Jones and Davis were published, and before they were generally known in Europe, appeared Bailly's elaborate work, entitled, "Traité de l'Astronomie Indienne et Orientale." His principal object is to prove, from the tables of Tirvalour, brought to Europe by Le Gentil, that the epoch of the Kali Yuga, 3102 B. c. was fixed by actual astronomical observations; and that there are remains of a state of science in an age of 1200 years preceding that æra. He takes frequent opportunities of advancing his favourite theory of a highly cultivated people, inhabiting the north of Asia, who were the inventors of all arts and sciences, and, to use the words of d'Alembert, "taught us every thing, except their name and their existence."

The reality of the observations, by which the epoch of the Kali Yuga was fixed, has been defended also by Playfair in the Edinburgh Transactions, 1789.

The impartial Montucla, (Histoire des Mathématiques, Part II. Liv. 111. §. 2), touches but slightly upon the antiquity of the æra Kali Yuga; but leans to the opinion of Anquetil, that it is, in reality, the æra of the deluge, and was communicated to the Indians by the Arabians of the 9th or 10th century of the Christian æra.

Delambre (Astronomie Ancienne, Livre 11. Chap. ii.) gives an Analysis of Bailly's Treatise, and points out the inconclusiveness of many of his deductions.

Marsden (Phil. Trans. 1790,) conceives that the supposed conjunction was calculated retrospectively.

J. Bentley considered the subject in two papers published in the 6th and 8th volumes of the Asiatic Researches, and concluded that the Surya Siddhanta was not written till about the year 1000 A. D. In the Edinburgh Review, vol. x. the accuracy of his conclusions respecting the recent date of the Surya Siddhanta was disputed. Bentley was much hurt at the Strictures of the Reviewer, and in 1825, a little before his death, published his "Historical View of the Hindu Astronomy, from the

earliest dawn of that science in India to the present time." He there draws conclusions to this effect.

The formation of the lunar mansions, the first authentic fact in Hindu Astronomy, took place about 1425

B. C.

The solar months were formed about 1181 B. C. From that time till A. D. 538, Hindu Astronomy was divided into eight periods, each containing 247 years and one month so that the year, at the commencement of each period, began one month later.

At the beginning of the fifth period, about the year 204 B. C. Hindu history was divided into periods for astronomical purposes. The data were fixed astronomically. The years with which each period was to begin and end having been previously fixed upon, the inventor computed the month and Moon's age on the day on which Jupiter was in conjunction with the Sun, in each year. From these conjunctions with Jupiter the name Yuga, conjunction, was given to the periods.

The first period immediately preceeding the time of their
introduction was denominated the.. Kali Yuga.
The second period was denominated... Dwapar Yuga.
The third.. .. .
..Treta Yuga.

The fourth.....

with this the Creation began.

Krita Yuga.

The end of the Kali Yuga was fixed by a conjunction of the Sun, Moon, and Jupiter, June 26, 299 B. C. This, he says, was called Satya Yuga, the true conjunction.

Bentley computed the following table, which shews that the commencement of these periods was computed backwards, from about 200 or 300 B. c. He fixes the commencement of the system to the year 204 B. C. which is known from other circumstances to have been the commencement of the fifth astronomical period.

The gradual diminution of the error shews approximately the epoch at which the system was introduced. It is very remarkable that the æra thus fixed for the Creation corresponds with the time assigned to the deluge by Usher..

At a later æra, their history was divided into nine Manwantaras, or patriarchal periods, the dates being fixed by the computed conjunctions of Saturn with the Sun, as the Yugas had been determined by the conjunctions of Jupiter. The epoch of the Creation was thrown back to

4225 B. C.

The following Table, also computed by Bentley, shews the gradually increasing error in the computations of the Hindus, and gives, approximately, the æra when the method was introduced.

The error in the mean annual motion of Saturn was about 26"+. Therefore the year in which the computed place of Saturn would agree with the observed place would be A.D. 64: the æra when this division of the Hindu history was invented.

This division of the Hindu history was, in the year 538 A.D. superseded by that already mentioned, at the beginning of this note, in which the Creation was thrown back 1,972,947,102 before the Christian æra. This was effected by adopting the names of the periods already known, and uniting them by a dextrous but complicated combination.

The Brahmins first increased the number of Manwantaras to 14, inserting their dates in the calendar and other books. (Bentley's Hindu Astron. p. 84.) Now this increase, it will appear, was necessary to fulfil the conditions which they had assumed. These conditions were, that the length of the Dwapar Yuga, Treta Yuga, and Krita, or Satya Yuga must be in arithmetical progression, and equal 2n, 3n, 4n, respectively. And their sum

10n is a Maha Yuga, or great age.

Also, a certain number (p) of Maha Yugas +4 n = a Manwantara (M), and a certain number (q) of Manwantaras + 4n = Kalpa, which is also to contain a thousand Maha Yugas, or 10,000 n.

That these conditions may be fulfilled, it is necessary to find two whole numbers, p and q, which will satisfy the equations

M = 10pn + 4n;

10,000 n = q M + 4 n.

Hence 10,000 n = g (10p + 4) n + 4n

=

{10 pq + 4 (q+1)} × ;

.. 10pg+4(q+1) = 10,000;

.. (5p+2) q = 4,998.

Now the only whole numbers, which will satisfy this

Hence, p being taken =71, and q = 14, the assumed conditions are fulfilled.

The change, therefore, in the number of Manwantaras, from 9 to some other number, of which 14 was the nearest to 9, which Bentley mentions as an historical fact, was necessary to complete the scheme.

It only remained to assume a value of n, which was taken to be 432,000, and the artificial system was completed.

Several conjectures, concerning the reasons which might lead to the selection of the number 432,000, which is equal to 10 times the product of 360 by 12, may be found in Sir W. Jones's Treatise on the Chronology of the Hindus. See also Montucla Histoire des Mathématiques, Part II. Liv. 111. §. 2. Vol. 1. p. 429. The cycle 360 × 12 is composed by multiplying the months by the number of days originally ascribed to the lunar or solar year. This was the number of days in the Egyptian year, according to Herodotus: and in the Latin year, before the correction of it by Numa. The Indians had a fictitious year of 360 days, used for calculation only; on the supposition that the Sun moved through 1o in a day. Bailly, Astron. Indienne, Preface, p. 9. Davis, in As. Res. Vol. II. Art. xv. p. 228, says the Maha Yuga 4,320,000 years, is an anomalistic period of the Sun and Moon, at the end of which the Moon, with her apogee and ascending node, is found with the Sun in the first point of Aries.

Cc