalities of very different magnitudes connected 
with the cause which produces them by analytical com- 
binations of totally different kinds have, however, both 
conducted to the same value of the ellipticity. It must 
be borne in mind, however, that the ellipticity thus de- 
duced from the movements of the moon, is not the ellip- 
ticity corresponding to such or such a country, the 
ellipticity observed in France, in England, in Italy, in 
Lapland, in North America, in India, or in the region of 
the Cape of Good Hope, for the earth’s materials having 
undergone considerable upheavings at different times and 
in different places, the primitive regularity of its curva- 
ture has been sensibly disturbed by this cause. The 
moon, and it is this circumstance which renders the result 
of such inestimable value, ought to assign, and has in 
reality assigned the general ellipticity of the earth; in 
other words, it has indicated a sort of mean value of the 
various determinations obtained at enormous expense, 
and with infinite labour, as the result of long voyages 
undertaken by astronomers of all the countries of Eu- 
rope. 
I shall add a few brief remarks, for which I am mainly 
indebted to the author of the Mécanique Céleste. They 
seem to be eminently adapted for illustrating the pro- 
found, the unexpected, and almost paradoxical char- 
acter of the methods which I have just attempted to 
sketch. . 
What are the elements which it has been found neces- 
sary to confront with each other in order to arrive at 
results expressed even to the. precision of the smallest 
decimals ? 
On the one hand, mathematical formule deduced from 
15 
