14

THE MOON:

take place in the circle M m, but in a path inclined tothat circle. But it is obviously in the power of mathe-matics to take into consideration all the effects due tothe moon’s real motion, and thus, as in the simplercase imagined, to deduce the relation between E Pand M e P.

But we may now look at the problem in a somewhatdifferent light. Hitherto we have only consideredthe effect of the earth’s size in causing an apparentwant of uniformity in the moon’s rate of motion. Wecan see, however, from fig. 2, that what in realityhappens is that the moon is not seen in the* samedirection from points on the earth’s surface as fromthe centre of the earth; and that the apparent dis-placement is greater or less according as the moon isnearer to or farther from the horizon. If we supposeM to represent the moon’s place when she is overhead,we see that she is seen in the same direction from Eas from P. But when she is on the horizon at M E ,she is seen as though ninety degrees from the pointoverhead; whereas, as seen from P, she would be lessthan ninety degrees from that point: that is, she isseen from E lower down than she is in reality. Inany intermediate position, as M', she would be seenlower down from E than from P; but not so muchdepressed as when she is near the horizon.

But it is clear that this is equally true, whereverthe station of the observer may be. The moon isalways seen below the place she would occupy if shecould be observed from the earth’s centre, except