. Astronomy for students and general readers . been oneof the most interesting scientific problems presented to thehuman mind. The first known attempt to effect a solu-tion of the problem was made by Aeistaechus, who flour-ished in the third century before Christ. It was foundedon the principle that the time of the moons first quarter 224 ASTRONOMY. will varj with the ratio between the distance of the moonand sun, which may be shown as follows. In Fig. 68let jE represent the earth, M the moon, and 8 the the sun always illuminates one half of the lunarglobe, it is evident that when on
. Astronomy for students and general readers . been oneof the most interesting scientific problems presented to thehuman mind. The first known attempt to effect a solu-tion of the problem was made by Aeistaechus, who flour-ished in the third century before Christ. It was foundedon the principle that the time of the moons first quarter 224 ASTRONOMY. will varj with the ratio between the distance of the moonand sun, which may be shown as follows. In Fig. 68let jE represent the earth, M the moon, and 8 the the sun always illuminates one half of the lunarglobe, it is evident that when one half of the moons diskappears illuminated, the triangle EMS must be right-angled at M. The angle M E S can be determined bymeasurement, being equal to the angular distance betweenthe sun and the moon. Having two of the angles, thethird can be determined, because the sum of the threemust make two right angles. Thence we shall have theratio between EM, the distance of the moon, and ES,the distance of the sun, by a trigonometrical Fig. 70. Then knowing the distance of the moon, which can bedetermined with comparative ease, we have the distance ofthe sun by multiplying by this ratio. Aeistaeohus con-cluded, from his supposed measures, that the angle M ESwas three degrees less than a right angle. We should then have -pr^ = sin 3° = Jj very nearly. It would follow from this that the sun was 19 times the distanceof the moon. We now know that this result is entirelywrong, and that it is impossible to determine the timewhen the moon is exactly half illuminated with any ap-proach to the accuracy necessary in the solution of theproblem. In fact, the greatest angular distance of the SOLAR PARALLAX. 335 earth and moon, as seen from the sun—that is, the angleESM—is only about one quarter the angular diameter ofthe moon as seen from the earth. The second attempt to determine the distance of theSim is mentioned by Ptolemy, though Hippaechus may bethe real inventor of it. I
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