78 LIBRATION OF THE MOON. [SECT. ix. 



force, therefore her polar axis is the least. The other two 

 are in the plane of her equator, but that directed towards 

 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, con- 

 stantly brings the greatest axis, and consequently the same 

 hemisphere, towards 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 centres 

 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 perceptible ; 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 rendered the libration sensible. According to 

 analysis, a similar libration exists in the motions of Jupiter's 

 satellites, 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 of the 

 western edge of her disc is visible, which is invisible at her 

 setting, and the contrary takes place with regard to her 

 eastern edge. There are also librations arising from the 

 relative positions of the earth and moon in their respective 

 orbits ; but, as they are only optical appearances, one hemi- 

 sphere will be eternally concealed from the earth. For the 

 same reason the earth, which must be so splendid an object 

 to one lunar hemisphere, will be for ever veiled from the 

 other. On account of these circumstances, the remoter 

 hemisphere of the moon has its day a fortnight long, and a 



