DISTANCE, SIZE, AND MASS.

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parallax in the Alphonsine Tables, viz. 58', was de-duced from a comparison of many such observations.This would give a distance somewhat exceeding 59times the earth’s radius, or more exactly, with the pre-sent estimate of the earth’s dimensions, 235,000 miles.

Tycho Brahe , from his own observations, based onthe same principle, found for the moon’s horizontalparallax 6T, corresponding to a distance somewhatless than 223,000 miles.*

But a more satisfactory method of determining themoon’s distance is that which is based simply on theconsiderations discussed at pp. 8, 9,—in other words,the method of observing the moon from two distantstations whose exact position on the earth’s globe hasbeen ascertained. •

Let us suppose, for convenience of illustration, thatone station is the Greenwich Observatory, and theother the Observatory at the Cape of Good Hope .

* Before passing from the consideration of the method of deter-mining the moon’s distance by observations made at a single station,it may be mentioned that, as applied in later times, it depends onthe moon’s apparent displacement from her path, calculated for theearth’s centre. Now since the moon’s parallax always causes herto appear vertically below her true place, it is obvious that the wholeof this displacement will operate to displace her from her calculatedpath, only when the part of the path which she is at the momenttraversing is horizontal,—in other words, when she is on thehighest part of that path at the moment above the horizon.Although her actual parallax would then not be a maximum,d would act solely to shift her from her calculated path.According to the old astronomical systems, such occasions wereheld to be particularly favourable for lunar observations. Thehighest part of the moon’s path was called its nonagesimaldegree ,—a term also applied to the highest part of the elliptic,c 2