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Bharatiya Jyotihshastra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s9: (6) Adhikāra on Shadow

Bhāratīya Jyotiḥśāstra (History of Indian Astronomy), translated by R. V. Vaidya v2.c12.s9

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(6) Adhikāra on Shadow

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Some Karaṇa works do not give a separate adhikāra to this subject. The Grahalāghava has given it separately. The chapter usually deals with the calculation of daily rises and sets of all planets (except the sun), the time of their remaining above the horizon i.e. length of their diurnal arcs, the length of shadow at any desired moment, observation etc.

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*See couplets 34-48, Golādhyāya in Brahma Siddhānta. **See verses 7 to 10 from Grahaṇa Vāsanā, in Siddhānta Śiromaṇi. †See page 127, of the Translation of S.S. by Burgess. Whitney suggests that these values were borrowed by Hindus from the Greeks, because the two agree rather closely. But this is simply a biassed view. Any sensible person will admit that in a case like this the difference of even a few minutes must be regarded as considerable.

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(7) HELIACAL RISING AND SETTING (EMERSION AND IMMERSION)

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The heliacal rising and setting of planets is a matter of great importance in our country. Religious rites like those of marriage etc. are forbidden when Jupiter and Venus are set. This has mainly raised the importance of this subject and it is believed to be one of the means to test the accuracy of astronomical calculations in the light of observation.

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When planets and stars are in the proximity of the sun, they are not visible before sunrise and after sunset, even though they are themselves on the horizon and the sun has not appeared above the horizon. The planets and stars thus continue to remain invisible for a week, a fortnight or for some months. After the stars and planets first become visible, their distance from the sun gradually diminishes till at last a day comes when they become invisible. They are then said to have ‘set’ on that day. Again, after they first become invisible being near to the sun, their distance from the sun begins to increase gradually, till a day comes when they emerge from its light and become visible. This phenomenon is termed the ‘rise’. The diurnal phenomenon of the appearance and disappearance above and below the horizon of the stars and planets is called the ‘udayāsta’ (i.e. rise and set) ; and their disappearance due to their proximity with the sun and reappearance,—these phenomena also are termed ‘astodaya’ (i.e. set and rise). It will thus be seen that the words ‘rise and set’ are used in two senses. It is desirable that the two phenomena should be known by different names. These are distinct terms in the case of the moon. During the dark half of the month as the moon gradually approaches the sun, her distance diminishes, till on the new moon day she disappears and then makes her first appearance in the west on the first or second lunar day after the new moon day. The phenomenon is then called Candra-darśana (first appearance of the moon). They do not characterize it as the rising of the moon. It is similarly desirable to speak of the first appearance of stars and planets after they have disappeared owing to their proximity with the sun, as their ‘darśana’ (emersion) and their first disappearance as the ‘adarśana’ (immersion). But most of our astronomers have indiscriminately used the terms ‘Udayāsta’ (rise and set) even for the phenomena of appearance and disappearance due to their nearness to the sun and the same terms are in use at present. People give much consideration to the daily rising and setting of the moon and it is very necessary for them. Similarly people use to notice its first appearance when it is very near the sun; hence in her case they naturally found it necessary to use different terms for the two phenomena. But no one ever cares much to think about the daily rising and setting of planets and stars; and hence it appears that they began to apply the term “rise and set” to their appearance and disappearance depending upon their proximity to the sun.

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Social rites like the thread ceremony and marriages and so also penances, house foundation, etc., are not performed when Jupiter and Venus are ‘set’.

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नीचस्थे वक्रसं स्थेप्यतिचरणगते बालवृद्धास्तगे वा
संन्यासो देवयात्राव्रतियमविधिः कर्णवेधस्तु दीक्षा ।।
मौंजीबंधोपनानां परिणयविधिर्वास्तुदेवप्रतिष्ठा
वर्ज्याः सद्धिः प्रयत्नात् त्रिदशपतिगुरौ सिंहराशिस्थिते वा ।।

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बाले वा यदि वा वृद्धे शुक्रे वास्तंगतो गुरौ । मलमास इवैतानि वर्जयेहे वदर्शनम् ।। बृहस्पति.

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“Good people should as far as possible avoid performing social and religious ceremonies like ‘Sanyās’ (initiation into Sanyāsī life), pilgrimage to a holy place, penance, perforation of ears, thread ceremony, marriages, etc., when Jupiter, the preceptor of gods, is in its fall or retrograde, has very swift motion, is in its ‘childhood’ or ‘old age’, or occupies the sign LEO. —Lalla

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“Visiting temples (places of gods) for darśana should not be undertaken if Venus or Jupiter are very young or very old, or if they are ‘set’, for these conditions are as inauspicious as the intercalary month”. —Bṛhaspati

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The compilers of works on Dharmaśāstra have made these and similar other statements. Now-a-days ceremonies like marriage are postponed only when Jupiter and Venus are ‘set’ (heliacally). No one generally cares to know their positions, like fall, retrogression or very swift motion. Anyway, of all the planets and stars the ‘setting’ of only Jupiter and Venus, is taken as unfavourable for the performance of religious rites. These two planets are far more brilliant than the other planets. As for the nakṣatras some nakṣatra or other is always set. The set of Mercury occurs about six times during a year. The ‘set’ of Mars occurs after a long period; but once it is set, it is not visible for five months. Hence the fact that the ‘sets’ of Mercury, Mars and nakṣatras are not treated as impediments to the performance of religious rites shows the tendency of Dharmaśāstra to remain in harmony with practical life. Again, it should also be borne in mind that the compilers of Dharmaśāstra did not consider whether to accept or reject the ‘set’ of Saturn for daily affairs, even though it did not come in the way of practical life. Its set may not have been considered worth rejection because it happens to be a malefic planet.

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A planet that is due to ‘set’, rises in the east, actually sets (heliacally) when the difference between the moments of sunrise and that of the planets’ daily rise becomes less than a particular amount of time and it rises (heliacally) when such difference exceeds that amount of time. Similarly the planet’s rise and set in the west are governed by the difference in the moment of sunset and that of the planet’s daily setting. Rules like these had been framed by our ancient astronomers. For example, Jupiter rises or sets (heliacally) when a difference of about 110 palas occurs between the moment of the daily rising and setting of the sun and Jupiter. The diurnal rotation of the earth carries the planets through 1° in 10 palas which gives 11° in 110 palas. Because these degrees (aṃśas) are related to time (kāla) they are termed ‘Kālāṃśas’ (time expressed in degrees). It has been mentioned that when a difference of 11 ‘kālāṃśas’ occurs between the sun and Jupiter the latter either rises or sets. The followiog table gives the Kālāṃśas relating to planets, as mentioned in different works :—

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| | ORIGINAL S.S. | Modern Sūrya : Romaka : S.-Brahma : Soma : Sid. | First Ārya Siddhānta | Brahmagupta : Siddhānta Śiromaṇi | Lalla : Karaṇa Kutūhala | Second Ārya Sid. | Karaṇa Prakāśa | Grahalāghava | Keropant's planetary tables | Ptolemy | Author's experience |
| Moon | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | | 12½ |
| Mars | 17 | 17 | 17 | 17 | 17 | 17 | 17 | 17 | 17 | 14½ | 17 |
| Mercury | 13 | 14 | 13 | 14 | 13 | 13 | 13 | 13 | 13 | 11½ | 13 |
| Mercury (Retro) | | 12 | | 12 | 12 | 12½ | | 12 | | | |
| Jupiter | 11 | 11 | 11 | 11 | 11 | 12 | 12 | 11 | 11 | 12½ | 11 |
| Venus | 9 | 10 | 9 | 10 | 9 | 8 | 9 | 7 | 9 | 5½ | 8 |
| Venus (Retro) | | 8 | | 8 | 8 | 7½ | | 6 | | | |
| Saturn | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 15 | 14 | 15 |

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Out of these, the Kālāṃsas of PTOLEMY*, are true for the planets when they are situated in the sign of Cancer and those for Mercury and Venus are related to their western sets.

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The kālāṃśas given by Keropant in his Planetary Tables are the same as those given by the Ārya Siddhānta. He does not appear to have given them as determined by his own experience since they are not found completely to agree with observed results.

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The compilers of the almanacs, published by Ganpat Krishnaji and the Nirnaya Sagar Press, calculate the rise and set of only Venus on the basis of the Kālāṃsas of the Grahalāghava. The times of the rise and set of all other planets in these almanacs and even those of Venus in other almanacs following the Grahalāghava system, are calculated by a crude method given by the Grahalāghava. Other almanacs in this country may be finding the rises and sets of planets on the basis of Kālāṃśas given in the works which they may be adopting as their authority. The new almanacs compiled with the help of the Nautical Almanac viz. the Keropanti i.e. Patwardhani Pañcāṅga that by Daivaji at Varanasi and our sāyana almanac find the times of the rise and set on the basis of kālāṃśa figures given by some ancient work or other. Not all the timings thus calculated are found to be correct in the case of any almanac. Some of them are correct and some are not. Now it is true that they are not as often wrong in the case of the new almanacs as in that of the old ones.

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*See page 223, Translation of the S.S. by Burgess.

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Some persons begin to maintain, therefore, that the calculations of even the new almanacs are at times as wrong as those of the Grahalāghava, simply because some of the timings in the new almanacs appear to be incorrect, without caring to consider why they seem to be incorrect. It cannot be argued that the calculations of the new almanacs are erroneous because the times of rises and sets given by them are not sometimes found to be correct. It can be proved from plenty of other evidence that their calculations are correct. The reasons for the failure of such timings are quite different. The main reason for the failure lies in the error in the Kālāmśa adopted. The planetary places as obtained from the Grahalāghava are at present found to be always erroneous to a certain extent. If the rises and sets calculated from it are sometimes found to be true it is merely by coincidence. In order to determine the Kālāmśas for a planet, either the difference in the moments of day to day rises and sets of the sun and the planet should be actually observed and recorded or they should be determined by calculation on the basis of the calculated positions of the sun and the planet. The sun, however, is immediately visible when it comes to the horizon. But the chance of observing the rise or set of a planet lasts for a short time before sunrise or after sunset. But as there is twilight at that time no planet is visible when it is on the horizon; it is visible only when it is somewhat above the horizon. Hence, the difference in the daily rise or set of the planets and the sun cannot be found correctly by actually observing them. Even if it were possible to have some means by which to find them, there was no possibility of people in ancient times possessing fine instruments for measuring time and angles with great precision as at present. Again, in order to find by calculation the difference in times of the day to day rises and sets of the sun and the planets from their positions at heliacal rises and sets, it is necessary that the positions be very accurately known. If it be correct, in other words, if it be accurately known that a particular planet is occupying a certain position or is situated at a particular distance from the sun, the time would be correctly calculated. But we do not think that in those ancient times when the Kālāmśas were determined, the calculation of planets' places used to be extremely minute-in fact, so minute that there would be no room even for the error of a 'pala' in the timing of daily rise and set.

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On account of these reasons, there was every possibility of errors having crept into the kālāmśas determined in those times. If the kālāmśas that are the very foundation of determining the (heliacal) rise and set, be erroneous, how could the times of the rise and set calculated on their basis found to be correct?

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In the sāyana almanac we adopt 11 as the kālāmśa for Jupiter; hence, we can say for certain that the difference in moments of the daily sets of Jupiter and the sun is definitely less than 110 palas on the day which the almanac has shown as the day of Jupiter's heliacal setting and can be verified and found correct by other means. But it is a difficult question altogether whether Jupiter will definitely set on that day on which the difference in times of the daily sets of Jupiter and the sun becomes less than 110 palas. Perhaps the set might take place a day or two earlier or later, and even it so happens it does not follow that the calculations of the new almanacs are wrong. It can, at the most, mean that the kālāmśas of Jupiter ought be changed to a quantity more or less than 11°.

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In the present times we have the means to test the accuracy of the places of planets and instruments to record the time correctly. The Kālāṃśas should be determined in such times. An attempt was made to do this for six or seven years up to Śaka 1811; but later on the author did not get leisure owing to several other pursuits. His eyesight too began to grow weaker gradually, but still he is carrying* on the observation work to some extent personally and with the help of keen-sighted students.

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MR. GOPAL BALLAL BHIDE**, a member of the group interested in the sāyana almanac, helped him much by his efforts in this direction. The work of finally determining the rules for the heliacal rise and set of planets, after coordinating the results of all our observations has not yet been completed. The rises and sets of Saturn used to occur mostly in the rainy season or about that time during five years preceding Śaka 1811 and hence we did not get an opportunity for observing them. We got the chance of observing the phenomena about Mars only once or twice. If any of the readers feels inspired by this and communicates to him his experiences in this subject, he would be doing a great service to the Science of Astronomy. The sky is sometimes cloudy even in summer; the planets when they are on the point of rising or setting, are situated very close to horizon. Many such obstacles come in the way of taking observations. It has, however, been gathered from experience, that the kālāṃśa mentioned in our old works are tolerably accurate. It is true that Mercury and Venus appear brighter when they are retrograde; however, the variation in their kālāṃśas mentioned by some works as due to their direct or retrograde motion is far from correct—as a matter of fact one may safely say that the variation is next to nothing.

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A NOTEWORTHY PECULIARITY

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A peculiarity relating to rise and set has come to the notice, which had not struck any author of our ancient works. When planets are about to set or rise heliacally, they are situated very near the sun. Their visibility depends upon their luminosity; and the luminosity varies according to their altitude i.e height above the horizon; and even if the time-interval between the planet's diurnal rise and sunrise be the same at different places on the earth, still the altitude of the planet would be different. Its altitude at a place in latitude 25° North would be less than that at a place in latitude 15° North and accordingly the luminosity wil be less; and its (heliacal) rise in 25° North latitude will take place some days after it has occured at a place in North latitude 15°, while its set will take place earlier. It can be mathematically proved by means of a diagram that even when kālāṃśas be the same, that is to say, even if the time-interval between the daily rise or set of a planet and that of the sun be the same, their altitudes and hence their

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*The author had written an essay on the subject of rise and set of planets in the Srishtijnan, a monthly Journal formerly published in Bombay, in the issues for May, June and July 1855. A chapter on the same subject, in his book Jyotirvilas may also be seen in addition to this.

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**Gopal Ballal Bhide used to take a keen interest in observing celestial phenomena. He was born in Śaka 1778 at Nirvedi, in Ratnagiri District and died in Śaka 1812. He was in the service of the Education Department in that district from 1874 A.D. to the end. He had recorded several observations about the rises and sets of planets, and had also seen the rises and sets of the junction stars of some of the naksatras. Had he lived longer, he would have been of great use in promoting the cause of the Science of Indian Astronomy.

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(heliacal) rises and sets will vary with the latitudes of different places; but it is not proposed to do so here for want of space. It will be easily understood from what follows. The twilight lasts for a longer time in England than in our country. If Venus, for instance, rose (diurnally) 32 min. earlier than the sun on a particular day (that is, if its kālāṃśas were 8), it would be visible in our country on that day, but will not be visible in England, even though it rose there 32 min. earlier than the sun, which means that its heliacal rise will not occur that day, but a number of days afterwards. If Venus has a north declination, and if it rises 32 min. before the sun in our country, it will have its daily rise in England more than 32 min. earlier. This means that if we consider only the kālāṃśas, Venus should rise heliacally some days earlier in England than in India; but experience will show a contrary result. Even at the same given place, although the kālāṃśa given for a planet be the same, its altitude will vary according to its declination, north or south. The variation in this case will not, however, be considerable. In short, the kālāṃśas for a planet should increase in value as the terrestrial latitude rises higher north of equator; and secondly it is better to establish the rules for heliacal rise and set on the basis of altitudes rather than that of kālāṃśa.

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These considerations about the factor of altitude and the author's own experience at Barsi (lat. 18° 13') have convinced him that the kālāṃśas mentioned in our old works were determined in our own country. As for kālāṃśas of Ptolemy it can be easily seen that they had no connection whatsoever with our works. On the contrary it can be said about Ptolemy's kālāṃśas that they had not been determined through experience, or if determined, the positions of planets on which they were based were erroneous, else he might have committed some other error. The kālāṃśas of Mars, Mercury and Venus do not amount to anything less than 16°, 12°, and 8° at 18° north latitude. These must therefore, be greater at Alexandria (latitude 31° 13'N). Hence, it follows that the kālāṃśas of Mars, Mercury and Venus mentioned by Ptolemy as 14½°, 11½°, and 5⅝° are considerably wrong. The kālāṃśas for rise and set, as also the altitudes, true for a particular place can be determined with precision. Even when they are so determined, the experience regarding kālāṃśas will be found to vary because of moon light, the reddish light seen at times near the horizon and the relative strength of the observer's eye-sight*. The clouds too serve as another obstructive factor. Hence, it was proper that our authorities on Dharmaśāstra have recommended the omission of few days after and before the mathematically obtained days of planets' rises and sets, because of 'childhood' and 'old age of the planets.

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The kālāṃśas which are based on actual experience and which are used for the sāyana almanac have been given above. It is the experience of G. B. Bhide at Hedavi (lat. 17° 20'N), that sometimes the kālāṃśa of Mercury is 7¾° at the time of rise or set is 11° that of Jupiter 10° and that of Venus (8) ‘ŚṚṄGONNATI’ OR ELEVATION OF THE MOON’S CUSPS

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∗ It has been my experience that if a weak-sighted person may not be able to see the rise of a planet even for three or four days after it has been seen by a keen-sighted person the times of rises and sets are more likely to go wrong when the difference in the motions of the sun and the planet is very small.

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A very small portion of the moon’s disc is illuminated in the first week of the bright half and the second week of the dark half of the month. It is termed Śṛṅga (horns) or cusp (of the moon). The subject matter of the chapter on Śṛṅgonnati is to find what end of the moon’s cusp would appear elevated and in what direction and what part of the moon’s disc will be illuminated on the earlier days of the bright half at the time of sunset and on latter days of the dark half at about sunrise, and particularly on the first or second lunar day of the bright half when the moon’s first appearance takes place. The Samhitā works discuss at great length the effects due to the elevations of the moon’s cusps. The moon becomes illuminated because of the sun, and the moon’s cusps will appear elevated on that side on which the sun stands. This has, of course, nothing to do with good or evil events on the earth; but it is natural for such beliefs to gain ground when the real causes are not known.

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