OF ASPECT, ROTATION, AND LIBRATION. 189

motion of this point involves implicitly the whole theoryof the moon’s motions.

We have not considered thus far the effects oflibration on those parts of the moon’s disc which lieso near to the edge that they pass at times out ofsight. These movements might be dealt with likethose we have just been considering, by regardingthem as due to two distinct libratory motions takingplace about P P' and E E' at known rates. But thematter may be simplified by noting that where (as inthe present instance) such small arcs as from 6° to 10°are concerned, the libratory motions of points near therim of the mean lunar disc may be regarded as vir-tually carrying those points backwards and forwardsat right angles to the rim. And it is very easy to seewhat will be the extent of this libratory motion at anygiven part of the rim when the libration of the meancentre is known. Thus, take the point P (fig. 72,Plate XV.). Here there is always an alternate sway-ing at right angles to the rim equal in range to thelibration in latitude ; for whatever the oval traversedby the mean centre, it always ranges in latitude fromAG to A' G'. In like manner at E and E' there isalways an alternate swaying at right angles to thelimb equal in range to the libration in longitude ; forthe oval traversed by the mean centre always rangesin longitude from A A' to G G'. But take the partM 2 of the disc’s edge. Here, when the mean centreis librating along A 0 G', points near the edge swaybackwards and forwards at right angles to the edge