1875.) Selenography: its Past, Present, and Future. 219 
possessed some special importance or interest of their own. 
Measured in an analogous method to Madler’s, they should 
preferably rest on two separate measures from different 
points, and as the increase in the number of available points 
would enable their distances from these to be much reduced 
from what Madler was obliged to use, their accuracy would 
be probably nearly tripled. 
In employing, as a point from which to measure other 
positions, a lunar spot instead of the limb, a considerable 
advantage is gained, inasmuch as a comparative great dis- 
crepancy between the assumed libration of the moon and 
the true would produce a scarcely sensible error in the 
resulting position; whereas, as measured from the limb, 
any error in the assumed libration produces a corresponding 
error in the position of the points, and thus, in the former 
case, the reduction of the measures made is much simplified, 
an additional advantage of no slight importance. Any 
conne¢tion, moreover, in the assumed position of the stand- 
ard point that further observations may indicate, would also 
admit of being applied without trouble sufficiently approxi- 
mately to the positions deduced from it by measures, unless 
it was of very considerable magnitude, which would hardly 
be conceivable under the conditions; and this, likewise, is 
no slight advantage. 
So far, with reference to the measurements for the deter- 
mination of the position on the moon’s surface of the principal 
lunar objects necessary for the proper construction of a 
trustworthy map of the moon, and for the further progress 
of those selenographical observations, requisite for any ad- 
vancement to be made in the solution of the many problems 
in connection with our satellite, and in the construCion 
from the visible records of the past history of the companion 
to the earth. 
Intimately connected with the subje&t of the measure- 
ment of the objects upon the moon is that of its librations, 
and a proper knowledge of the conditions introduced by 
these into lunar observations is essential to accurate seleno- 
graphical work. It has been already stated that the moon 
is subjected to two classes of librations, the greatest, which 
may be termed the optical libration, being due to the 
nearly uniform rotation of the moon on its axis, and its 
variable motion in its orbit, in conjunction with the results 
of the inclination of the lunar equator and orbit to the 
ecliptic ; whilst the other may be called the real libration, 
and is due to the actual motion as if it were of the major axis 
which is directed towards the earth. The optical libration 
