DISTANCE, SIZE, AND MASS.

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radius, where P B represents the distance of the moon.Such a construction—or, if preferred, the correspond-ing calculation—would thus at once show what relationthe moon's distance bears to the earth’s diameter.

It is obvious that although atmospheric refractioncauses the moon’s apparent place, when she is nearthe horizon, to be somewhat higher than the place shewould have if the atmosphere did not exist, yet thisis a circumstance which the astronomer can take fullyinto account; since it is in his power, by observingthe stars, to determine the exact value of atmosphericrefraction on celestial bodies at different altitudes.

This method of determining the moon’s distance isnot the less available, that the moon is not at rest.Thus, suppose the moon to be travelling, in the circleM m, fig. 3; then, if the rate of the moon’s motion beknown,—that is, the length of time in which the mooncompletes the circuit of the stars,—the observer canapply to the moving moon precisely the same con-siderations which he would apply to the moon regardedas at rest. He would still be able to compare togetherthe periods during which the moon is above and belowthe horizon, since her own motion would cause boththese periods to be correspondingly affected. Hewould thus obtain the two unequal arcs M E M M w andM, t to M e (fig. 3), which would give him the crossline M e E M w , as before, and therefore the relativemagnitude of E P and P M E .

The actual problem is rendered somewhat lesssimple by the fact that the moon’s motion does not