But what is even more decisive as showing that the Hindûs observed the stars, and in the same way that we do, marking their position by their longitude, is a fact mentioned by Augustinus Riccius that, according to observations attributed to Hermes, and made 1,985 years before Ptolemy, the brilliant star in the Lyre and that in the heart of the Hydra were each seven degrees in advance of their respective positions as determined by Ptolemy. This determination seems very extraordinary. The stars advance regularly with respect to the equinox: and Ptolemy ought to have found the longitudes 28 degrees in excess of what they were 1,985 years before his time. Besides, there is a remarkable peculiarity about this fact, the same error or difference being found in the positions of both stars; therefore the error was due to some cause affecting both stars equally. It was to explain this peculiarity that the Arab Thebith imagined the stars to have an oscillatory movement, causing them to advance and recede alternately. This hypothesis was easily disproved; but the observations attributed to Hermes remained unexplained. Their explanation, however, is found in Hindû Astronomy. At the date fixed for these observations, 1,985 years before Ptolemy, the first point of the Hindû Zodiac was 35 degrees in advance of the equinox; therefore the longitudes reckoned for this point are 35 degrees in excess of those reckoned from the equinox. But after the lapse of 1,985 years the stars would have advanced 28 degrees, and there would remain a difference of only 7 degrees between the longitudes of Hermes and those of Ptolemy, and the difference would be the same for the two stars, since it is due to the difference between the starting-points of the Hindû Zodiac and that of Ptolemy, which reckons from the equinox. This explanation is so simple and natural that it must be true. We do not know whether Hermes, so celebrated in antiquity, was a Hindû, but we see that the observations attributed to him are reckoned in the Hindû manner, and we conclude that they were made by the Hindûs, who, therefore, were able to make all the observations we have enumerated, and which we find noted in their Tables.
6th. The observation of the year 3102, which seems to have fixed their epoch, was not a difficult one. We see that the Hindûs, having once determined the moon's daily motion of 13° 10´ 35´´, made use of it to divide the Zodiac into 27 constellations, related to the period of the moon, which takes about 27 days to describe it.
It was by this method that they determined the positions of the stars in this Zodiac; it was thus they found that a certain star of the Lyre was in 8s 24°, the Heart of the Hydra in 4s 7°, longitudes which are ascribed to Hermes, but which are calculated on the Hindû Zodiac. Similarly, they discovered that the Wheat-ear of Virgo forms the commencement of their fifteenth constellation, and the Eye of Taurus the end of the fourth; these stars being the one in 6s 6° 40´, the other in 1s 23° 20´ of the Hindû Zodiac. This being so, the eclipse of the moon which occurred fifteen days after the Kali Yuga epoch, took place at a point between the Wheat-ear of Virgo and the star θ of the same constellation. These stars are very approximately a constellation apart, the one beginning the fifteenth, the other the sixteenth. Thus it would not be difficult to determine the moon's place by [pg 728]measuring her distance from one of these stars; from this they deduced the position of the sun, which is opposite to the moon, and then, knowing their average motions, they calculated that the moon was at the first point of the Zodiac according to her average longitude at midnight on the 17th-18th February of the year 3102 before our era, and that the sun occupied the same place six hours later according to his true longitude; an event which fixes the commencement of the Hindû year.
7th. The Hindûs state that 20,400 years before the age of Kali Yuga, the first point of their Zodiac coincided with the vernal equinox, and that the sun and moon were in conjunction there. This epoch is obviously fictitious;[1141] but we may enquire from what point, from what epoch, the Hindûs set out in establishing it. Taking the Hindû values for the revolution of the sun and moon, viz., 363d. 6h. 12m. 30s., and 27d. 7h. 43m. 13s., we have—
20,400 revolutions of the sun = 7,451,277d. 2h.
272,724 revolutions of the moon = 7,451,277d. 7h.
Such is the result obtained by starting from the Kali Yuga epoch; and the assertion of the Hindûs, that there was a conjunction at the time stated, is founded on their Tables; but if, using the same elements, we start from the era of the year 1491, or from another placed in the year 1282, of which we shall speak later, there will always be a difference of almost one or two days. It is both just and natural, in verifying the Hindû calculations, to take those among their elements which give the same result as they had themselves arrived at, and to set out from that one among their epochs which enables us to arrive at the fictitious epoch in question. Hence, since to make this calculation they must have set out from their real epoch, the one which was founded on an observation and not from any of those which were derived by this very calculation from the former, it follows that their real epoch was that of the year 3102 before our era.
8th. The Tirvaloor Brâhmans give the moon's motion as 7s 20° 0´ 7´´ on the movable Zodiac, and as 9k 7° 45´ 1´´ as referred to the equinox in a great period of 1,600,984 days, or 4,386 years and 94 days. We believe this motion to have been determined by observation; and we must state at the outset that this period is of an extent which renders it but ill suited to the calculation of the mean motions.
In their astronomical calculations the Hindûs make use of periods of 248, 3,031, and 12,372 days; but, apart from the fact that these periods, though much too short, do not present the inconvenience of the former, they contain an exact number of revolutions of the moon referred to its apogee. They are in reality mean motions. The great period of 1,600,984 days is not a sum of accumulated revolutions; there is no reason why it should contain 1,600,984 rather than 1,600,985 days. It would seem that observation alone must have fixed the number of days and marked the beginning and end of the period. This period ends on the 21st of May, 1282 of our era, at 5h. 15m. 30s. at Benares. The moon was then in apogee, according to the
Hindûs, and her longitude was .. 7B 13° 45´ 1´´