i873«] Condition of the Moon's Surface. 491 



very considerable indeed on places considerably removed 

 from o (Fig. 1). It is indeed clear that places which, when 

 the moon is in mean libration, are near the lunar limb, but 

 not near enough to be carried actually out of view, must be 

 very importantly affected, since d e (Fig. 3) would vanish 

 altogether with a slight reduction of the angle at which the 

 parallels of the figure are inclined to A c. 



Remembering that every point of the visible lunar hemi- 

 sphere undergoes libration, and that in every lunar month 

 there is a complete oscillation of the point o over a certain 

 libration-ellipse, which is continually varying in different 

 months as well in position and size as in the direction in 

 which it is traversed, while the maximum libratory effects 

 (always considerable) are attained at different epochs in 

 different lunations, we see that we have here a very impor- 

 tant cause of changes in appearance. It is utterly im- 

 possible that any surface like the moon's could, as a whole, 

 undergo such remarkable librations without some note- 

 worthy changes of appearance being produced, even without 

 those changes of illumination which have been referred to 

 above. Further evidence on this point will presently be 

 cited. 



Now the cycle of libratory changes for the moon, regarded 

 without reference to her phases, is a long one. It amounts, 

 on the average, to almost exactly six years ; and we may 

 say that the same libratory condition is not restored until 

 this period has elapsed. There are momentary coincidences 

 of position, but these positions are arrived at, and passed 

 away from, in different ways, until at the end of the long 

 cycle the same series of changes is re-commenced. But this 

 is not all. We must consider phase in this inquiry; indeed, 

 it is the most important consideration of all. Now, the six- 

 yearly period brings back the same libratory condition, but 

 not the same phase when given libration effects are pro- 

 duced. This is manifest if we consider that the node 

 regredes only 19 21/ per annum, and therefore in six years 

 regredes little more than 116 , having, therefore, a totally 

 different position with respect to ecliptical longitude. In 

 two six-yearly periods it regredes rather more than 233 , or 

 has still a totally different position. In three six-yearly 

 periods it regredes 348° 23' 24", or is now n°36 / 36" from its 

 first position. This is the nearest approach. The fourth, 

 fifth, and sixth six-yearly periods bring the node to 

 23 13' 12" from its first position. We may call this a 

 second eighteen-yearly period. Ten such eighteen-yearly 

 periods bring the node 116 6' from its first position, and 



