HISTORY OF PHYSICAL ASTRONOMY.

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lie found a satisfactory agreement between the results of theory and thoseof observation. But when he was enabled by means of the astrolabe toobserve the position of the moon in other parts of her orbit, and moreespecially in the quadratures, he detected a series of discordances betweenher actual and computed places, which seemed irreconcilable with thetheory of her motion as established by him. The true explanation ofthese anomalies was reserved for Ptolemy ; but it must be borne in mindthat Hipparchus first detected their existence, and that he also executeda great number of the observations which served as the basis of Ptolemy ’sresearches on the subject*.

Hipparchus did not fail to make numerous observations of the planets,which at a subsequent period formed precious materials to Ptolemy inestablishing the theory of their movements. But the most remarkableresult which crowned the labours of this great astronomer was his dis-covery of the precession of the equinoxes. It was doubtless with theview of enabling posterity to arrive at a more accurate knowledge of thissingular phenomenon, that he conceived the gi-and design of determiningthe positions of all the stars visible in the firmament, so as to give afaithful representation of the celestial sphere as it appeared in his time.It was necessary for this purpose to determine the exact place of eitherof the equinoxes among the stars, but a serious obstacle stood in the wayof effecting this object. The position of the equinox in the celestialsphere is determined by the passage of the sun across the equinoctialcircle; but when the sun is above the horizon there are no stars visiblewhose position might be determined with respect to him, and when thestars have become suitable objects for observation, the Sun has alreadydisappeared. This seems to have formed an insuperable impediment tothe earlier astronomers in their endeavours to ascertain the absolute rightascension or longitude of a star. Hipparchus devised two distinct modesof obviating this difficulty. One of these was by observations madeduring eclipses of the moon. Since the angular distance between thesun and moon is exactly 180° on all such occasions, it follows that theplace of the moon during an eclipse is directly deducible from that ofthe sun; and as the place of the sun with respect to the equinox is knownby the solar tables, the place of the moon with respect to the equinoxhence becomes known also. It is clear, then, that if the difference of thelongitudes or the right ascensions of the moon and a star be determinedwith the astrolabe during the occurrence of a lunar eclipse, the absoluteposition of the star with respect to the equinox may hence be ascertained f.

* It is a curious fact that the inequality here referred to, termed the evection, confoundsitself in syzygees with the elliptic inequality or the equation of the centre. Hence it hap-pened that observations confined exclusively to eclipses failed to indicate its existence.Ptolemy , in his preliminary exposition of the inequality, cites two observations, one byHipparchus and the other by himseif, both made when tire moon was in the second quadra-ture. The observation of Hipparchus is of so exceptional a nature, that it is impossiblenot to conclude that it was taken from a great mass of observations, although Ptolemy himself is silentupon this point. In the first place the apsides were in syzygees; secondly,the moon was in quadratures; thirdly, she was in the nonagesimal, or that point in herdiurnal course at which the effect of her parallax took place wholly in latitude. ( Syntaxis ,lib. v., cap. iii.) With the view of confirming bis explanation of the inequality, Ptolemy subsequently cites two additional observations of the moon, both of which are in this caseby Hipparchus. ( Syntaxis , lib. v., cap. v.)

t If an eclipse of the moon happened when the sun was in either of the equinoxes,the moon would necessarily be in the opposite equinox, and hence the position of thelatter point among the stars might be ascertained without the use of solar tables, bysimply measuring the distance, in right ascension, of the moon from any of the neighbour-