English
Moon, 8065'33"- 6>10'15''- 3045'18''- 1045' 9"- on4'ii"- 0Ol4'22*4- Moon's 7 apogee ) 3 52 5 + 2 5849 + 2 5 33 + 1 1217 4- 0 19 1 + 0 331 - Moon's i node \ Meroiuy, Vonns, Mars, Jupiter, Satnm, 3 5940 - 3 656 - 2 14 12 - 12128 - 0 2844 - 0 625 _ 24 035 + 35 4539 - 12 1337 + 19 42 0 - 21 1320 + 18 3042 + 27 5956 - 9 2737 + 15 29 9 - 15 5844 + 13 049 + 20 1413 - 6 4137 4 11 16 9 - 10 44 8 4- 7 3056 4- 12 2830 - 3 5537 + 7 3 9- 5 2932 4- 2 1 8 4- 4 4247 - 1 937 4- 2 50 9 - 0 1456 + 9 1829 ~ 1 2547 - 0 036 - 1 256 - 1 58 6 - Having thus proved the time the Arya Siddhanta vs^as written, independent of the date, we shall now proceed to show the age of the Parasara Siddhanta by the like process, The positions of the planets at the beginning of the Kali Yuga, according to this system, will be obtained by the rule of proportion, in the usual manner, or more concisely, by multiplying the four right-hand figures of the number of revolutions for each of the planets, by 4567, reserving the four right-hand figures in the product, which will be decimal parts of a re- volution, denoting the planets' mean place. The following Table, shows the mean places of the planets at the beginning, of Kali Yuga, Hindu sphere, at 6 A.M. on the meridian of Ujeirij by the Parasara Siddhanta and La Lande's Tables, with the errors or differences. Planets. Parasara Siddhanta. La Lande's Tables. Errors or Differences. San^ ••.••••• Moon, ; Mercury, Venns, Mars, ••..•••• Japiter, • Saturn, ...••• Moon's apogee.. Node, 0 0° 0 0 O' 0^ 10 48 11 21 17 16,8 11 26 58 33,6 29 14 88,4 2 11 11 27 52,8 11 28 57 21,6 4 5 12 28,8 5 2 49 12 0 0 10 1 11 0 11 3 5 0° 0' 0^ 8 8 48 27 21 0,9 2 52 50,9 17 47 22,9 16 49 20,7 8 46 40 29 58 19,2 6 38 3,8 0® O' 0^ 2 58 0 — 28 56 15,94- 35 54 17,3- 11 27 15,5 4- 19 46 27,9. 20 10 41,64- 5 14 9,64- 3 48 51,8— The following Table, shows the mean annual mo- tions of the planets in the Hindu sphere, according Digitized by Google OF THE HINDUS. 151 1^ to tlie Parasara Siddhanta and La Lande's Tables, with the errors or dilSerences. PUoets. Sub, • Moon,,,, Bferouiry, Ifan, •• Jopiter, •••••• Satan, ••••... Moon't apogee, Node, .••• Pariaara Siddhanta. 0 90 d^ 4 12 40 24 46 16 11 11 24 0 21 12 12 10 40 19 21 0^ 404646 10,64 61,6444 9,9111 6,9862 61,6489 81,8902 88,9705 La Lande't Tables. Bnon or DilTareiioei. 0 00 O' 0^ 4 12 46 87,6286 1 24 46 863979 7 16 11 28,1828 6 11 24 18,8799 1 0 20 6O4O68 0 12 18 9,1864 1 10 40 85,4106 0 19 21 81,2866 0^ 2,7809 + 193667^ 284116 + 8,9688. 16,6794 + 17,6416- 4,0208. 2,7860 + Having now the errors or differences in the mean places of the planets at the beginning of the Kali Yuga^ and the errors or differences in the mean annual motions, let the fcmner be divided by the latter, aiKi we have. FUoeta, &o. DiTUora. Di?idendi. QootienU. Moon, Node,.... Vemu, r,7809 4,0208 2,7860 19,2667 284116 8,9688 16,6794 174416 20 68' 0^ 6 14 94 8 48 51,8 28 66 16,9 86 64 174 11 27 164 19 46 27,9 20 10 414 8910 4688 6090 4476 4688 4697 4540 4117 Man, Ji^iter, Satnni, The anm of the qootienta or reanlts • . 86880 Which divided by 8, gives for a mean result 4485, or A.D. 1384; which, therefore, coupled with the comparisons already made, shows that it was the work of Aryabhatta, though it comes out a few years later than his date ; but that can be of very little" consideration here, for the object of the work was not ex;traordinary accuracy, but as an authority to suppOTt by name an imposition : indeed the nearer the system of the Parasara Siddhanta agreed with im own work, the more it became liable to suspi* Digitized by Google 152 THE MODERN ASTRONOMY cion; and I am therefore rather surprised that he did not use more artifice than to frame it for his own time. The following Table, will now show the errors in the mean places of the planets by the Paramra Sidd- hanta, compared with La Lande's Tables at different periods, from the beginning of the Kali Yuga to A.D. 1322. Planets, KaU Yoga, or B.C. 3102. Mood, Moon's ) apogee J Moon's i Node^ Meroarj, Venus, Mars, Japiter, Saturn, 5 1410 + 3 4862 - 23 6616 + 36 64 17 . 11 27 16 + 19 4628 . 20 4042 + KaU Yuga 1000. 6° 0'28''- 4 710 + 3 217 - 18 3520 + 27 69 6 — 8 6747 + 16 26 9 - 5 1640 + Kali Yaga 3°36'33''- 3 010 + 2 1642 - 13 1424 20 3 63 6 2818 11 360 10 22 38 Kali Yuga 3000. 1037/26''- 163 9 + 1 31 7 - 7 6328 + 12 841 - 3 6849 + 6 4231 6 2836 Kali Yoga 4000. 00 7'29'' + 0 46 9 + 0 4632 - 2 3232 + 4 13 29 - 1 2920 + 2 21 12 - 0 3434 - K.Y.4W, 1322 A.D. 0O20'44" + 0 1749 + 0 2616 - 0 1647 + 0 6229 - 0 26 6 + 0 3040 -. 1 2948 As this Table will, I think, be suflScient to show, by inspection, the time nearly when the Parasara Siddhanta was framed, it must be altogether unne- cessary to dwell longer on this point. We shall therefore now proceed to such other matters, con- tained in the Arya Siddhanta^ as may be deemed curious or deserving of notice. In the twelfth chapter of ih^Arya Siddhanta ^ Aryab- hatta gives us a table of the longitudes and latitudes of the stars in the Lunar Asterisms. The longitudes, as usual, are all reckoned from the beginning of the Lunar Asterism Aswiniy as the commencement of the modern Hindu sphere, but determined by the points of the ecliptic, being cut by the circles of latitude, and not by the circles of declination ; therefore, dif- fering from the Brahma Siddhanta, and others that follow the latter method. The author of the Sarva Bhauma, a modern writer, appears to have followed Digitized by Google OF THE HINDUS. 153 Aryabhatta in his method : it will therefore be useful to exhibit both their tables at one view. TABLE of the Lamgitudei and Latitudes of the Stars m Lmar Mansions^ reckoned from the beginning of Aswini, according to the Arya Siddhanta and Sanra Bhauma Siddhanta. Lanar Asterisms. Arj a SiddboU. Strra Bhaama. Stan supposed to be meant Longitudes ' Latitades Longitudes Latitudes 1 Aswint, 12^ O' lOo O'N. \%o 4/ ICOoO'N. 7 or /3 Arietis, 2 Bkaram, 24 80 12 25 8 12 55 36 ArieUs, % JCrUikd, SB 83 6 89 2 4 44 The Pleiades. 4 Bolunx, 47 83 6 S. 48 9 4 40 S. Aldebaran. 6 BiHgoMuraSf 61 8 10 61 1 10 12 37, 89, 40 Ononis? 6 Ardra, 68 2-i 11 65 8 11 7 137Taari? 7 PuHorvasu, 02 68 6 N. 94 -53 6 0 N. 78 or 83 Geminoruiq. 8 Pushyd, 106 0 0 106 0 0 0 Pnesepe.or y ,^ Cancri ? 49 or 60 Cancri. 9 A/leshd, 111 0 7 S. 109 0 7 4 S. 10 Magha, 129 0 0 129 0 0 0 Regulns. U P.Pkalff^i, 140 23 12 N. 142 48 12 42 N. 70 or 71 Leonis. 12 U.Pkalmmt, 150 23 18 160 0 13 55 3 Leonis. 13 Htuta, 174 8 10 S. 175 13 12 0 S. ^Co vi. U Ckitra, 182 53 2 188 60 1 62 Spic4i Virginis, 15 Swdti, 194 0 37 N. 182 24 41 6 N. Arcturus ? 16 VUdkha, 212 23 1 30 S. 212 36 1 25 S. 24 Libre, 17 Anuradha, 224 63 3 224 88 1 60 7Soorpu. 18 Jytsktha, 230 3 4 280 6 8 28 Antares. 19 Muld, 242 24 9 248 36 8 40 84Soorpur 20 P^AshadTka, 254 83 6 20 254 84 5 22 ^ Sagittarii. 21 UrAshad'ha, 260 38 5 S. 260 21 6 0S. f Sagittarii. Ab^jU, 263 0 68 N. 262 10 62 14 N. ahjrm. 22 Sravand, 280 8 30 280 8 30 6 y or a Aquilee. /3 or a Delphini ] •a Dhauiskfhd, 296 83 86 294 12 26 26 U Satabhisha, 319 63 0 20 S. 819 15 0 46 S. \ Aquarii. 25 P.Bhadrapada, 3.J4 53 24 886 8 26 3 aPegasi? 26 U.Bhadn^ada, 347 0 26 848 44 28 0 78 or Y Pegasi. 27 ilevafi. 360 0 0 859 60 0 0 ^ Piscium. On comparing the above latitudes and longitudes, some differences will be observed; but whether such differences arise from error, or from different stars being intended, cannot be so readily ascertained. Thus Aryabhatta gives the longitude of the star in the sixth mansion Ardra, 68"^ 23' ; but in the Sarva Bhauma, it is set down 65"^ 8', making a difference of upwards of 3°. The position of this star by the Brahma Siddhanta is 67° and ITS.