204 Selenography : its Past, Present, and Future. [April, 
making many new observations during a period of twenty- 
two years, announced in 1693 his complete theoretical 
solution of the problem of the lunar libration, and showed 
the peculiar relation between the nodes of the moon’s 
equator and orbit on the ecliptic; so that planes through 
the moon’s centre, parallel to the planes of its equator, 
orbit, and ecliptic, intersect one another on the same 
straight line, and the two former always on opposite sides 
of the third—the ascending node of the lunar equator being 
thus coincident with the descending node of the moon’s 
orbit, both on the ecliptic. Cassini deduced from his obser- 
vation the value 2° 30’ for the inclination of the lunar 
equator to the ecliptic, and a mean value of 5° 0’ for the 
inclination of the orbit to the ecliptic, thus completing 
a work of the very highest importance to selenography. 
Cassini also published in 1680 a small map of the moon, 
some 20 inches in diameter, containing the results of his 
earlier observations, but, like its predecessors, only founded 
on eye estimates of the positions of the spots ; whilst though, 
from his superior optical means, it was more complete, than 
Hevelius’s, it was on a whole not more accurate, and for 
a considerable period remained little known. 
In 1748 Tobias Mayer, the celebrated mathematician and 
astronomer of Gottingen, as part of his researches on the 
moon, investigated the problem of the lunar lbrations, and 
by determining the difference in right ascension and decli- 
nation between the apparent centre of the moon and the 
lunar spots Manilius, Dionysius, and Censorinus, obtained 
material for ascertaining how far Dominic Cassini’s theory 
of libration agreed with observations. By the middle of 
1849 Mayer had obtained 27 measures of Manilius, 9 of 
Dionysius, and 12 of Censorinus; and in a memoir in the 
volume for 1750 of the ‘‘ Societe Cosmagraphique,” of 
Nuremburg, by employing equations of condition, showed 
that the inclination of the moon’s equator to the ecliptic was 
1° 29’, and that sensibly Cassini’s theory was correct, though 
he found a slight difference between the positions of the 
nodes of the lunar equator and orbit, which he made 3° 45’ 
apart, a result sufficiently small to indicate that its origin was 
in the errors of observation. 
Mayer had intended to form a complete map of the moon 
in 25 sections, and with this view made a series of 47 ad- 
ditional measures of 21 lunar spots, besides those already 
mentioned ; whilst he determined the position of 63 other 
formations by careful estimates, in which he excelled, of 
their distance from the measured *obje¢ts. From the few 
