English
The longi- tude V 28' 4-7 in P. Ashad'ha, m the division of 28, becomes 1° in Niriti. The star U. A^had'hd, whose longitude is 7° 37' 1-7 in the division of 28, falls into 6^40' of P. Ashad'huy in the division of 27, The star Abhijit^ vsrhose longitude is 1° 25' 5-7 in the mansion Abhtjit, in the division of 28, falls into the end, or 13° 20' of P. AshM'ha of the division of 27. . The longitude of the star Sravkna, T 54' 2-7 in the division of 28, falls into the end, or 13° 20' of U. Ashad'ha; and the star in the beginning of Da- nisht'ha in the division of 28, falls into 10° 57' of Sravana in the division of 27 : the whole of which corresponding to what the author of the Surya Sidd- hanta states, and shewing, in a clear manner, that the cause of the supposed deviations, arises from still using the names of three Lunar Asterisms, which belong to the division of 28, without its being known or suspected that they are so. Mr. Colebrooke says, the cause arises from the longitudes being reckoned by the circles of declinations, and not by the circles of latitude, cutting the ecliptic ; but this circumstance could not cause the deviations alluded to. We shall now take a view of the subject of the precession of the equinoxes. The method given in the system of Varaha (contained in the Surya Siddkanta), for com- puting the precession, diflfering widely from that of the system of Brahma, a particular explanation of the cause and foundation of that method may perhaps not only be acceptable, but also useful in doing away the incorrect notions that have been enter- tained by some on that subject. By the system of Brahma, the number of revolu- Digitized tDy VjOOQIC OF THE HINDUS. 131 tions of the equinoxes in a Kalipa, or 4320000000 years = 199669. These revolutions are retrograde, and were determined in the same manner as those of the planets already explained. Now, suppose we wanted to determine the precession of the equinoxes for the end of the year 4900 of the Kali Yuga (A. D. 1799), from this number, we must first find the years elapsed of the system, thus : — To the begmning of the Kali Yuga, 1972944000 Add, 4900 Total years to April 1799, . 1972948900 Then we get the precession by the following for- mula, viz. ;^^^^^^=^^^^=91189'-0'21^9'34'.205; that is to say, the precession of the equinoxes was then (April, A.D. 1799), 21° 9' 35''.205, or the quantity by which the vernal equinoctial point had fallen back from the beginning of Jl^m. This example is sufficient to show how troubles<ne the operation of finding the precession is, from the number given in the system of Brahma. So it must have likewise appeared to the author of the system of Varaha: but how to remedy the evil was a task of no small diffi- culty. He succeeded in lessening the labour of cal- culating the places of the planets, by giving their revolutions in small cycles: but here that method could not answer, because the peiiod of one single revolution of the equinoxes, would exceed 25000 years; and to begin such periods from the com- mencement of the Kalpa, they would become equally as troublesome in computation, as the number in the system of Brahma. Therefore, to avoid all this, he conceived, that as the most perfect astronomical Digitized by Google 132 THE MODliRK ASTRONOMY system that was ever framed could not always last, the best plan would be, to make his rule answer within a certain limited period of time. He was aware, that the earliest observation the Hindus had on record, only placed the vernal equinoctial point in the beginning of Kritica, or 26° 40' to the east of the beginning of Aswim : therefore, by taking into his rule, as far as 27° on the east side, and just as many oh the west side, he would not only include the most ancient observations, but also give a suffi cient scope of time to elapse before his rule would become useless. The next thing was to adjust this space of 27° on each side of the beginning of Aswini, tp time and circular motion ; for without the idea of circular motion, he could not connect it with his system. He therefore assumed the space of time in which the equinoxes would fall back 54°, or 27° x 2, at 3600 years. Then, to get a circular motion, he assumed the equinoxes to move in the periphery of an epicycle, the centre of which is fixed to the be- ginning of Aswini^ and the dimensions of the peri- phery 108°, or 54° X 2, so that one complete revolu- tion of the equinoxes in the epicycle would be 7200 years. By this ingenious contrivance, he transfers the 54° in the iodiac to the periphery of the epicycle, of which it takes up the lower half. The rest of the contrivance will now be explained by the following Diagram : — Digitized by Google OF THE HINDUS. 133 Let the large circle be the Hindu zodiac, divided into 12 parts or signs, and marked 1st, 2ndj 3rd, &c. And ABCD the epicycle, the centre of which is at 12 in the beginning of Aswinl. The line AC, divides the epicycle into two equal halves; and as it cuts through the beginning of Aswinl at 12, its two extremities in the periphery of the epicycle form the points of superior and inferior conjunctions, where the precession is nothing. In the point B the precession is at its greatest quantity to the east, viz. 27°, and in the point D it is at its greatest quantity to the west, or 27°, these being the limits beyond which it does not increase by the rule. Digitized by Google 134 THE MODERN ASTRONOMY From A to B the precession increases from 0 to 27% in proportion to the time; from B to C it diminishes from 27° to 0 ; from C to D it again increases from 0 to 27° ; and from D to A it diminishes from 27° to 0 ; thus making a complete revolution from west to east through 108° in 7200 years, being twice within that period in 0, or in the extremities of line AC, and twice in points of greatest precession B,D. Now to show how this scheme has been applied to the system, we have the number of years elapsed of the system of Varaha, at the beginning of Kali Fw^flf= 1955880000: at the commencement of this period of years, the vernal equinoctial point coincided with the begin- ning of Aswiriiy in the point A of the epicycle : there- fore, dividing the years elapsed by 7200, the years in one revolution, we have ^^^^=271650 revolu- tions, complete without a remainder : consequently, at the beginning of Kali Yuga, the vernal equinoctial point would be again in A, in the beginning of the epicycle commencing another revolution. At the end of 1800 years from the beginning of the Kali Yuga, the equinoctial point would arrive at B, where its distance from Aswim, reckoned on the periphery of the epicycle, would be 27° to the east. The vernal equinoctial point, still moving onwards in the peri- . phery, diminishes its distance from Aswinl, until in the year 3600 of the Kali Yuga, A.D. 499, it coin- cided with the point C or 0, being then in the line with the beginning of Aswim; and therefore in that year the precession was 0. Since that time, the equinoctial point proceeds from C towards D ; and therefore the precession must continually increase, until it amounts to 27° at D ; after which (by the scheme), it proceeds from D to A, and completes the revolution. Digitized by Google OF THE HINDUS. 135 From the explanation thus given, it must be easy to perceive how the precession is to be computed. In 1800 years, the precession increases to its greatest quantity, 27°. Therefore all that we have to do, is to say, as 1800 years, to 27°, so any number of years less than 1800, to the corresponding precession ; which is to be counted to the east of Aswinl, in the two first quadrants of the epicycle, but to the west in the two last. Thus, suppose we wanted to know the precession of the equinoxes, or the distance of the vernal equi- noctial point from the beginning ofAswini, for the endof the year 4900 of the Kali Vuga, (A. D. 1799,) we subtract two periods of 1800 years each =3600, the remainder is 1300 years; then 1800: 27°:: 1300: 19° 30', which is to the west of the beginning of Aswim, being in the third period of the cycle. This example is given for the same year, that the calcu- lation was made for by the system of Brahma, in order to show the diflference in labour, &c. : by the latter, the precession was found to be 21° 9' 34\2|. which is nearest the truth.