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widely distant stations, they had not the requisiteacquaintance with the geographical position of dif-ferent places to know what base-line they were makinguse of, it may appear surprising that Hipparchus orPtolemy should have been able to form any satis-factory estimate of the moon’s distance. But Hip parchus showed how the astronomer could deal withthis problem without leaving his observatory. Theearth’s daily rotation carries the astronomer’s stationeach day round a vast circle, and he has but to noticethe effect of this motion on the moon’s position, tobe enabled to form almost as satisfactory an estimateof her distance as by observations made at stationsfar apart. It is true that Hipparchus probably (andPtolemy certainly) regarded the earth as fixed. Butit is a matter of no importance (so far as the problemof determining the moon’s distance is concerned)whether we regard the daily rotation of the moonwith the celestial vault as due to the motion of theheavens themselves around the fixed globe of theearth, or as brought about by the rotation of the earthupon her axis.
Let us now consider the features of this methodattentively :—
In the first place, let us conceive the moon (fig. 2,Plate I.) to be at rest on the celestial equator, e E e'being the earth’s equator, and P the earth’s pole.Then, a place at e is carried by the diurnal rotationround the circle e E e'. If M e and M e touch thecircle eEe E', then, when the place is at e, the moon