English
These explanations are of the utmost importance, and should be particularly attended to, as they serve to show more clearly the impositions of the modems, which will be noticed in their proper place. There is another passage of Parasara, respecting the heliacal rising of Canopus in his time, which it is proper to notice here. He states, that " the star Agastya (or Canopus) rises heliacallt/ when the sun enters the Lunar Asterism Hasta, and disappears of sets heliacally, when the sun is in Rohini." As Parasara was contemporary with Yudhishthira, and the latter ascended the throne in the year 575 B.C. we shall make the calculation for that year. The difference between the time of rising and setting of Canopus, points out the latitude of the place of observation to have been the same, or nearly the same as that of Delhi, which lies in latitude 28° 38' North. Digitized by Google 68 THE ANCIENT ASTRONOMY The longtitude of Canopus in A. I>. irSOwas 3^ 11° SC 40" Snbtract precession for 2325 years. according to modern theory, .... 1 2 17 0 Remain, 2 9 13 40 Subtract variation in longitude of the starchy reason of the change in the ecliptic*, 26 SO Remain trae longitade of Canopus A.D.576B.C. .,, 2 8° 47' 10^ Latitode of Cofu^m^ A. D. 1750, .. 75 51 20 Add Tariation for the change in the ecKptic*, 17 12 True Latitude of Cofiopii* 576 B. C. 76 8 32 From which data we now get the right ascension and declination of Canopus at that time by the fol- lowing proportions : 1 As radius sine OO** O' 0^10.0000000 Is to sine of the longitude of CofMjnfi •• 68 47 10 9.9695259 So cotangent of the latitude 76 8 32 9.3921570 To cotangent of an / 72 2 55 9.3616829 Snbtract obliquity of the ecliptic 575 B.C.. 23 46 46 Leaves. 3 16 9 2 As ladius sine 90 0 0 10.0000000 To cosine of the longitude of Canoptw ...... 68 47 10 94^585293 So cosine of the latitude of Canopus 76 8 32 9.3793284 Tocosineof 86 1 41 8.9378577 3 As radius sine 90 0 0 10.0000000 Tooosine 53 16 9 9.7767422 Sotangentof 85 1 41 11.0605043 Totangentof the right ascension of ConopM.. 81 43 25 10.8372465 Then for the declination : 4 As radius sine...... OO^ 0' O'' 10.0000000 Tosine 53 16 9 9.9038786 Sosine 85 1 41 9.9983628 To sine of the declination of Canopus S .52 58 53 9.9022414 Having thus obtained the right ascension and declination of Canopus 575 years B. C. we are now * These corrections might have been dispensed with, a^ the result would come out nearly the same without them. Digitized by Google OF THE HINDUS. 69 prepared to proceed in the calculation of the heliacal rising of that star at the period given. Let P be the pole of the equator. PZ = 90°— 28° 38'=6r 28'=ACS T C the equator. T D the ecliptic. S place of the star. 5 AstangeatoftheoolatitiidePZsACS .... 61<^ 22' To tangent of the declination AS 52 68 So radios sine •• ^ ^ To sine of the ascensional difference AC ... • 46 23 Add the right ascension, 81 43 The sum is the oblique ascension T C ..... . 128 6 the Equator rising with dmcynw 0" 10.2628291 53 10.1225046 0 10.0000000 22 9.8697655 25 47 or the pwntof Digitized by Google ^ 70 THE ANCIENT ASTRONOMY Now to find the point D of the ecliptic rising with S and C : In the right-angled triangle r CB, right-angled at C, there is given r C 128° 6' 47" and the obliquity of the ecliptic C t B, to find t B : — t C being more than a quadrant, take its complement to the next equinoctial point = 180°— 128° 6' 47"=51° 53' 13^ then in the supplementary triangle C^j^B we have C^=5r53'13": the z^ =23° 46' 46", the obliquity of the ecliptic, to find B^. 6 As oosine of the obliquitj of the ecliptic ^ i^ 23^^ 46' A&* ==9.9614706 Is to radios sioe ...• 90 0 0 10. ' So tangent C:£:b 61 63 13 10.1054247 To tangent B£^ 64 19 36 10.1439541 Which taken from 180^ leaves r B = 125° 40' 24', the point of the ecliptic B, or the longitude of that point of the equator C, which rises with Campus. Now, the next portion of the ecliptic to be found isBD. 7 Say as radios sine 90° O' O'' 10. TosineCd^ .• 61 63 13 9.8958613 So tangent Z:£^ 23 46 46 9.6430682 TotangentBC. 19 4 6 9.6389295 8 And as radios sine ..•• 90 0 0 10. Tosine/^ 23 46 46 9.6056389 So cosine C^ 51 63 13 9.7904366 To cosine CB£^ 75 36 21 9.3959755 9 And as radios sine • • • • 90 0 0 10. Is to cosine BC 19 4 46 9.9754623 So tangent of the latitude of the place of observation, 28 38 0 9.7371709 To cotangent of an / which call e 62 42 26 9.7126332 Which taken from CB£^s76<' 35^21'' leaves 12 62 65 which call/ 10 As cosine// 12 62 65 9.9889296 Istocosine/e 62 42 26 9.6613749 SotangentCB 19 4 46 9.5389246 TotangentBD 9 14 26 9.2113699 To which adding T B 125 40 24 We have the longitude of the point 1> •••••• 134 54 50 coascendent with S and C, or the cosntieai point. The next portion of the ecliptic to be found is DM depressed 10° below the horizon. Digitized by Google OF THE HINDUS. 71 11 As radios sine INF O' (T 10. TocosineBD 0 14 26 9.9943272 Sotmogent // 10 52 55 9^692642 TootaiigotCDB 77 16 47 9J6S6914 12 AssineNDMsCDB 77 16 47 9.9892080 IstosioeMN 10 0 0 9.2S96702 So radios sine 90 0 0 10. TosineDM 10 15 15 9.2504622 Now the different portions of the ecliptic thus found, being added together, we have r B+BD + DM= T M = 125*" 40' 24" + 9^ 14' 26' +10° 15' 15" = 145° 10' 5" = the sun's longitude from the vernal equinoctial point, when the star Canopits rose heliacally at Delhi 575 years before the Christian era ; and as the sun^ at the time of the heliacal rising of Canopus, was, according to Parasara, in the beginning of the Lunar. Asterism Hasta, the next thing we have to ascertain is the longitude of the beginning of Hastdy Ireckoned from the beginning of Aries, or the vernal equinoctial point, in the year 575 B.C. For this purpose we make choice of the star Cor Leonis, whose fixed longitude is 9° in the Lunar Asterism Magha. The longitode of this star in A. D. 1760 from the beginning of ^rtM was 4^ ^^ ^V \T Sobtract its longitode in the Lonar Asterism MagU 0 9 0 0 Remain longitode of the beginning of Magha in A.D. 1750, 4 17 21 12 From the beginning of Magha to the beginning of Hasta, is jost three Lonar Mansions of 130 20^ each ; therefore add 1 10 0 0 The som is the longitode of the beginning of ITaxfd in A. D. 1750, 5 27 21 12 Sobtract from this the precession for 2325 years, (seebefore,) • 1 2 17 0 Leaves longitode of the beginning of Hastd 575 jearsB.C 4 25 4 12 Son's longitode at the time of the heUacal rising of CanopiM576B.C 4 25 10 6 The difference is onl J .••• *••••• 0 0 6 63 Digitized by Google 72 THE ANCIENT ASTRONOMY . Which I think is a sufficient proof of the accuracy of the observation of Parasara on the heliacal rising of Canopus. If the place of observation wras a few miles more to the southward of Delhi^ which is ge- nerally supposed to have been the case, and at a place called Hastina-pura, the ancient seat of go- vernment in the time of Yudhisht'hira, then the agreement of the observation with the result of cal- culation would be still more perfect. We have now to notice Garga, an ancient astrono- mer that was contemporary with Parasara and Yud- hisht'hira. He states the positions of the sun, moon, and planets, at the commencement of the year (1st Agrahayand), at sunrise, as follows : The sun he states to be then in Anuradha, The moon . . . in Rohiniy Jupiter . . . in Pushy a, Mercury . . .in Satabhisha, Mars .... in Mula, Venus .... in Kritika. These positions, therefore, refer us to the 29th of October, in the year 548 B.C. the time when Garga wrote his Sanhita.