64 ITERATIONS OF THE MOON SECT. IX. 



affected by the same inequalities, it would cease exactly 

 to counterbalance the motion of revolution ; and the 

 moon, in the course of ages, would successively and 

 gradually discover every point of her surface to the 

 earth. But theory proves that this never can happen ; 

 for the rotation of the moon, though it does not partake 

 of the periodic inequalities of her revolution, is affected 

 by the same secular variations, so that her motions of 

 rotation and revolution round the earth will always 

 balance each other and remain equal. This circum- 

 stance arises from the form of the lunar spheroid, which 

 has three principal axes of different lengths at right 

 angles to each other. 



The moon is flattened at her poles from her centri- 

 fugal force ; therefore her polar axis is the least. The 

 other two are in the plane of her equator ; but that 

 directed toward the earth is the greatest (N. 139). The 

 attraction of the earth, as if it had drawn out that part 

 of the moon's equator, constantly brings the greatest 

 axis, and, consequently, the same hemisphere, toward 

 us, which makes her rotation participate in the secular 

 variations of her mean motion of revolution. Even if 

 the angular velocities of rotation and revolution had not 

 been nicely balanced in the beginning of the moon's 

 motion, the attraction of the earth would have recalled 

 the greatest axis to the direction of the line joining the 

 centers of the moon and earth, so that it would have 

 vibrated on each side of that line in the same manner as 

 a pendulum oscillates on each side of the vertical from 

 the influence of gravitation. No such libration is per- 

 ceptible ; and, as the smallest disturbance would make 

 it evident, it is clear that, if the moon has ever been 

 touched by a comet, the mass of the latter must have 

 been extremely small. If it had been only the hundred 

 thousandth part of that of the earth, it would have ren- 

 dered the libration sensible. According to analysis, a 

 similar libration exists in the motions of Jupiter's satel- 

 lites, which still remains insensible to observation, and 

 yet the comet of 1770 passed twice through the midst 

 of them. 



The moon, it is true, is liable to librations depending 

 upon the position of the. spectator. At her rising, part 



