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Mr. W. R. Birt on the Moon's Libration. 



computing the librations, we do not appear to have at present 

 the means for tracing out on the moon's disk the curves repre- 

 senting the moon's equator and first meridian for any other 

 epochs than that of mean libration, when, as before mentioned, 

 they cross the disk in two straight lines intersecting at the 

 centre ; and this inquiry is perhaps the more important as show- 

 ing how necessary it is, for accurately mapping the surface, to 

 have good determinations of points of the first order. Taking, 

 therefore, the spot on the moon's surface at which the equator 

 and first meridian intersect each other, we may inquire the path 

 it will describe on the apparent disk during the changes of libra- 

 tion through one revolution of the nodes. 



" In fig. 9 let W E N S represent a small circle concentric with 

 the limb or margin of the apparent disk of the moon, W E being 



Fig. 9. 



a portion of the equator, and N S of the first meridian in mean 

 libration at the passage of the descending node and perigee re- 

 spectively, and o the point of intersection of the two (0° of lati- 

 tude and longitude), and o' the position occupied by the point o 

 by the joint effect of both librations, o E will consequently repre- 

 sent the greatest excursion of the point o in longitude, and o S 

 that in latitude, the equator being projected in the curve e 1 o 1 q, 

 and the first meridian in c o ] m. The displacement of o being in 

 the line o o\ the libration of the centre of the apparent disk a 

 will be W in longitude and N in latitude. It is easy to see that 

 the path of the point of intersection of the equator and first me- 

 ridian, a short time before and after the epoch of mean libration, 

 will be in a very narrow ellipse, the line o' o" being the major 



