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Bharatiya Jyotihshastra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s10: (9) Conjunctions of Planets

Bhāratīya Jyotiḥśāstra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s10

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(9) Conjunctions of Planets

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When two planets come very close to each other, they are said to have formed or come into CONJUNCTION. At that moment, the distance between them measured east to west, must be zero. Even then there may be some distance between them, north to south, according to their latitudes. When at the moment of conjunction, their rays are found to intermingle, or when their north-south distance is found to be less than 1°, they are said to have formed *yuddha* (fighting), and if the distance exceed 1°, they are said to have formed a *Samāgam* (companionship). If the discs of planets would simply touch, they would be said to have “grazed” *i.e.* formed an ‘*ullekha*’ and when the discs penetrate each other, they are said to have formed a *bheda* (i.e. penetration or occultation). The results of ‘*bheda*’ and other types of conjunctions are described at length in Samhitā works. The definition and calculation of the ‘*bheda*’ type of conjunction are given in our works. It is, however, not known if our people knew the penetration of the sun’s disc by Venus (Pages 163-164).

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(10) BHA-GRAHA-YUTI OR CONJUNCTION OF PLANETS WITH STARS

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LONGITUDES AND LATITUDES OF STARS

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This chapter describes the calculation of the conjunction of planets with the junction-stars of nakṣatras and for this purpose lists of polar longitudes and latitudes of junction-stars and of some other stars are given. The figures denoting longitudes are generally corrected by “*ayana-dṛk-karma-saṃskṛta*” *i.e.* they are governed by the following conventional definition. ‘BHOGA’ (*longitude*) is the ecliptic arc between the initial point and the point where the perpendicular drawn from the star to the celestial equator cuts the ecliptic and the ŚARA (*latitude*) is the distance of that point from the star. Let us call such longitudes and latitudes, polar longitudes and latitudes. The longitudes and latitudes in certain works conform to this definition. BHOGA (longitude) is the ecliptic arc between the initial point and the point where the perpendicular drawn from the star to the ecliptic cuts the ecliptic : and the perpendicular so drawn is the Śara (latitude). The pole of the ecliptic is also known as Kadamba. Let these longitudes and latitudes be, therefore, called 'KADAMBĀ-BHIMUKHA' (facing the pole, *kadamba*). On pages 338 and 339, later on, have been given the polar latitudes and longitudes of stars, as given in six works. The polar longitudes and latitudes of those* stars which in the author's opinion, should be regarded as junction-stars are also given. The correction due to 'ayana-dṛk-karma' is not always the same owing to the shifting of the eqinoxes. Hence the polar longitude of a star will not always remain the same. It may be partly due to this reason that the longitudes of stars mentioned in six works, which have been given below differ from one another to a certain extent ; some differences may be due to the fact that different stars might have been adopted as junction-stars. The *dhruvas* (polar longitudes and latitudes) mentioned by the Sūrya-Siddhānta, Brahmagupta Siddhānta and Lalla Tantra, belong to a period when the amount of ayanāṃśa was exceedingly small. About this BHĀSKARĀCĀRYA remarks :

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इत्थभावेऽयनांशानां कृतदृक्कर्मकाध्रुवाः ।
कथिताश्च स्फुटा बाणाः सुखार्थं पूर्वसूरिभिः ॥ १७ ॥
* सिद्धांतशिरोमणि, ग्रहयुति.

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"Thus have been mentioned (in the absence of any ayanāṃśas) polar longitudes, after the application of the 'dṛk-karma', and also the apparent latitudes, by ancient Ṛiṣis, for the sake of convenience".—Sid. Śiromaṇi, chapter on conj. of planets with stars.

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The works of BRAHMAGUPTA and LALLA do not refer to the motion of the ayana-point and the S. S. does refer to it ; still the longitudes of the stars given in the latter agree for the most part with those mentioned by Brahmagupta and Lalla. This shows that Bhāskarācārya's remark applies to the longitudes given by all the three works. Some figures showing longitudes and latitudes in the Sundara Siddhānta are missing, because the procured copy was very inaccurate and those figures were unintelligible.

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The polar latitudes and polar (sāyana) longitudes for 1887 A.D. of the junction-stars as adopted by the author, have been calculated from their right ascensions and declinations given in the French Connaissance-des-Tempes. The longitude of Spica thus obtained is 201° 26' 16".3. Assuming the longitude of Spica to be 180°, the author has mentioned in the column headed "his opinion" the longitudes of all stars after subtracting from their (Sāyana) longitudes the ayanāṃśa figure 21°-26'-16".3. These are true for Śaka 1809. The latitudes also are true for the same year. But because the longitudes are nirayaṇa, only a very slight variation will occur in them with the lapse of time. If Mu Piscivm be assumed to be the star at the initial point, the longitudes of stars according to "his opinion" will have to be reduced by 1° 20'.

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*These very stars have been adopted as junction-stars for giving moments of conjunctions in the sāyana almanac since Śaka 1815. The European names of such junction-stars as have been selected by different researchers may be seen in tables given later on.

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POLAR LONGITUDES OF JUNCTION STARS AND SOME OTHERSTARS

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| Serial No. | Names of Stars | Modern S.S. | Brahma Gupta S. | Lalla Tantra | B. Tulya | Sundara S. | Graha-lāghava | Author's opinion |
| | | ° | ° | ° | ° | ° | ° | ° |
| 1 | Aśvinī | 8 | 8 | 8 | 8 | 8 | 8 | 43 |
| 2 | Bharaṇī | 20 | 20 | 20 | 21 | 20 | 21 | 51 |
| 3 | Kṛttikā | 37 | 37 | 36 | 37 | 38 | 38 | 2 |
| 4 | Rohiṇī | 49 | 49 | 49 | 49 | 50 | 49 | 37 |
| 5 | Mṛgaśiras | 63 | 63 | 62 | 62 | 63 | 62 | 26 |
| 6 | Ārdrā | 67 | 67 | 70 | 66 | 67 | 66 | 43 |
| 7 | Punarvasu | 93 | 93 | 92 | 92 | 93 | 94 | 21 |
| 8 | Puṣya | 106 | 106 | 105 | 106 | 106 | 106 | 43 |
| 9 | Āśleṣā | 109 | 108 | 114 | 107 | 108 | 106 | 28 |
| 10 | Maghā | 129 | 129 | 128 | 129 | 129 | 129 | 59 |
| 11 | P. Phālgunī | 144 | 147 | 139 | 148 | 155 | 148 | 31 |
| 12 | U. Phālgunī | 155 | 155 | 154 | 155 | 155 | 155 | 1 |
| 13 | Hasta | 170 | 170 | 173 | 170 | 155 | 170 | 6 |
| 14 | Citrā | 180 | 183 | 184 | 183 | 183 | 183 | 28 |
| 15 | Svāti | 199 | 199 | 197 | 198 | 199 | 198 | 11 |
| 16 | Viśākhā | 213 | 212 | 212 | 212 | 212 | 212 | 8 |
| 17 | Anurādhā | 224 | 224 | 222 | 224 | 224 | 224 | 59 |
| 18 | Jyeṣṭhā | 229 | 229 | 228 | 224 | 229 | 230 | 45 |
| 19 | Mūla | 241 | 241 | 241 | 242 | 229 | 242 | 23 |
| 20 | Pūrva Āṣāḍha | 254 | 254 | 254 | 255 | 254 | 255 | 5 |
| 21 | Uttara Āṣāḍha | 260 | 260 | 267 | 260 | 260 | 261 | 10 |
| 22 | Abhijit | 266 | 265 | 267 | 260 | 260 | 261 | 58 |
| 23 | Śravaṇa | 280 | 278 | 283 | 275 | 278 | 275 | 47 |
| 24 | Śatātārkā | 290 | 290 | 296 | 287 | 290 | 286 | 43 |
| 25 | P. Bhādrapadā | 320 | 320 | 313 | 320 | 320 | 320 | 3 |
| 26 | U. Bhādrapadā | 326 | 326 | 327 | 325 | 326 | 325 | 35 |
| 27 | Revatī | 359 | 337 | 335 | 337 | 337 | 337 | 57 |
| | | | 0 | 359 | 0 | 0 | 0 | 20 |
| | Agastya | 90 | 87 | 87 | | 87 | 80 | |
| | Vyādha | 80 | 86 | 86 | | 86 | 81 | |
| | Agani | 52 | | | | 52 | 53 | |
| | Brahmā | 52 | | | | 52 | 55 | |
| | Prajāpati | 57 | | | | 57 | 61 | |
| | Apāṃvatsa | 180 | | | | | 183 | |
| | Apas | 180 | | | | | | |

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POLAR LATITUDES OF JUNCTION STARS AND SOME OTHER STARS

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| Serial No. | Names of Stars | Modern S.S. | Brahma Gupta S. | Lalla Tantra | Dāmodarīya B. Tulya | Sundara S. | Graha- Jēghava. | Author's opinion | Direction of latitude |
| 1 | Aśvinī | 10 | 10 | 10 | 10 | 10 | 10 | 9 | N |
| 2 | Bharaṇī | 12 | 12 | 12 | 12 | 12 | 12 | 10 | N |
| 3 | Kṛttikā | 5 | 4 | 5 | 4 | 4½ | 5 | 5 | S |
| 4 | Rohiṇī | 5 | 4 | 5 | 4 | 5 | 5 | 4 | S |
| 5 | Mṛga | 10 | 10 | 10 | 10 | 10 | 10 | 13 | S |
| 6 | Ārdrā | 9 | 11 | 11 | 11 | 11 | 11 | 6 | N |
| 7 | Punarvasu | 6 | 6 | 6 | 6 | 6 | 6 | 6 | N |
| 8 | Puṣya | 0 | 0 | 0 | 0 | 0 | 0 | 0 | N |
| 9 | Āśleṣā | 7 | 7 | 7 | 7 | 7 | 7 | 0 | N |
| 10 | Maghā | 0 | 0 | 0 | 0 | 0 | 0 | 0 | N |
| 11 | P. Phālgunī | 12 | 12 | 12 | 11 | 11 | 12 | 11 | N |
| 12 | U. Phālgunī | 13 | 13 | 13 | 12 | 11 | 13 | 10 | N |
| 13 | Hasta | 11 | 11 | 8 | 11 | 11 | 11 | 13 | N |
| 14 | Citrā | 2 | 1 | 2 | 1 | 1½ | 2 | 2 | N |
| 15 | Svati | 37 | 37 | 37 | 37 | 37 | 37 | 32 | N |
| 16 | Viśākhā | 1 | 1 | 1 | 1 | 1 | 1 | 0 | S |
| 17 | Anurādhā | 3 | 3 | 3 | 3 | 3 | 3 | 2 | S |
| 18 | Jyeṣṭhā | 4 | 8 | 4 | 8 | 8 | 8 | 4 | S |
| 19 | Mūla | 9 | 5 | 8 | 5 | 5 | 5 | 4 | S |
| 20 | Pūrva Āṣāḍhā | 5 | 5 | 5 | 5 | 5 | 5 | 13 | S |
| 21 | Uttara Āṣāḍhā | 5 | 5 | 5 | 5 | 5 | 5 | 2 | S |
| 22 | Abhijit | 60 | 62 | 63 | 62 | 62 | 62 | 20N | S |
| 23 | Śravaṇa | 30 | 30 | 30 | 29 | 30 | 30 | 61 | S |
| 24 | Śatētārakā | 36 | 36 | 36 | 25 | 36 | 36 | 29 | S |
| 25 | P. Bhādrapadā | 0 | 0 | 0 | 0 | 2½ | 0 | 34 | S |
| 26 | U. Bhādrapadā | 24 | 24 | 24 | 23 | 24 | 24 | 0 | S |
| 27 | Revati | 26 | 26 | 26 | 26 | 26 | 26 | 25 | S |
| | | 0 | 0 | 0 | 0 | 0 | 0 | 0 | N |
| | Agastya | 80 | 77 | 80 | 77 | 77 | 76 | 13 | S |
| | Vyadha | 40 | 40 | 40 | 40 | 40 | 40 | 21 | S |
| | Agni | 8 | | | 8 | 8 | 8 | 13 | S |
| | Brahmā | 30 | | | 30 | 30 | 30 | 0 | S |
| | Prajapati | 38 | | | 38 | 38 | 39 | 3 | S |
| | Apamvatsa | 3 | | | | | | 14 | S |
| | Āpas | 9 | | | | | | 18 | S |

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CELESTIAL LONGITUDES OF JUNCTION STARS

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| Serial No. | Stars | Sūrya Siddhānta | Brahmagupta Siddhānta | 2nd Ārya Siddhānta | Sārvabhauma Siddhānta | Venkateś B. Ketkar | Author's opinion |
| 1 | Aśvinī | 11 59 | 12 5 | 12 0 | 12 40 | 14 6 | 10 8 |
| 2 | Bharaṇī | 24 35 | 24 41 | 24 23 | 25 8 | 28 20 | 24 22 |
| 3 | Kṛttikā | 39 8 | 38 58 | 38 33 | 39 2 | 40 7 | 36 9 |
| 4 | Rohiṇī | 48 9 | 48 11 | 47 33 | 48 9 | 49 55 | 45 57 |
| 5 | Mṛgaśiras | 61 3 | 61 0 | 61 3 | 61 1 | 63 50 | 59 51 |
| 6 | Ārdrā | 65 50 | 65 5 | 68 23 | 65 8 | 68 53 | 75 16 |
| 7 | Punarvasu | 92 52 | 92 52 | 92 53 | 92 53 | 93 22 | 89 24 |
| 8 | Puṣya | 106 0 | 106 0 | 106 0 | 106 0 | 108 51 | 104 53 |
| 9 | Aśleṣā | 109 59 | 109 58 | 111 0 | 108 56 | 113 45 | 110 44 |
| 10 | Maghā | 129 0 | 129 0 | 129 0 | 129 0 | 129 58 | 126 53 |
| 11 | P. Phālgunī | 139 58 | 139 45 | 140 23 | 142 48 | 143 32 | 139 34 |
| 12 | U. Phālgunī | 150 10 | 150 4 | 150 23 | 149 40 | 151 45 | 147 47 |
| 13 | Hasta | 174 22 | 174 28 | 174 3 | 175 13 | 173 35 | 169 37 |
| 14 | Citrā | 180 48 | 180 49 | 182 53 | 183 50 | 183 58 | 180 0 |
| 15 | Svāti | 183 2 | 183 41 | 184 0 | 182 24 | 184 22 | 180 24 |
| 16 | Viśākhā | 213 31 | 212 34 | 212 53 | 212 36 | 211 8 | 201 14 |
| 17 | Anurādhā | 224 44 | 223 33 | 224 53 | 224 38 | 222 42 | 218 44 |
| 18 | Jyeṣṭhā | 230 7 | 230 4 | 230 3 | 230 5 | 229 54 | 225 56 |
| 19 | Mūla | 242 52 | 242 48 | 242 44 | 242 16 | 243 0 | 240 44 |
| 20 | Pūrva Āṣāḍhī | 254 39 | 254 0 | 254 33 | 254 34 | 254 42 | 252 28 |
| 21 | Uttara Āṣāḍhī | 260 23 | 260 37 | 260 23 | 260 21 | 262 47 | 262 24 |
| 22 | Abhijit | 264 10 | 264 46 | 263 0 | 262 10 | 265 26 | 261 28 |
| 23 | Śravaṇa | 282 29 | 282 3 | 280 3 | 280 3 | 281 53 | 277 55 |
| 24 | Dhaniṣṭhā | 296 50 | 296 15 | 295 33 | 294 12 | 297 31 | 293 33 |
| 25 | Śatabhiṣak | 319 50 | 319 54 | 319 53 | 319 54 | 321 42 | 317 44 |
| 26 | P. Bhādrapadī | 334 25 | 334 46 | 334 53 | 336 8 | 334 40 | 330 42 |
| 27 | U. Bhādrapadī | 347 16 | 347 29 | 347 0 | 348 44 | 354 26 | 345 19 |
| 28 | Revatī | 359 50 | 359 0 | 359 0 | 359 50 | 359 0 | 359 17 |

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CELESTIAL LATITUDES OF JUNCTION STARS

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| Serial No. | Stars | Direction of Latitudes | Sūrya Siddhānta | Brahmagupta Siddhānta | 2nd Ārya Siddhānta | Sārvabhauma Siddhānta | Veṅkaṭesh B. Ketkar | Author's opinion |
| 1 | Aśvinī | N | 9 | 9 | 10 | 0 | 55 | 8 | 29 |
| 2 | Bharaṇī | S | 11 | 11 | 12 | 0 | 56 | 10 | 26 |
| 3 | Kṛttikā | S | 4 | 4 | 5 | 0 | 44 | 4 | 2 |
| 4 | Rohiṇī | S | 4 | 4 | 5 | 0 | 40 | 5 | 28 |
| 5 | Mṛgaśiras | S | 4 | 4 | 5 | 0 | 13 | 5 | 23 |
| 6 | Ārdrā | N | 9 | 9 | 10 | 0 | 7 | 13 | 13 |
| 7 | Punarvasu | N | 8 | 10 | 11 | 0 | 16 | 16 | 3 |
| 8 | Puṣya | N | 0 | 6 | 0 | 0 | 0 | 6 | 6 |
| 9 | Āśleṣā | S | 6 | 6 | 6 | 0 | 4 | 0 | 40 |
| 10 | Maghā | S | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 11 | P. Phālgunī | S | 6 | 0 | 7 | 0 | 5 | 5 | 5 |
| 12 | U. Phālgunī | S | 11 | 11 | 0 | 0 | 0 | 0 | 28 |
| 13 | Hasta | S | 12 | 12 | 12 | 0 | 9 | 9 | 9 |
| 14 | Citrā | S | 10 | 10 | 13 | 0 | 42 | 12 | 42 |
| 15 | Svāti | S | 1 | 1 | 10 | 0 | 55 | 16 | 16 |
| 16 | Viśākhā | S | 33 | 33 | 2 | 0 | 4 | 12 | 12 |
| 17 | Anurādhā | S | 1 | 1 | 37 | 30 | 12 | 11 | 11 |
| 18 | Jyeṣṭhā | S | 2 | 1 | 3 | 0 | 2 | 3 | 3 |
| 19 | Mūla | S | 3 | 3 | 4 | 0 | 5 | 2 | 2 |
| 20 | Pūrva Āṣāḍhā | S | 8 | 8 | 9 | 0 | 30 | 30 | 49 |
| 21 | Uttara Āṣāḍhā | S | 5 | 5 | 5 | 0 | 1 | 1 | 30 |
| 22 | Abhijit | N | 4 | 5 | 5 | 20 | 25 | 4 | 48 |
| 23 | Śravaṇa | N | 59 | 61 | 63 | 0 | 50 | 4 | 58 |
| 24 | Dhan iṣṭhā | N | 29 | 29 | 30 | 0 | 37 | 6 | 33 |
| 25 | Śatabhiṣak | N | 35 | 35 | 36 | 0 | 22 | 6 | 36 |
| 26 | P. Bhādrapadā | N | 22 | 22 | 0 | 0 | 1 | 3 | 27 |
| 27 | U. Bhādrapadā | N | 24 | 23 | 24 | 20 | 14 | 27 | 27 |
| 28 | Revatī | S | 0 | 0 | 26 | 0 | 61 | 61 | N1 |
| 29 | | | | | | | 29 | 29 | 61 |
| 30 | | | | | | | 25 | 25 | 44 |
| 31 | | | | | | | 20 | 20 | 18 |
| 32 | | | | | | | 26 | 26 | 2 |
| 33 | | | | | | | 28 | 28 | 33 |
| 34 | | | | | | | 0 | 0 | 0 |
| 35 | | | | | | | 0 | 0 | 23 |
| 36 | | | | | | | 0 | 0 | 19 |
| 37 | | | | | | | 0 | 0 | 12 |
| 38 | | | | | | | 0 | 0 | 36 |
| 39 | | | | | | | 0 | 0 | 13 |
| 40 | | | | | | | 0 | 0 | 3 |

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The celestial latitudes and longitudes calculated from the polar latitudes and longitudes given by the Sūrya-Siddhānta and the Brahmagupta Siddhānta* have been given in tables on pages 340-341. The latitudes and longitudes given by the second Ārya Siddhānta appear to be celestial (based on the pole of the ecliptic) and hence are given in the same table. It has been clearly mentioned in the Sārvabhauma Siddhānta that the longitudes and latitudes given in it are celestial and hence they are also given in the table. The celestial latitudes and longitudes calculated by the author and Ketkar were first calculated from the French or English Nautical Almanac. Longitudes given by Ketkar are nirayaṇa and are measured from the star, Zeta Piscium, which he assumed as the initial point, and his ones have been calculated by assuming the longitude of Citrā to be 180°. Otherwise, our figures are, in fact, identical. Seven of his junction stars are, however, different from those of Ketkar. Their longitudes and latitudes are, therefore, actually different. The author has given two figures for the star Revati. The first belongs to Zeta Piscium and the second to Mu Piscium. If Mu Piscium be taken as the initial point, 43 minutes will have to be added to the longitude of each star.

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The PAÑCASIDDHĀNTIKĀ has not recorded the polar longitudes of stars as given in the original Sūrya-Siddhānta. It appears that they had been given in the original. ĀRYABHAṬA I has mentioned nothing about the junction stars of nakṣatras. BHĀSKARĀCĀRYA has adopted the polar longitudes and latitudes of nakṣatras from BRAHMAGUPTA.

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AL BERUNI has quoted latitudes and longitudes as given by Brahmagupta, some of which are different from those given by the author. They are:— longitude of Uttarā Bhādrapadā, 336°; latitude of Mṛga, 5°; of Āśleṣā 6°; and of Mūla 9½°. Some error in this respect appears to have crept into Beruni's work either in the original or in its later transcriptions. The figures denoting Brahmagupta's longitudes and latitudes are given in code words in verse form in the original, and they are the same, both in the Brahmagupta Siddhānta and in Khaṇḍakhādya; and the author has collected them from four different copies of the work, so that there is no doubt about their reliability. Brahmagupta has in the beginning given the latitudes of Kṛttikā, Rohiṇī, Citrā, Viśākhā, Anurādhā and Jyeṣṭhā respectively as 5, 5, 2, 1½, 3, and 4 and Beruni has quoted them thus. But Brahmagupta has immediately added that these latitudes must be reduced by certain number of minutes each. Accordingly his figures have been given after reduction, but Beruni has not done so. The latitude of Mūla has been given in the original as "ardhanavama". Beruni has assumed this to be 9½°. But the word "ardhanavama" means 8½°.

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As for the polar longitudes, according to the modern Sūrya-Siddhānta given above, there is a difference of opinion about Ārdrā. It appears from the remarks of Ranganath, the commentator of the Sūrya-Siddhānta that according to Narmad, the longitude of Ārdrā is 73° 47′, and according to Parvat, 73° 10′; and he also adds that according to popular view, it is 74° 50′. But the longitude of Ārdrā as given by the Śākalya Saṃhitā is 67° 20′ only and Ranganath has accepted it**. Kamalakara, the author of the Siddhānta-

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*The longitudes and latitudes of the S.S. have been given as calculated by Whitney by the methods given in that Siddhānta, and those for Brahma Siddhānta have been taken from Bentley's book and they are calculated by Bently himself.

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**The polar longitudes of stars as given by the modern Sūrya-Siddhānta, the Romaśa, Śākalya's Brahma Siddhānta, and the same are given in units of ten minutes each, measured from the initial point of the corresponding nakṣatra division. The Sūrya-Siddhānta has cited the longitude of Ārdrā as "abdhayah" i.e. 4. One comes across other reading also like "gobdhayah" meaning 49, and "gognayah" meaning 39.

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tatva-viveka, has accepted all the longitudes and latitudes as in the Sūrya-Siddhānta, but has taken 74° 50′ as the longitude of Ārdrā. The modern Romaśa, Soma and Śakalya’s Brahma Siddhāntas are followers of the Sūrya-Siddhānta and these contain the same longitudes and latitudes of stars as in the Sūrya-Siddhānta. There is, however, a difference of view about Ārdrā. Śakalya’s Brahmasiddhānta has given longitudes and latitudes as mentioned above. The Soma Siddhānta gives 74° 50′ as the longitude of Ārdrā. The figures for all the remaining longitudes and latitudes are identical with those of the Sūrya-Siddhānta. The author had procured two editions of the Romaśa Siddhānta. Some of the longitudes given in them are different from those of the Sūrya-Siddhānta but the difference seems to be due to copyist’s errors. One may safely say, therefore, that the polar longitudes and latitudes given by the Romaśa Siddhānta are almost the same as those of the Sūrya Siddhānta.

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In the Sūrya Siddhānta, the longitudes and latitudes of Agastya (Canopus) Vyādha (Sirius), Agni and Brahmā have been given in three verses (Adhikāra 8). But they are not immediately followed by the verses relating to Prajāpati; Apāmvatsa and Apa have not been immediately given. The longitudes and latitudes of Prajāpati and the other two stars have been repeated in verses 20 and 21 in the end. It, therefore, appears that these verses may have been interpolated later. In the 9th Adhikāra (Chapter) certain stars which never set are mentioned and they include Brahmahṛdaya as one. Hence, Prajāpati-one of above three stars—ought to have been included in the list, because the latitude of Prajāpati is 8° more to the north than that of Brahma-hṛdaya. In spite of this it has not been included, which shows that these verses may have been interpolated later. However, one of these stars, Apāmvatsa, is referred to in the Bṛhat-Samhitā*. This shows that all these three stars were known in Śaka 427 also. Prof. Whitney** observes that the star Prajāpati, Apāmvatsa and Āpa have not been mentioned in Śakalya’s Brahma-siddhānta, but that is wrong. They occur in all the three siddhāntas, Śakalya Brahma, Romaśa and Soma. Of these, only Āpa has not been mentioned by the Grahalāghava. Śakalya’s Brahmasiddhānta has given the longitudes and latitudes of Saptarṣis (the Great Bear), which are not found in any other work. The YANTRA RĀJA has given sāyana longitudes and latitudes of 32 stars. The SIDDHĀNTA RĀJA has given those for 84 stars.

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NUMBER OF STARS IN ASTERISMS

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Some nakṣatras consist of only one star and some have many. In the case of those which have many stars, their junction star is indicated by its position and description by Sūrya and three other Siddhāntas, and these descriptions are almost similar; but they do not help in identifying the junction star correctly. Of the four Siddhāntas, the Śakalya Brahmasiddhānta alone has mentioned the number of stars in each nakṣatra, while others have not. A mere indication of the direction without the number of stars is not of much avail. Apart from Śakalya Brahmasiddhānta, it is only the Khaṇḍakhādya among other astronomical works which has mentioned the junction stars, as also the number of stars in the nakṣatra. They are found in some Samhitā

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∗ “Samamuttareṇa tārā chitrāyāḥ kirtyate apāmvatsaḥ”—meaning “The star Apāmvatsa is described as situated exactly to the north of Chitrā”—Brihat-Samhitā, Chapter 25, Verse 4.

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∗∗ See page 218, Translation of the S.S. by Burgess.

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| Serial No. | Names of Stars | Taittirīya Śruti | Nakṣatra Kalpa | Vṛddha Garga Saṃhitā | Nārada Saṃhitā | Varāha Mihira | Khaṇḍa Khādya | Lalla's Ratna-kośa | Śakalya Brahma Sidd. | Śrīpati's Ratna-mālā | Muhūrta Tatva | Muhūrta Cintāmaṇi |
| 1 | Aśvanī | | 2 | 2 | 3 | 3 | 2 | 3 | 2 | 3 | 3 | 3 |
| 2 | Bharaṇī | | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| 3 | Kṛttikā | | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 | 6 |
| 4 | Rohiṇī | | | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 | 5 |
| 5 | Miga | | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| 6 | Ārdrā | 1 or 2 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 7 | Punarvasu | 2 | 2 | 2 | 4 | 5 | 2 | 4 | 2 | 4 | 4 | 4 |
| 8 | Puṣya | 1 | 1 | 1 | 3 | 3 | 1 | 3 | 3 | 3 | 3 | 3 |
| 9 | Āśleṣā | | 6 | 6 | 5 | 5 | 6 | 5 | 5 | 5 | 5 | 5 |
| 10 | Maghā | | 6 | 6 | 5 | 6 | 6 | 5 | 5 | 5 | 5 | 5 |
| 11 | P. Phālgunī | | 2 | 2 | 2 | 5 | 2 | 2 | 2 | 2 | 2 | 2 |
| 12 | U. Phālgunī | | 2 | 2 | 2 | 8 | 2 | 2 | 2 | 2 | 2 | 2 |
| 13 | Hasta | | 5 | 5 | 5 | 2 | 5 | 5 | 5 | 5 | 5 | 5 |
| 14 | Citrā | | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 15 | Svāti | | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 16 | Viśākhā | 2 | 2 | 2 | 2 | 5 | 1 | 4 | 2 | 4 | 4 | 4 |
| 17 | Anurādhā | | 4 | 4 | 4 | 4 | 4 | 3 | 3 | 3 | 3 | 3 |
| 18 | Jyeṣṭhā | 1 | | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
| 19 | Mūla | 1 or 2 | | 6 | 11 | 3 | 2 | 11 | 3 | 11 | 11 | 11 |
| 20 | Pūrva Āṣāḍhā | | 4 | 4 | 4 | 2 | 4 | 2 | 9 | 4 | 4 | 2 |
| 21 | Uttara Āṣāḍhā | | 4 | 4 | 2 | 8 | 4 | 2 | 4 | 4 | 4 | 2 |
| 22 | Abhijit | | | | | | | | | | | |
| 23 | Śravaṇa | 1 | 3 | 3 | : : | : : | 3 | 3 | 3 | 3 | 3 | 3 |
| 24 | Dhaniṣṭhā | 4 | 5 | 4 | 3 | 3 | 5 | 4 | 5 | 4 | 4 | 4 |
| 25 | Śatabhiṣak | 1 | 1 | 1 | : : | : : | 1 | 1 | 100 | 100 | 100 | 100 |
| 26 | P. Bhādrapadā | | 2 | 2 | 100 | 100 | 100 | 100 | 2 | 2 | 2 | 2 |
| 27 | U. Bhādrapadā | 4 | 2 | 2 | 2 | 8 | 2 | 2 | 2 | 2 | 2 | 2 |
| 28 | Revati | 1 | 1 | 4 | 32 | 32 | 1 | 32 | 32 | 32 | 32 | 32 |

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European astronomers have prepared catalogues of most of the stars visible to the naked eye during the last two or three centuries. They have named those stars and have determined with precision their right ascensions and declinations. The views of different research workers regarding the junction stars of our nakṣatras o't of those stars have been given in the table below :—

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JUNCTION STARS OF NAKSATRAS

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| Srl. No. | Names of Stars | Colebrooke | Bentley, Keropant | Whitney, Burgess | Bāpudeva | V. B. Ketkar | The Author |
| 1 | Aśvinī | Alpha Arietis | Beta Arietis | Beta Arietis | A'pha Arietis | Beta Arietis | Beta Arietis. |
| 2 | Bharaṇī | Mu or 35 Arietis. | 35 Arietis | 35 Arietis | 35 Arietis | 41 Arietis | 41 Arietis. |
| 3 | Kṛttikā | E'ta Tauri | Eta Tauri | Eta Tauri | Eta Tauri | Eta Tauri | Eta Tauri. |
| 4 | Rohiṇī | Aldebaran | Aldebaran | Aldebaran | Aldebaran | Alcebaran | Aldebaran. |
| 5 | Mṛga | Lambda Orionis. | 116 Tauri | Lambda Orionis | Lambda Orionis | Lambda Orionis | Lambda Orionis |
| 6 | Ārdrā | A'pha Orionis | 133 Tauri | Alpha Orionis | Alpha Orionis | Alpha Orionis | Gamma Geminorum. |
| 7 | Punarvasu | Pullux | Pollux | Pollux | Pollux | Pollux | Pollux. |
| 8 | Puṣya | Delta Cancri | Delta Cancri | Delta Cancri | Delta Cancri | Delta Cancri | Delta Cancri. |
| 9 | Āśleṣā | Al'pha Cancri | 49 Cancri | Epsilon Hydrae | Alpha Cancri | Alpha Cancri | Zeta Hydrae. |
| 10 | Maghā | Regulus | Regulus | Regulus | Regulus | Regulus | Regulus. |
| 11 | Pūrva Phālgunī | Delta Leonis | Theta Leonis | Delta Leonis | Delta Leonis | Theta Leonis | Theta Leonis. |
| 12 | Uttara Phālgunī | Denebola | Denebola | Denebola | Denebola | Denebola | Denebola. |
| 13 | Hasta | Gamma or Delta Corvi. | Delta Corvi | Delta Corvi | Gamma or Delta Corvi. | Delta Corvi | Delta Corvi. |
| 14 | Citrā | Spica | Spica | Spica | Spica | Spica | Spica. |
| 15 | Svātī | Arcturus | Arcturus | Arcturus | Arcturus | Arcturus | Arcturus. |
| 16 | Viśākhā | Alpha or Kapp Librae. | 24 Librae | 24 Librae | A'pha or Kappa Librae. | 24 Librae | Alpha Librae. |
| 17 | Anurādhā | Delta Scorpii | Beta Scorpii | De'ta Scorpii | Delta Scorpii | Delta Scorpii | Delta Scorpii. |
| 18 | Jyeṣṭhā | Antares | Antares | Antares | Antares | Antares | Antares. |
| 19 | Mūla | Nu or 34 Scorpii. | 34 Scorpii | Lambda Scorpii | 34 Scorpii | 45 Op'iuchi | Lambda Scorpii. |
| 20 | Pūrva Āṣāḍhā | Delta Sagittarii | Delta Sagi | Delta Sagi | Delta Sagi | Delta Sagi | Lambda Sagittarii |
| 21 | Uttara Āṣāḍhā | Tau sagittarii | Phi Sagi | Sigma Sagi | Tau Sagi | Sigma Sagi | Pi Sagi. |
| 22 | Śravaṇa | Wega | Wega | Wega | Wega | Wega | Wega. |
| 23 | Dhaniṣṭhā | Altair | Altair | Altair | Altair | Altair | Altair. |
| 24 | Śata'hiṣak | Alpha Delphini | A'pha Del'ph | Alpha De'phi | A'pha De'ph | Alpha De'ph | Alpha De'phi. |
| 25 | P. Bhādrapadā | Lambda Aquarii. | Lamb'a Aquarii. | Lambda Aquarii. | Lambda Aquarii. | Lambda Aquarii | Lambda Aquarii. |
| 26 | U. Bhādrapadā | Markab | Markab | Markab | Markab | Markab | Markab. |
| 27 | Revatī | Al'pheratz | Algenib/Alpheratz. | Algenib/Alpheratz. | A'pheratz | Alpheratz | Algenib. |
| | | Zeta Piscium | Zeta Piscium | Zéta Piscium | Zeta Piscium | Zeta Piscium | Zeta or Mu Piscium. |

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works. Opinions differ regarding the number of stars in a nakṣatra. On page 344 the number of stars in nakṣatras have been given in a tabular form according to 11 different works. First come those stars which can be definitely known on the basis of information gathered from the Taittirīya Śruti given in part I. Nakṣatra Kalpa* is an appendix to the Atharvaveda. Mahādeva, the commentator of Śrīpati's Ratnamālā has given the number of stars as mentioned by Lalla and those have been reproduced here. These may probably have been borrowed from the Ratnakoṣa.

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From all considerations, it appears that although there may be a difference of opinion regarding the number of stars in each nakṣatra (asterism) there is no difference of opinion as regards the identification of any ‘cluster of stars.’ The word ‘śata’ (hundred) in the name śatabhiṣak’ has led to the misunderstanding that it contains 100 stars and hence the name Śatabhiṣak was changed into Śatatārā. But this belief seems to have been current since the time of VARĀHA MIHIRA. Similarly, in the opinion of all, the latitude of the junction star of Revati is zero ; and the longitude also is very nearly zero. Hence, there is no difference of opinion about the junction star of Revati. There are several stars situated near it in the cluster forming the shape of a Mṛdaṅga (tabor). But it is not that they are exactly 32. It is not known on what basis the number was fixed ; but this number too has been handed down from VARĀHA’S TIME. If the regions occupied by all the remaining nakṣatras in the sky be seen, it will be found that every assumption regarding the number of stars has some basis or other. Hence the numbers of all authors are justifiable.

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Among the European scholars Colebrooke has made a comparative study of our nakṣatra system and that of the Arabs, and has considered in full details the question of the names and places of our junction stars in the light of the European system. Sir William Jones had done it (in 1790 A.D.) before him, but it was inadequate. Colebrooke’s thesis on this subject was published in Vol IX of Asiatic Researches, in 1807 A.D. from which the stars acceptable to Colebrooke, have been given in the above table. The efforts made by Colebrooke have been of much use for later investigators. A book entitled A Historical View of Indian Astronomy by BENTLEY was published at Calcutta in 1823. He has considered in it the stars on the basis of their longitudes and latitudes given by BRAHMAGUPTA. The junction stars of his choice have been given from the book in the above table. Among these, he has given only Algeib as the star for Uttarā Bhādrapadā. KEROPANT, however, has taken Alpheratz in its place. Excepting this, KEROPANT has taken all the stars as in the list of BENTLEY**. In addition to the above, Bentley has suggested some other stars as alternative. They are :—Gamma Arietis for Aśvini ; 113, and 117 Tauri for Mṛga ; 50 Cancri for Āśleṣā ; 71 Leonis for Pūrvā Phalguni ; 8 Corvi for Hasta ; 35 Scorpii for Mūla. WHITNEY has made a very detailed study*** of this subject ; and has determined the junction stars after careful consideration. BAFUDEVA’S Junction stars have been given

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*The author has not yet actually seen the works Nakṣatra Kalpa and Vṛddha Garga Samhitā himself. He has quoted the number of stars from the information given by Prof. Thibaut in Indian Antiquary, Vol. XIV PP. 43-45. Prof. Thibaut has quoted the lines from Vṛdha Garga Samhitā and Khaṇḍakhādya. The author has corrected an error committed by him regarding Revati and Aśvini.

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**See pages 324-25, Planetary Tables.

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***See pages 175-220, Translation of S.S.

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in the above table from the list given in his English translation of the S.S.* All of them** are according to the choice of COLEBROOKE. But Bapudeva has changed seven of them in his almanac. Thus, he has abondoned his first choice in the case of the junction stars of Aśvinī, Aśleṣā, Viśākhā, Mūla, Uttarāṣāḍhā, Dhaniṣṭhā, Uttarā Bhādrapadā, and substituted Beta- Arietis, Epsilon Hydrae, 24 (Iotā) Libra, Lambda Scorpii, Sigma Sagittarii, Gamma Pegasi; and it is easily seen that these changes are made in conformity with WHITNEY'S views. The author has given the junction stars acceptable to Venkatesh Bapuji Ketkar, from the list which he supplied. He has attempted to establish as much agreement as possible between the longitudes and latitudes of the stars given in our ancient works and those of the stars determined by Colebrooke and others. He has, however, attempted to see that in addition to the above point that the distances between consecutive junction stars be as near to 13°20' as possible, so that they would be found to occupy a place in their own divisions. It is not proper to adopt a star from the constellation of Mṛga as junction star of Ārdrā. The line “ārdrayā rudraḥ pathamāna eti” (Tai Br.3.1.1) suggests that God Rudra accompanies the constellation of Ārdrā. The star adopted by the author for Ārdrā transits the meridian only 9 minutes earlier than Sirius. There is no other bright star nearer to Sirius in that region.

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The above table will show that there is unanimity of opinion about the following 14 stars :—Kṛttikā, Rohiṇī, Punarvasu, Puṣya, Maghā, U. Phalguni. Citrā, Svāti, Jyeṣṭhā, Abhijit, Śravaṇa, Śatabhiṣak, P. Bhadrapadā and Revati, Opinion differs regarding the rest. There is no sense in trying to see whose opinion seems probable, because, it cannot be at all claimed that the longitudes and latitudes of stars given in our old works agree completely with those of all or some stars chosen by any one of them. The longitudes and latitudes of stars given by our works may not be found to agree either because they have not been recorded accurately or because, it is not known to what time they belong; or else, because, they have been calculated by the modern method of calculating ancient longitudes and latitudes, which itself may not be quite accurate. Nevertheless the fact remains that they do not agree. Hence, those stars are to be determined as junction stars whose co-ordinates agree at least approximately. It so often happens that one out of the two or three stars in a nakṣatra shows a close agreement in point of latitude but not longitude, while quite another agrees in point of longitude. This being so, some have laid a stress on the agreement in latitude and others in longitude. Some others have paid attention to the direction of their position in the group. Thus each author has paid attention to the direction of their position in the group. Thus each author has some point or other to support his view. When once it is decided that a particular nakṣatra is the same as some particular cluster of the present times, i.e. Bharaṇī is the same as Musca known to Europeans, the question of deciding which star in the cluster is the junction star naturally remains controversial. If, however, some one adopted some star outside the cluster as junction star, it will be a mistake unless he has some ground for doing so. Thus, for instance, there is a cluster of star visible in the sky, known as Mṛga and its Śirṣa” (i.e. the head of the antelope ; Orion). One of the three stars forming the head of the antelope must be taken as the junction star of Mṛgaśirṣa. But KEROPANT'S star is outside the region. This is of course an error. All works have described the shape of the nakṣatra Mūla as resembling the tail of a lion. But Ketkar's star remains far away from the cluster and hence should be taken to be erroneous. The planetary tables by Keropant have given by mistake 27° in place of 37° as the declination of Mūla; Keikar appears to have committed the error because of this. Apart from these considerations every investigator can be said to be justified in his views.

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∗ In the Bibliotheca Indica New Series, of 1860, A.D. he has taken Musca for Bharaṇī; but in the almanac, he takes 35 Arietis, and hence the author has given the latter in the table.

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∗∗ It appears that Pi Tauri has been wrongly taken in place of Eta Tauri through an error in printing.

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CATALOGUES OF STARS

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HIPPARCHUS (150 B.C.) was the first in Europe to prepare a catalogue of stars showing their longitudes and latitudes after taking necessary observations. It is not at present available; but PTOLEMY after making allowance for ayana motion, prepared another catalogue (138 B.C.). It is at present available in his work entitled Syntaxis. It contains 1022 stars, grouped into 48 constellations. A second Catalogue after this, was prepared by 'ULUĞ BEY, grandson of Tamerlane, and Emperor of Samarkand in 1437 A.D. It contains 1019 stars. Another catalogue containing 777 stars was prepared by TYCHO BRAHE, in 1600 A.D. Afterwards, several catalogues were prepared in Europe. No one in our country appears to have prepared such a catalogue by taking actual observations. MAHENDRASŪRI has, in his work Yantrarāja, given polar longitudes and latitudes of 32 stars from the works of Greeks. Malayendu Sūri, the commentator of that work observes,”

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शकमतेन नक्षत्रगोले नक्षत्राणां द्वाविंशत्यधिकसहस्र १०२२ मुक्तमस्ति । तन्मध्य ग्रंथ- कारेण यावनं नक्षत्रगोलं सम्यग् बुध्वा यंत्रोपयोगीनि द्वात्रिंशत् नक्षत्राणि गृहीतानि । अध्याय १ श्लोक २१—३८ टीका.

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“According to the Greek work, there are 1022 stars described from the celestial globe. The author of this work, after studying the starry globe, has selected only 32 useful stars out of them.”

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The catalogue of stars referred to in this, appears to be that of Ptolemy, as can be seen from the number of stars which is 1022 and from the date of the writer and that of the commentator (pages 230-231) It seems to have come to this country through the Muslims; but it does not appear to have gained currency or came into use.

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IDENTIFICATION OF STARS

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Now-a-days we do not generally find Joshis who can correctly point out at least all the nakṣatras, let alone their junction stars. Colebrooke remarks, “None of the native astronomers, whom I consulted, were able to point out, in the heavens all the asterisms for which they had names.” Beruni observes*, “I took great pains in this respect; but I did not come across a single Joshi who could point out with his finger the junction stars of all the nakṣatras by merely looking at them.” Even in the present times, a Joshi who can point out the junction stars can be rarely found. There are several Joshis who are unable to point out even the nakṣatras. Once, a Joshi who was very proficient in preparing horoscopes and selecting muhūrtas came accross the author. This Joshi did not know that the nakṣatras are seen in the sky in order from West to East; he was under the impression that Aśvinī and other nakṣatras are seen from East to West in the sky. However, we do find some people who can recognize most of the nakṣatras. Once the author happened to meet a Vaidik Brāhmaṇa named Phaphe from Chaul in the Colaba district. He knew all the nakṣatras. He recited a verse showing how to find the length of the night by observing the star transiting the meridian. It is given here because of its much usefulness.

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∗ INDIA II, P. 83

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| Khau | Kha | Jā | Tri | Gu | Chu | Cai/ | Cho | Chho | Bhū | 1 yuk. |
| 102 | 112 | 128 | 140 | 153 | 156 | 183 | 196 | 197 | | |
| Chha | Khi | Tri | Ku | Chū | Chhe | Ko | Dvi | 2 yuk. | | |
| 217 | 232 | 240 | 251 | 266 | 277 | 291 | | | | |
| ṅau | Kha | Chhā | ṅi | Ku | Ghu | Tri | 3 yuk. | | | |
| 305 | 312 | 327 | 345 | 351 | 354 | | | | | |
| Kha | Ja | Ku | Chū | Ghe | Gho | | | | | |
| 12 | 28 | 51 | 64 | 74 | 94 | | | | | |

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When the nakṣatra Aśvinī is transiting the meridian, the ascendant at the time is 102° (that is to say 12° of Cancer have risen at that time). It thus gives the degrees of the ascendant in the case of 28 nakṣatras. The time should be determined by the useful method of finding the (unknown) time when the ascendant is given. This quotation is based on the numerical code (Page 97) of Āryabhaṭa II, in which the consonants ka, ta, pa, ya, etc. indicate numerals; but in addition to these the vowels a,ā, i,ī,u,ū,e,ai, o,au, also indicate the natural numbers from 1 to 9 and 0 respectively. The Muhurtasindhu by Gaṇeśa Daivajña contains* three verses having the same meaning. The numbers indicating ascending degrees have been given in it by usual method, and it has been mentioned there that these are true for a place of Palabha 4, and that for other places these values would vary. From this and also from the fact that the village of Chaul is very near to Nandagaon where Gaṇeśa Daivajña lived, it appears that the quotation ‘Khau, kha, ja’ etc. and nakṣatras known to the Vaidic Brāhmaṇa mentioned above must have been handed** down traditionally from Gaṇeśa Daivajña.

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ORIGIN OF NAKṢATRA SYSTEM

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The Chinese, Persians and Arabs had the nakṣatra system in common use among them. Hence, European scholars raise the question whether the nakṣatra system was evolved by the Hindus independently or borrowed from other nations, and attach much importance to it. But I do not consider it very important, because, the decision of the question whether the entire system of mathematical astronomy has been independently developed by the Hindus or borrowed from others does not depend much upon the decision of the question who originated the nakṣatra system. It is not that the knowledge of planetary calculations is bound to follow immediately the knowledge of nakṣatras, or that the nation that establishes the nakṣatra system can alone establish the theory of planetary movement, or that the nation that borrows the nakṣatra system from another cannot independently discover the planetary theory. Weber, a German scholar, says that the nakṣatra system did not originate with the Hindus. M.Biot, a French scholar emphatically maintains that it was first established by the Chinese and was then borrowed by the Hindus, and Whitney taking his cue from Biot observes that it did not originally belong to the Hindus. Now both Biot and Whitney admit that "The Chinese had been working in the same beaten track, and never developing out of so promising a commencement anything deserving the name of a science, never devising a theory of planetary motions, never even recognising and defining the true character of the cardinal phenomenon of precession.*" Our People have established the nakṣatra system independently. The Chinese may have also established theirs independently. But it is certain that our people did not borrow it from others. This point has already been discussed before (on page 130 of pt. I). It does not require any elaborate treatment here. But let us briefly examine the views of the European scholars. Biot gave a detailed exposition of only the nakṣatra system of the Chinese and that of the corresponding system of the Hindus in a French monthly** journal in 1840, 1845 and 1859 A.D. The gist of his argument is: "Their instruments and their methods of observation, have been closely analogous with those in use among modern astronomers in the West; they have employed a meridian circle and a measure of time, the clepsydra, and have observed meridian-transits, obtaining right ascensions and declinations of the bodies observed. To reduce the errors of their imperfect time-keepers, they long ago selected certain stars near the equator. The stars thus chosen are the sieu. Twenty-four of them were fixed upon more than two thousand years before era. (M. Biot says, about B.C. 2357***) The considerations which governed their selection were proximity to the equator of that period, distinct visibility, conspicuous brilliancy, not being demanded for them. To those twenty-four stars four more—Maghā, Viśākhā, Śravaṇa and Bharaṇī—were added in the time of Cheu-Kong B.C. 1100."

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∗ They give 263° as the ascending degrees for Spica and 61° for Śata tārakā. If in the above quotation the correct letters be ‘gu and ku’ In place of ‘chu and ku’ the agreement will be complete.

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∗∗ When the Vaidic Brāhmaṇa showed him the nakṣatras, he pointed out the wrong ones as Revatī and Visākhā. Of these two, the star which he showed him as Revatī was the same as the one shown to J.B. Modak by a good Joshi from Ratnagiri. The same star was identified as Revtī by another good Joshi of Dhulia. One wonders how the same kind of error crept in at three places which are not related with one another. But it is not at all probable that the error could have originated with Gaṇeśa. The author’s book, Jyotirvilāsa, contains the description of nakṣatras and one can easily learn how to recognize nakṣatras without any one’s help.

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BIOT's study of the stars does not contain as much consideration of the Hindu nakṣatras as that of Chinese. WHITNEY has explained and compared in detail all the three systems viz. those of the Chinese, the Arabs and the Hindus. All the three systems have points of resemblance in some respect and divergence in others. On account of this, WHITNEY had to start with the assumption that no one among them can be regarded as the immediate source from which either of the other two has been derived. In spite of this he further remarks, "We would suggest then that a knowledge of the Chinese astronomy, and with it the Chinese system of division of the heavens into 28 mansions was carried into Western Asia at a period not much later than B.C. 1100, and was there adopted by some Western people, either Semitic or Iranian. That in their hands it received a new form, such as adapted it to a ruder and less scientific method of observation, the limiting stars of the mansions being converted into Zodiacal groups or constellations, and in some instances atlered in postion, so as to be brought nearer to the general planetary path of the ecliptic. That in this changed form, it passed into the keeping of the Hindus—very probably along with the first knowledge of the planets themselves—and entered upon an independent career of history in India; and that it made its way so far westward as finally to become known and adopted by the Arabs.” Our Indian system of nakṣatra has been built up merely on the basis of actual observations taken by the naked eye, whereas the Chinese system had been evolved mainly for helping the observations by instrument. The junction stars selected by us for Rohiṇī, Punarvasu, Maghā, Purva, & Uttara Phalgunī, Svāti, Anurādhā, Jyeṣṭhā, Mūla, Abhijit & Śravaṇa, belong to the first or second magnitudes (rarely of the third magnitude); but instead of taking these, the Chinese have* adopted quite different stars of inferior magnitude for junction stars, because they were useful to them for observation. In short, the Indian system is natural, while the Chinese system is artificial. In these circumstances, when WHITNEY could not assert that the Indians borrowed the nakṣatra system directly from the Chinese, he had to imagine that the system was first passed on to some Semitic or Persian people whose nakṣatra system has left no trace whatsoever, and that by a distortion of the order of progress in nature, the system assumed a still underform and was then transmitted to India. This would suffice to show what WHITNEY’S contention is.

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∗ The above views of Biot and Whitney have been cited from pages 180, 200 to 209 and 324, of the translation of the S.S. by Burgess.

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∗∗ Journal des Savants.

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∗∗∗ This time has been calculated on the assumption that the stars begin from the Kṛttikās. It has not been mentioned in the Chinese works.

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The Persians had their own nakṣatra system. But WHITNEY himself observes about it: “There are, as has been noticed above, traces of an Iranian system to be found in the Bundehesh; but this is a work which, although probably not later than the times of Persia’s independence under her Sassanian rulers (3rd century A.D.), can pretend to no high antiquity, and no like traces have as yet been pointed out in the earliest Iranian memorial, the Zendavesta.” As regards the question whether the Chaldeans had a system of nakṣatra divisions he writes: “Weber sees in the mazzaloth and mazzaroth of the—Scriptures (Job XXXVIII.32; II Kings xxiii.5)—words radically akin with the Arabic manzil—indications of the early existence of the system in question among the western Semites, and suspects for it a Chaldean origin: but the allusions appear to us too obscure and equivocal to be relied upon as proof of this, nor is it easy to believe that such a method of the division of the heavens should have prevailed so far to the west and from so ancient a time, without our hearing of it from the Greeks; and especially, if it formed a part of the Chaldean astronomy.” Hence, those Semitic or Indians through whom the Chinese system, according to WHITNEY, was introduced in India, were neither Chaldeans nor the Persians; and it is not known if the nakṣatra system was in vogue in any other Semitic or Iranian country, and has continued up to the present time. Hence, it is proved on this basis of WHITNEY’S own argument that the intermediaries Semitics or Iranians—suggested by him are not traceable at all.

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Up to 1100 B.C. the Chinese had only 24 stars in their system. Hence, WHITNEY and BIOT canot say at all that the Chinese system was imported into India before that time. BIOT says that Abhijit which used to be included in the Hindu nakṣatra system was omitted in 972 A.D. In other words, he suggests that the Chinese system of 28 nakṣatras was in vogue in India till then; but, WHITNEY has himself refuted Biot’s arguments by pointing out that long before that time, the Hindus had adopted 27 nakṣatras for calculations and that the Taittirya Saṃhitā mentions only 27 nakṣatras. Hence, the contention of WHITNEY and BIOT, that the Hindus adopted the nakṣatra system from the Chinese, is utterly worthless. Even WEBER observes, “The view that the Hindus borrowed the nakṣatra system from the Chinese cannot be accepted”.*

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∗ *Translation of S.S. by Burgess, P. 324.

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Sir WILLIAM JONES has made a comparative study** of the nakṣatra system of the Arabs and the Hindus; but WHITNEY remarks, “but it is incomplete and crude, and the inferences drawn therefrom are neither reliable nor important,” and JONES has made the comparison not with respect to nakṣatras only but with respect to nakṣatras related to signs; and he has expressed the view that the Hindus have borrowed the system of nakṣatras and rāśis, not from the Greeks, but from the Chaldeans. The opinion of WHITNEY*** has already been stated to be that the Chaldeans had no nakṣatra system. COLEBROOKE has made a detailed comparision**** of the Hindu and Arabian system of nakṣatras and rāśis. But neither Colebrooke nor any other scholar holds that the Hindus adopted the system from the Arabs. Colebrooke †says that it was the Arabs who borrowed it from the Hindus and it is evident from the information given on pages 187 and 188 before. MAX MULLER ‡says that the system of nakṣatras spread into all countries from BABYLONIA. WEBER also observes that the Hindus borrowed it either from the Babyloneans or from the Chaldeans. But MAX MULLER had not made a detailed study of the question and examined its pros & cons; it has been pointed out above ††that, according to Whitney †‡the views of neither of them are acceptable. In short, this discussion and the arguments advanced on page 130 of pt. I prove beyond all question that our people have established the nakṣatra system quite independently.

Cites (24)