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6S8 ; bnt whether he was or was not, is of no consequence whatcTcr : we can ascertain pretty neariy the age of any system of astronomy, if genaine, though we cannot tell who framed it ; neither can we tell who has been the author of any book, where tiie name given, as generaUy the case, is fiotitioai. What gave rise to the idea of Varaha being the author of the books just mentioned was, that the system they contained was called that of Varaha, a name naturallj supposed to be given to the system, in consequence of his being the real or sup- posed author of these works. Systems may have no names conferred on them for many centuries after they are framed, as is the case with that given by Aryabhatta, Sec. III. which, I believe, to this day has no particular name assigned to it. * The author pretends to have written it at the vernal equinox, beginning of tbe Satya Yuga, or 8027101 years before Christ Digitized by Google OF THE HINDUS. 117 Tbelongitodeof CaBopasiaA.D.lTSOwas...* S 11<> S(K SO' 6 The difference of longitode linoe the obfferratioo, 0 11 SO SO 6 Which reduced to time, at 1^ in 71 J years, we get 822 years, which being taken from 1750, leaves A.D. 928, the time of the observation. From this fact, supposing we had no other, it would most undoubt- edly appear that the Surya Siddhanta could not be written earlier than the 10th century. But besides the observation above given, we have also the time from the positions of the planets ; which prove, that -the system of Varaha, is even posterior to the obser- vation on Canopus by the supposed Vasisht'ha. Before we proceed, however, to show the time from the positions of the planets, it is proper that we should first exhibit the system, and explain its structure. The following Table exhibits the revolutions of the planets, &c. in 4320000000 years according to the system : — Names. ReTolations. Apsides. Nodes. Swi, ..., Moon, . Mercury, Venus, . , Man, .. Japiter, Saton, • . Pays 4Sa0000000 6776SSS6000 • 170S7024000 7022S76000 S2068S20eO 364220000 146568000 1577917828000 ReTol. S87 48820S000 S86 5S5 204 900 S9 ReroL 2S22S8000 488 90S 214 174 662 Revolntions of the equinoxes (in the epicycle,) 600000 The number of years in this system, is exactly the same as in that of Brahma; but they do not commence at the same time. The system or Kalpa . * This is the correct nomber : in the system it is 179S7060 for a Maha Ym§a, owing to an error in the nomber for the primary cycle, whioh should have been 4484256, and not 4484265. The digits are the same, but the two last are mis- ]^aced ; the 6 sboold folbw the 5. Digitized by Google 118 THE MODERN ASTRONOMY of Varaha begins later by 17064000 years, a circum- stance owing to the formation of the revolutions of the planets into small cycles, for the convenience of calculation. Therefore, in computing the number of years elapsed of this system, the time must be first found according to the system of Brahma, as already shown, and from that time 17064000 must be deducted, to give the years elapsed of the system, of Varaha. Thus, at the beginning of the Kali Yugay there were elapsed of the system of Brahma, . . . 1972944000 years. Deduct the above number, 17064000 Remain time elapsed of the system of Varaha, . 1955880000 Hence, it must be obvious, that the system of Brahma had existed and was in use long before that of Varaha ; as the computation of the time elapsed must be made in the first instance by the former system, otherwise we should not know when the latter began. The Kalpa of Varaha begins with Sunday, as the first day of the week, at the instant of midnight, on the meridian of Ujein ; and the Kali Yuga begins with Friday at midnight. The year, therefore, begins earlier by six hours than in the system of Brahma, which would therefore cause it to be some- thing longer ; but the true length depends on other circumstances. The revolutions of the planets given in the Table, all terminate with three cyphers : these being cut off, the remainder will be the revolutions in a Maha Yugay or 4320000 years. The numbers may be further reduced by dividing them by four, the quo- tient will be the revolutions in 1080000 years ; which is the least common cycle, in which the planets Digitized by Google OF THE HINDUS. 119 return to a line of mean conjunction in the beginning, both of Aswinl and Aries. The years elapsed of the system of Varaha, at the beginning of the Xflr/i Fw^,are, as above, 1955880000. If this number be divided by the years in the least common cycle, 1080000, the quotient will be 1811, the number of cycles in that period. Now since the system begins with a Sunday, as the first day of the week, and the Kali Yuga begins with Friday, it is evident that the whole number of days to be assigned to the 1811 cycles, must, when divided by seven, leave a remainder of five : then the question is, how many odd days, over and above complete weeks, we must assign to each cycle, so as to answer this purpose. This is easily known by assuming one day in excess above the weeks: then 1811 cycles will have 1811 days, which, being divided by seven, leaves a remainder of five, which is the very num- ber we want. Therefore, each cycle must contain a complete number of weeks, and one day over. The time elapsed from the beginning of the Kali Yuga at midnight, to the instant of the vernal equi- nox in A. D; 538, which was supposed, or assumed to coincide with the beginning of the Lunar Asterisn^ Astoim, is 1329176 days, 6 hours, and 40 minutes in 3639 years : therefore, as 3639 years are to ' 1329176 ^^ &" 40^ so 1080000 years to 394479356 days, rejecting fractions. If we divide this number by seven, there will be a remainder of five ; but firom the conditions already stated, it must be one : there- fore we add to the number three days more, and make it 394479359, firom which the length of the year would be obtained, that would answer all the terms, because divisible by seven, leaving a remain- der of one. But the number of days to be assigned Digitized by Google 120 THE MODERN ASTRONOMY to the cycle of 1080000 years, must also give the relative motions of the sun and moon correct, and the lunation of a true length; in consequence of which, a further correction must be made to the time by the addition of 14 complete weeks, or 98 days, to the above number, which will make it 394479457 days* This number being multiplied by four, makes 1577917828, the number of days in the Maha Yuga, or 4320000 years ; and the days in a Maha Yuga being multiplied by 1000, the product will be 1577917828000, the days in a Kalpa, or 4320000000 years, the same as in the Table : and the days in either of the periods being divided by the corresponding number of years, we get the adjusted length of the Hindu year, according to the system of Varaha,=365^ 15** 31° 31' 24'", The length of the year might be computed in another manner; but as the result would be the same, by reason of the adjustment, it was thought unnecessary. Having found the length of the adjusted Hindu year, vre are now enabled to proceed to show how the revolutions of the planets have been obtained : — one example will be perfectly sufficient. I have shown above, that the observations of Vasishtha on the position of Canopus, refer us about to the year A. D. 928, or of the Kali Yuga 4029. Let us, therefore, suppose the system was framed about that period, and that the author had determined, by accurate observations, the positions of the planets in the Hindu sphere, at the end of the year 4029 of the Kali Yuga ; which position formed the basis of the revolutions in the system. Thus, suppose we take Venus as an example : — The mean heliocentric longitude of Venus at the end of the year 4029 of the Kali Yuga, A.D. 928, Digitized by Google OF THE HINDUS. 121 March 23d. at 19^ 48' 56*, meridian of Paris, by La Lande's Tables European sphere, was 4* 9® 30' 26' Or Hindu sphere, . . . 4 2 49 39 Now suppose this to have been the precise position determined by the author, it is required to deter- mine the ninnber of revolutions of the planet in the primary cycle of 1080000 years, that will give this position, reckoning from midnight at the beginning of the Kali Yuga, as an epoch of mean conjunction of all the planets.