^{page 479 note 1} It may be useful to note that in terms of the Julian Period beginning with Monday, 1 January, b.c. 4713, and regarded as having its days running for Indian purposes from sunrise (instead of the preceding midnight), the first civil day of the Kaliyuga era, the Friday mentioned above, is the day 588,467 current, or, as it is taken for purposes of calculation, the day 588,466 elapsed.

^{page 479 note 2} As, for instance, by Whitney in his notes below Burgess's, E. translation of the Sūrya-Siddhānta, published in the Journal of the American Oriental Society, vol. 6 (1860), pp. 145–498Google Scholar.

^{page 480 note 1} As regards the method of stating the lengths of the ages, Brahmagupta (ed. Sudhakara Dvivedi, p. 3, verses 7, 8) first gives the length of the Chaturyuga, 4,320,000 years, which, he says, comprises “the four, the Krita and the others, with dawns and twilights.” He then takes the tenth part of that, viz. 432,000 years: and he multiplies this latter figure by 4, 3, 2, and 1.

A different course is taken by Lalla, an early exponent of Āryabhaṭa, who may or may not have come before Brahmagupta. He differs from his master regarding the divisions of the Chaturyuga (for Āryabhaṭa's arrangement of this matter see p. 486 below), and agrees with Brahmagupta, but fixes the lengths of them by other means. He takes the orbit of the moon, 216,000 yōjanas, as stated by Āryabhaṭa on the assumption that the moon is at such a distance from the earth that one minute of arc along her orbit round the earth measures ten yōjanas; and he gets the figures for the ages by multiplying this figure by 8, 6, 4, and 2: see his Śishyadhīvṛiddhida, ed. Dvivedi, Sudhakara, p. 3, verse 14, with p. 27 f.Google Scholar, verses 2, 3 (there are rather serious mistakes in some of the explanatory figures interpolated by the editor here).

^{page 481 note 1} I follow Whitney and other scholars in using the terms ‘dawn’and ‘twilight’. The original texts sometimes discriminate by presenting xaṁdhyā where the term ‘dawn’has been adopted, and saṁdhyāṁṠa where ‘twilight’ is used. But in other places they use the term saṁdhyā in both senses, and also another term, saṁdhi, which, however, is perhaps used more specially in connexion with the Manvantaras, to which we shall come next.

The term saṁdhyā, lit. ‘a holding together, union, junction’, occurs freely in literature in the sense of both the morning and the evening twilight. Saṁdhyāṁśa, lit. ‘a portion of saṁdhyā’, seems to have been selected simply in order to obtain, for the purpose of the ages, saṁdhyā in the sense of the opening ‘twilight’, and another term for the closing one. Saṁdhi, lit. ‘junction, connexion, place or point of contact’, appears also to occur in the sense of ‘twilight’, both of the morning and of the evening. But the saṁdhis are not parts of the Manvantaras, as the saṁdhyās and saṁdhyāṁśas are of the Ages; and the idea seems to be more that of ‘a junction-period’, and to be better taken in this way: see, further, p. 482 below, and note 2.

^{page 481 note 2} For instance, in the Vishṇu-Purāṇa, 4. 24. 41: trans., vol. 4, p. 236.

^{page 482 note 1} The term is saṁdhi, regarding which see note 1 on p. 481 above.

^{page 482 note 2} The Sūrya-Siddhānta, 1. 18, says that the saṁdhi at the end of a Manvantara is a jalaplava, ‘a deluge’. The Vāyu-Purāṇa, 61. 136, says that there is a saṁhāra, ‘a suppression, destruction’, at the end of a Manvantara, and a saṁbhava, ‘a birth, production’, at the end of the saṁhāra.

^{page 482 note 3} The astronomers had no need to go beyond the Kalpa: and neither does Āryabhaṭa nor does Brahmagupta seem to have done so. The Sūrya-Siddhānta, 1. 21, however, found it worth while to add that the extreme age of Brahman is 100 (years) of such days-and-nights, and that half of his life has passed.

^{page 483 note 1} This part of the matter is obscure. But it was recognized at an early period (see, e.g., Āryabhaṭa's Kālakriyā chapter, verse 11) that, though time is measured by the courses of the planets (including in this term the sun and the moon), time itself has no beginning and no end: and it was consequently seen that even the life of Brahman, as specified above, would not cover the duration of time. The idea seems to be that even Brahman himself dies, and is followed by a new Brahman; not that he sinks into quiescence and becomes revivified. Thus Bhāskarāchārya, writing in a.d. 1150, says that at the end of the 100 years, which period, he tells us, was named Mahākalpa by early people, there comes “another Brahman”: on the point as to how many such beings there may have been, he adds:—“Since this same time had no beginning, I know not how many Brahmans have passed away:” see his Siddhāntaśirōmaṇi, and his own commentary on it, edited by Sastri, Bapu Deva, p. 10, verse 25Google Scholar.

^{page 484 note 1} See, e.g., the Sūrya-Siddhānta, ed. Hall, FitzEdward and Sastri, Bapu Deva, 1. 21, 22Google Scholar; where we are further told that the Manu of the current Manvantara is Vaivasvata. See also the Vishṇu-Purāṇa, 1. 3. 26, 27, which adds that the present Kalpa is named Vārāha, and the last preceding one was Pādma: in verse 4 it uses the terms Para and Parārdha to denote respectively the whole and the half of the life of Brahman.

There has been, however, a difference of opinion on this point. Bhāskarāchārya says in his Siddhāntaśirōmaṇi, ed. cit., p. 11, verses 26, 27, and his own commentary thereon:—“How much of the life of the existing Brahman has gone, I know not; some say half of it; others, eight and a half years. Let the tradition be: there is no use for it either way, because the planets are to be calculated only according to the elapsed time of his current day. Since they are created at the beginning of such a day and are destroyed at the end of it, it is proper to examine their courses only for the time during which they exist: those persons who, on the other hand, consider their courses for times when they were not, — I give my compliments to those great men!”

The Sūrya-Siddhānta, 1. 21, teaches that half of the life of Brahman has elapsed, and that we are now in the first Kalpa of the second half. The other view appears to be taught by some followers of the Brāhma-Siddhānta.

The Lashkar Pañchāṅg, printed at Gwalior, says in the introductory passages of its issue for the Vikrama year 1966 and the Śaka year 1831, expired, = a.d. 1909–10, that the view that half of the life of Brahman has passed is the Saura-mata, the opinion of those who follow the Sūrya-Siddhānta (see just above), and the other view is the Brāhma-mata. It adds that in the first day of the remainder of his life there had elapsed, up to the year of its issue, 1,972,949,010 years, or, in terms of the time of Brahman, 13½ ghaṭikās, 12 palas, 3 vipalas; that is, 5 hrs. 28 min. 49·2 sec. Some other almanacs make similar statements: but it is enough to cite this one as an example.

^{page 485 note 1} In rock-edict 4 we have:—“And the sons of the king Dēvānaṁpiya Piyadassi, and the sons' sons and their sons, will cause this observance of dhamma to increase throughout the aeon.” The Kālsī text, line 12, has āva kaparṁ, = yāvat = kalpam: and the Shāhbāzgarhī and Mansehra texts yield the same expression. The Girnār text, line 9, has āva saṁvaṭa-kapā, = yāvat = saṁvarta-kalpāt, “until the aeon of destruction”; which indicates a recognition of an ensuing aeon of non-existence, following the aeon of existence in which we now are.

In rock-edict 5, again, Aśōka speaks of “my sons and sons' sons, and my offspring after that throughout the aeon.” Here, also, we have āva kapaṁ in the Kālsī text, line 14, and in the Shāhbāzgarhī and Mansehra texts; while the Girnār text, line 2, has again āva saṁvaṭa-kapā.

The Dhauli text has in edict 5, line 21, āva kapaṁ, but in edict 4, line 17, ā-kapaṁ, which may be of course a mistake for āva kapaṁ, but also may represent quite regularly ā-kalpam. In the Jaugada text both the expressions are lost.

Early epigraphic references to the system of cosmical periods are rare: but two instances may be cited. The Junāgaḍh inscription of Rudradāman, , dated in a.d. 150, says (Epi. Ind., vol. 8, p. 42, text line 6–7)Google Scholar that the dam of the great lake Sudarśana was burst by the effects of a great fall of rain, which swelled to excess the rivers that filled the lake and was accompanied by “a wind of a most tremendous fury befitting the end of the Yugas.” And the Gaṅgdhār, inscription of a.d. 423 (Gupta Inscriptions, p. 74, text line 7–8)Google Scholar, describes the king Viśvavarman as “surpassing in brilliance the most unendurable saṁvartaka-fire”. These allusions may be explained from the Mahābhārata, 3, Vanap.:, § 188. 12869–90. At the end of the 1000 Yugas (which make the daytime of a day of the Creator) there will appear seven blazing suns, which will dry up all the waters in the rivers and the oceans. They will be followed by the saṁvartaka-tire, ‘the fire of destruction’, accompanied by a great wind, which will invade the earth, already dried up by the suns, and will burn up everything that is left, penetrating even through the earth down to the nether regions. This fire will be quenched eventually by a tremendous fall of rain, lasting for twelve years, from vast masses of clouds driven by the same terrible wind, which will flood the whole surface of the earth. Then, when the clouds are exhausted, the Self-existent One will drink up that terrible wind, and will go to sleep.

^{page 486 note 1} Detailed remarks on this point must be held over: but the following may be said. The original scheme of the Yuga seems to have been on the decimal system of notation; a cycle of 10,000 years (Atharvavēda, 8. 2. 21), which was then divided, when the idea of the Ages with fixed decreasing periods arose, into four parts of 4000, 3000, 2000, and 1000 years. It was subsequently recast on duodecimal lines; by adding 2000 years, which were divided in the same proportion into 800, 600, 400, and 200, and were attached to the Ages as their ‘dawns’ and ‘twilights’, thus making 4800, 3600, 2400, and 1200, = 12,000 years. This enabled the primitive Yuga to be adapted to the astronomical Yuga of 4,320,000 years, by multiplying the 12,000 years and the divisions thereof by 360.

^{page 486 note 2} See page 111 above.

^{page 486 note 3} Ed. cit., p. 4, verse 11.

^{page 488 note 1} There is, I believe, now a tendency to refer this receipt of the Greek sciences to a somewhat earlier period. As far as the matter is clear to me, it cannot be placed before about a.d. 225–50, and a.d. 350 seems more probable.

^{page 489 note 1} The first point of Mēsha is the fixed initial point of the Hindū sphere: it is either at, or 10′ on the east of, the star ζ Piscium, which is about 10° west of the beginning of our constellation Aries. Our “first point of Aries”, i.e. of our sign Aries, which gives the tropical equinox, is now about 18° farther to the west from ζ Piscium.

The Hindū mean vernal equinox is the time when their mean sun comes to the first point of Mēsha. According to the Hindū bases, this was, in b.c. 3102, on 18 February: now, as a result partly of the Hindūs maintaining the sidereal solar year and disregarding the precession of the equinoxes in connexion with their calendar, partly of our introduction of New Style in a.d. 1752, it comes on 13 or 14 April. The Hindū true vernal equinox occurs two days and a few hours earlier, when their true sun comes to the first point of Mēsha.

^{page 490 note 1} As I have said on a recent occasion, for the term exeligmos, which is frequently a very convenient one to use, we are indebted to Dr. Burgess (this Journal, 1893. 721), who brought it to the front from Gemīnos and Ptolemy in the course of his instructive article entitled “Notes on Hindu Astronomy and the History of our Knowledge of it.”

^{page 490 note 2} This conjunction is usually indicated, perhaps not too clearly, by statements such as that made by Āryabhaṭa in his Kālakriyā chapter, verse 11:—“The Yuga (i.e. the Mahāyuga or Chaturyuga), the year, the month, and the day began all together at the beginning of the bright fortnight of Chaitra;” which is to be read in connexion with the statement in the Daśagītikasūtra, verse 2 (a part of his work, whether he himself composed it or not: see p. 115 above), that the revolutions of the sun, etc., laid down for the Yuga in that verse and the preceding one, are counted from (the first point of) Mēsha and from sunrise on a Wednesday at Laṅnkā.

But it is defined in very plain terms in the Sūrya-Siddhānta, 1. 57. This work purports to have been revealed by the Sun to the great Asura Maya when the Kṛita age was being superseded by the Trētā: and we are here told that: “At this same end of the Kṛita age, all the planets, by mean motion, but excepting (their) nodes and apsides, have come to equality (conjunction) at the beginning of Mēsha.” The term ‘planets’ here includes, as usual, the sun and the moon. The sequel will show that the conjunction thus referred to the end of the Kṛita age, that is, to the beginning of the Trētā, comes also at the beginning of the Kaliyuga.

^{page 491 note 1} The passage has been given by Professor Jacobi in the Acts of the Tenth Oriental Congress, Geneva, 1894, part 1 (1897), p. 106, in nis article “Contributions to our Knowledge of Indian Chronology.” See also this Journal, 1893. 721, note 2, where it has been given by Dr. Burgess, to whom it was communicated by Professor Jacobi. It goes on to say:—“Aristarchus [between b.c. 280 and 264] estimated this year at 2484 successive years; Aretes Dyrrachinus at 5552; Heraclitus [about b.c. 513] and Linus at 10,800; Dion at 10,884; Orpheus at' 120,000; Cassandrus at 360,000. But others have expressed the opinion that it is infinite and cannot ever complete itself.”

^{page491 note 2} An example may be given, to make the meaning clear. For the planet Jupiter, Āryabhaṭa had 364,224 revolutions in the Yuga, giving a certain rate of motion and a certain length in years for each revolution. Brahmagupta found reasons for making the motion of the planet somewhat quicker and the period of its revolution somewhat less; and he did this by increasing the number of revolutions in a given time. With the Yuga as the exeligmos, he would have had to state the number of revolutions, taken by him, as 364,226: but, using the Kalpa, he was able to put it as 364,226,455.

Further, the Sūrya-Siddhanta, while using the Yuga as its exeligmos for all ordinary purposes, had to adopt the Kalpa for stating (1. 41–44) the revolutions of the apsis of the sun and the apsides and nodes of the five planets; because the numbers are too small to be stated as integers for the Yuga.

^{page 492 note 1} Before the publication of Kern's edition of the Āryabhaṭīya in 1874, Āryabhaṭta was known only from quotations from him in other Hindū Works; and even in those quotations he was confused with the author of the later work, the Arya-Siddhānta: the real Āryabhaṭa, in fact, was so little known that Colebrooke thought it possible (see Essays, 2. 429) that he might be placed even before b.c. 58. Whitney, however, recognized and illustrated that the Yugapāda might be substituted for the Yuga for purposes of calculation: see the Sūrya-Siddhānta, trans., p. 160f.

The reason for the precise length of the Hindū exeligmos in either form, Yuga or Yugapāda, does not come within the scope of this article: it has been much debated, but is still a matter of conjecture, and seems likely to remain such. In respect, however, of any suggestion that it was selected to suit some particular rate of precession of the equinoxes (see, e.g., Cunningham, , Indian Eras, p. 4)Google Scholar, it may be observed, in the first place, that (as may be seen, loc. cit.) more rates of precession than one can be manipulated, according as we deal with any fractions that are involved, in such a manner as to yield the period of either a Yuga or a, Yugapāda; and in the second place, that it is tolerably certain that the Hindūs did not pay any attention to precession, even if they knew exactly what it is, until about the tenth century, and that, when they did take the matter up, they fixed their estimates of the annual rate of precession at 54″ and 1′ simply because these rates gave periods which go without fractions into the period of their exeligmoi. And it may be noted that the Greeks had an exeligmos of 10,800 years (see note 1 on p. 491 above); also, that the Chaldaeans had a period of 432,000 years, extending from Creation to the Flood, which was supposed to represent the reigns of ten kings, but seems more likely to be of the nature of an exeligmos: the Hindū exeligmos, either the shorter one, the Yugapāda, or the longer one, the Yuga, may have been an adaptation by extension of one or the other of those two periods.

There can, however, be little doubt, that, as was intimated by Dr. Burgess in this Journal, 1893. 722, it is a natural development of the system of sexagesimal subdivision, which is ancient enough: its ultimate origin lies in such facts as that there are 10,800′ in 180°, and 21,600′ in the whole circle, and also, by the Hindū divisions of time, 21,600 nāḍīs or ghaṭīs, periods of 24 minutes, in 360 days. And, it the subject should ever be taken up again, attention might be paid to the manner in which Lalla obtained the figures for the subdivisions of the Yuga from 216,000 as the number of yōjauas in the orbit of the moon (see note 1 on p. 480 above): this item was used also to determine the circumference of space, in the sense of the visible universe lit up by the sun, and to deduce from that the orbits and distances of the sun, the planets, and the nakshatras. That the moon was an important factor in the determination of the period seems also to be indicated by the point that the numbers of the revolutions of her apsis and node are integers only for the Yuga: divided by four, they give fractions, three-quarters and one-half.

^{page 493 note 1} The Kaliyuga era was known to the Arabian astronomers as the Era of the Deluge: see Albērūnī's, Chronology of Ancient Nations, trans. Sachau, , p. 29Google Scholar; also the Aīn i Akbarī, trans. Jarrett, , vol. 2, p. 22Google Scholar. It is not impossible that some tradition about the Flood, obtained from the Greeks or the Romans, may have indicated to the Hindūs the period in which, in a general way, they should look for the date of the great conjunction.

^{page 494 note 1} It cannot be said safely, off-hand, as has been said, that no such conjunction ever did or ever will occur: as Albērūnī observed (see his Chronology of Ancient Nations, trans. Sachau, , p. 30)Google Scholar, it must have occurred and must occur again, if only our solar system lasts long enough. This, however, is a question which must be left to the astronomers in consultation with the geologists.

^{page 494 note 2} Whitney gave the mean places of the planets for mean sunrise at Ujjain on Friday, 18 February, b.c. 3102, in accordance with three of the Hindū books: of those three, the Ārya-Siddhānta gives the nearest approach to a conjunction; and according to it the sun, the moon, Mars, and Saturn were exactly at the first point of Mēsha; Venus and Jupiter were 2° 52′ 48″ west of that point; and Mercury was 8° 38′ 24″ west of it: see Sūrya-Siddhānta, trans., p. 425. For the true positions of the planets for the preceding midnight at Ujjain, furnished to Whitney by Professor Winlock, see ibid., p. 162.

Two items may be added, as worked by Schram's, Kalendariographische und Chronologische Tafeln (1908)Google Scholar. The true new-moon in February, b.c. 3102, was at about 7.13 a.m., for Ujjain, on Thursday, the 17th. The true vernal equinox of b.c. 3102 was at about 1.25 p.m., for Ujjain, on Sunday, 17 April.

^{page 494 note 3} Āryabhaṭa belonged to the sunrise school: the midnight school is represented by the original Sūrya-Siddhānta, which existed before the time of Varāhamihira (died a.d. 587), and by the present work of the same name, which dates from probably about a.d. 1000. Brahmagupta also placed the conjunction at sunrise: but his position in respect of its connexion with the Kaliyuga seems to have been an anomalous one which cannot be conveniently examined here.

Colebrooke, said (Essays, 2, 384)Google Scholar:—“A third school began the astronomical day, as well as the great period, at noon.” But that is a mistake. In the place alluded to by him, Bhaṭṭōtpala dealt with a different matter, and mentioned four views as to the moment —sunset, midnight, sunrise, and noon—at which a planet becomes the lord of a day: see the Bṛihat-Saṁhitā, ed. Sanskrit, Vizianagram Series, vol. 1, p. 32Google Scholar.

^{page 495 note 1} It is a curious point that the length of the daytime of this age is the same with the length of the true original exeliymos, the Yugapāda, 1,080,000 years. This, however, is perhaps a mere coincidence, a natural result of the period which had to be redistributed and of the principles on which that was to be done.

^{page 496 note 1} See, e.g., the Vāyu-Parāṇa, 99. 413:—

Yadā chandraś=cha sūryaś=cha tathā Tishya-Bṛihaspatī |

ēka-rāśau bhavishyanti tadā Kṛitayugaṁ bhavēt ||

The Matsya does not seem to include this statement: at any rate, it is not found in the passage, 272/273. 27 ff., where in agreement with the other Purāṇas it should be. The Brahmāṇḍa, however, has the verse, 74. 225, word for word the same.

The Vishṇu, 4. 24. 30, has the first half of the verse in the same words: its second half runs:—ēka-rāśau samēshyanti bhavishyati tataḥ Kṛitam.

The Bhāgavata, 12. 2. 24, follows the Vishṇu, except that its last pāda runs:—tadā bhavati tat=Kṛitam.

The verse is found also in an interpolated passage in the Mahābhārata, 3, Vanaparvan, § 190. 13099: here it agrees with the Vishṇu and the Bhāgavata, except that the last pāda runs:— pravartsyati tadā Kṛitam.

This verse does not exactly assert what is technically known as a conjunction: it only says that the sun, the moon, Jupiter, and Tishya “will come together, or will be (together), in one sign.” But a conjunction is obviously implied; because otherwise the occurrence would be too common. Jupiter spends nearly one year out of every twelve in Karka; and, on each occasion while he is there, he will be in conjunction with Tishya, and the sun and moon will be in conjunction with each other in that same sign once if not twice: but it is only at very long intervals that all the four will be in conjunction.