Nnhe Kaliyuga Era Is a Hindu Reckoning Beginning at Mean Sunrise, 6.0 A.M., Lanka Or Ujjain Time, on Friday, 18 February, B.C. 3

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THE KALIYUGA ERA OF B.C. 3102

BY J. F. FLEET, I.C.S. (Rum), PH.D., C.I.E. nnHE Kaliyuga era is a Hindu reckoning beginning at mean sunrise, 6.0 a.m., Lanka or Ujjain time, on Friday, 18 February, B.C. 3102.1 Its 5013th year will have begun just before the time when these pages come into the hands of readers of this Journal. In consequence of the seeming antiquity of this reckoning, there has been manifested recently in certain quarters a desire to demonstrate that it is a real historical era, founded in Vedic times and actually in use from B.C. 3102. But any such attempt ignores the fact that the reckoning is an invented one, devised by the Hindu astronomers for the purposes of their calculations some thirty-five centuries after that date. And it ignores, not a theory of the present writer or of anyone else, but a position which was clearly established as soon as the Hindu astronomy had been well explored, and was fully recognized at least half a century ago.2 There is, however, this to be said ; that the statements of the fact are mostly confined to writings which are not often consulted or even seen now, except by specialists who are concerned more with the study of the Hindu astronomy than with that of the calendar and the eras and other reckonings.

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. a As, for instance, by Whitney in his notes below E. Burgess's trans- lation of the Surya-Siddhanta, published in the Journal of the American Oriental Society, vol. 6 (1860), pp. 145-498.

Downloaded from https://www.cambridge.org/core. University Library Frankfurt, on 14 Feb 2018 at 20:27:14, subject to the Cambridge Core terms of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0035869X00041563 480 THE KALIYUGA ERA OF B.C. 3102

In these circumstances, the present article is given in order to bring the matter into an easily accessible publication, and to show, without entering into the complex question of the antiquity of the Vedas and the various topics connected therewith, the real nature of this reckoning and the circumstances in which it was established. Also, taking the matter farther, to show the leading part which the reckoning has in the Hindu system of cosmical periods, and the extent of its connexion with historical chronology, legendary and real.

The Kaliyuga or Kali age is the Hindu Iron Age. It is the last and worst in each cycle of the Four Ages in the Hindu system of cosmical periods. Nevertheless, it is intrinsically the most important item in the whole scheme, since, as will be seen, the beginning of it is the pivot of the entire system. Each cycle of the Four Ages, called sometimes Chaturyuga, ' the four ages', sometimes Mahayuga, ' the great age', sometimes simply Yuga, ' the age', has the duration of 4,320,000 solar years or, as some of the books explain, years of men ; that is, years beginning at the Hindu nominal vernal equinox, and measuring 12 minutes and a few seconds more than 365^ days. According to the view now prevailing, which is traced back to the time of Brahmagupta (wrote A.D. 628), each Chaturyuga is divided in the descending scale of 4, 3, 2, and 1 tenths, into the Krita or Golden Age of 1,728,000 years, the Treta or Silver Age of 1,296,000 years, the Dvapara or Brazen Age of 864,000 years, and the Kali or Iron Age of 432,000 years.1 Each age opens with a ' dawn' and

1 As regards the method of stating the lengths of the ages, Brahma- gupta {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

closes with a ' twilight', each of which measures one- twelfth of the whole period assigned to the age, and is included in that period; so that what we may call the full daytime of the age lasts for ten-twelfths of that period:x and it is from this point of view that the Kali age is sometimes mentioned as measuring 360,000 years.2 The divisions of the Chaturyuga on these lines are shown on p. 483 below. And the table shows also the con- stitution of the cycle on the principle of ' divine years', the basis of which is the idea that one year of men is a day of the gods, and 360 such days are one divine year.

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 Aryabhata, who may or may not have come before Brahmagupta. He differs from his master regarding the divisions of the Chaturyuga (for Aryabhata's arrangement of this matter see p. 486 below), and agrees with Brahma- gupta, but fixes the lengths of them by other means. He takes the orbit of the moon, 216,000 yojanas, as stated by Aryabhata 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 yojanas ; and he gets the figures for the ages by multiplying this figure by 8, 6, 4, and 2 : see his Sishyadhivriddhida, ed. Sudhakara Dvivedi, p. 3, verse 14, with p. 27 f., verses 2, 3 (there are rather serious mistakes in some of the explanatory figures interpolated by the editor here). 1 I follow Whitney and other scholars in using the terms ' dawn ' and ' twilight '. The original texts sometimes discriminate by presenting xayhdhyd where the term ' dawn ' has been adopted, and sarhdhydthsa where ' twilight' is used. But in other places they use the term narhdhyd in both senses, and also another term, samdhi, which, however, is perhaps used more specially in connexion with the Manvantaras, to which we shall come next. The term samdhyd, lit. ' a holding together, union, junction ', occurs freely in literature in the sense of both the morning and the evening twilight. Samdhydrhsa, lit. ' a portion of mrhdhyd', seems to have been selected simply in order to obtain, for the purpose of the ages, samdhyd in the sense of the opening ' twilight', and another term for the closing one. Sarhdhi, 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 sarhdhis are not parts of the Manvantaras, as the sarhdhyds and sarhdhydriisas 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. 2 For instance, in the Vishnu-Purdna, 4. 24. 41 : trans., vol. 4, p. 236.

Such are the divisions of the Yuga, Mahayuga, or Chaturyuga. In the other direction, 71 Chaturyugas constitute a Manvantara, ' the period of a Manu or patriarch': and during each Manvantara the Four Ages run on, in cycle after cycle, without any break; the ' twilight' of one age gliding straight into the ' dawn' of its successor, and the events proper to each age beginning at once to repeat themselves. There are 14 Manvantaras, each presided over by a different Manu, who is the progenitor and protector of the human race of his period: and the first of them is preceded by a 'junction-period',1 of the same length with a Krita age, which seems to be the time that was originally allotted for the process of creation, before the Surya-Siddhdnla found reasons for greatly lengthening that time ; and each of them is followed by a ' junction-period' of the same duration, which appears to be a time of abeyance of existence.2 The 14 Manvantaras, with the 15 'junction-periods', constitute a Kalpa or aeon, which thus measures 1000 Chaturyugas or 10,000 Kaliyugas. The Kalpa is the daytime of a day of the god Brahman; and his night is of the same length.3 At the end of the daytime of a day of Brahman everything is destroyed: during his night a state of chaos prevails: and then creation is renewed by him. This process of creation and destruction alternates during the whole life of Brahman,

1 The term is samdhi, regarding which see note 1 on p. 481 above. 2 The Surya-Siddhdnta, 1. 18, says that the samdhi at the end of a Manvantara is a jalaplava, ' a deluge '. The Vdyu-Purdna, 61. 136, says that there is a saifihdra, ' a suppression, destruction ', at the end of a Manvanfcara, and a sambhava, ' a birth, production', at the end of the saihhdra. '' The astronomers had no need to go beyond the Kalpa : and neither does Aryabhata nor does Brahmagupta seem to have done so. The Surya-Siddhdnta, 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.

The divisions of the Chaturyuga

THE AGES YEARS OF MEN' DIVINE YEARS

Krita :— 144,000 400 1,440,000 4,000 Twilight 144,000 400 1,728,000 4,800 Treta:— 108,000 300 1,080,000 3,000 Twilight 108,000 300 1,296,000 3,600 Dvapara :— Dawn . .... 72,000 200 720,000 2,000 Twilight 72,000 200 864,000 2,400 Kali :— Dawn . . 36,000 100 Daytime 360,000 1,000 Twilight 36,000 100 432,000 1,200 Y uga, Mahayuga, or Chaturyuga .... 4,320,000 12,000

which is known as the Mahakalpa and lasts for 100 years, each composed of 360 such days and nights. Then everything is overwhelmed by a final destruction and resolution into ultimate sources, and apparently remains so until another Brahman comes spontaneously into existence.1 1 This part of the matter is obscure. But it was recognized at an early period (see, e.g., Aryabhata's Kalakriya 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 Bhaskaracharya, writing in A.D. 1150, says that at the end of the 100 years, which period, he tells us, was named Mahakalpa 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

It may be added that we are held to be now in the Kaliyuga or Iron Age of the twenty-eighth Chaturyuga or cycle of the Four Ages in the seventh Manvantara in the first Kalpa in the second half of the life of Brahman.1 But we are still in only the ' dawn' of the Kali age: this dawn lasts for 36,000 years; and the daytime of the age, with all its depraved characteristics fully developed, will not begin until A.D. 32,899.

The general idea of the Ages, with their names, and with a graduated deterioration of religion and morality how many Brahmans have passed away : " see his Siddhdntasiromaiii, and his own commentary on it, edited by Bapu Deva Sastri, p. 10, verse 25. 1 See, e.g., the Surya-Siddhdnta, ed. FitzEdward Hall and Bapu Deva Sastri, 1. 21, 22 ; where we are further told that the Manu of the current Manvantara is Vaivasvata. See also the Vishnu-Purana, 1. 3. 26, 27, which adds that the present Kalpa is named Varaha, and the last preceding one was Padma : in verse 4 it uses the terms Para and Parardha to denote respectively the whole and the half of the life of Brahman. There has been, however, a difference of opinion on this point. Bhaskaracharya says in his Siddhdntasiromani, 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 Surya-Siddhdnta, 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 Brahma- Siddhanta. The Lashkar Panchang, printed at Gwalior, says in the introductory passages of its issue for the Vikrama year 1966 and the Saka 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 Surya- Siddhanta (see just above), and the other view is the Brahma-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, 13J ghatikds, 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.

and shortening of human life, —with also some conception of a great period known as the Kalpa or aeon, which is mentioned in the inscriptions of Aloka (B.C. 264-227),—• seems to have been well established in India before the astronomical period.1 But we cannot refer to that early time any passage assigning a date to the beginning of any of the Ages, or even allotting to them the specific lengths, whether in solar years of men or in divine years,

1 In rock-edict 4 we have :—"And the sons of the king DevanampiyaT Piyadassi, and the sons' sons and their sons, will cause this observance of dhamrna to increase throughout the aeon." The Kalsi text, line 12, has dva kaparh, = yavat - halpam : and the Shahbazgarhi and Mansehra texts yield the same expression. The Girnar text, line 9, has dva sarhvata-kapd, = ydvalz sarhvarta-lcalpdt, "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, Asoka speaks of "my sons and sons' sons, and my offspring after that throughout the aeon." Here, also, we have dva kaparh in the Kalsi text, line 14, and in the Shahbazgarhi and Mansehra texts ; while the Girnar text, line 2, has again dva saihvata-kapd. \ The Dhauli text has in edict 5, line 21, dva kapath, but in edict 4, line 17, d-Jcapam, which may be of course a mistake for dva Icapatii, but also may represent quite regularly d-lcalpam. 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 Junagadh inscription of Rudradaman, dated in A.o. 150, says (Epi. Ind., vol. 8, p. 42, text line 6-7) that the dam of the great lake Sudarsana 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 Gangdhar inscription of A.D. 423 {Gupta Inscriptions, p. 74, text line 7-8), describes the king Visvavarman as "surpassing in brilliance the most unendurable samvartaka-fire". These allusions may be explained from the Mahabharata, 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 sarhvartaka-Hre, ' 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.

JKAS. 1911. " 32

njeationed above.1 And .as regards their lengths, taking; the,.earliest evidence to which a definite period can be assigned, we find a different scheme of the system of cOSlnical periods presented to us by Aryabhata, who wrote in, or soon after A.D. 499. He had the period of the Ghaturyuga, called by him simply Yuga, with the same duration of 4,320,000 solar years of men. But he took the Manvantara as consisting of 72 (instead of 71) Yugas, = Chaturyugas; so that his Kalpa, consisting similarly of 14 Manvantaras, but without the fifteen 'junction-periods', measured 1008 (instead of 1000) Yugas, = Chaturyugas. And, in the other direction, he has not mentioned or indicated the graduated division of, .the Yuga into the four ages, but has divided it into four equal parts, called by him Yugapadas,'quarter Yugas', each consisting of 1,080,000 years. Further, he has not assigned names to the Yugapadas, but has given us his date by saying that he was 23 years old when there ^ad expired, not 3600 years of the Kali age, but three Yugapadas and 3600 years of the fourth Yugapada.2 To the above account we must add that Brahmagupta mentions still another scheme of the Kalpa, according to which it was composed of 14 Manvantaras, each of 71 Chaturyugas, without the fifteen 'junction-periods'; SiO that it measured 994 Chaturyugas.3 This represents

•. i1,,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 (Atharvaveda, 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. 2 See page 111 above. 3 Ed. cit., p. 4, verse 11.

The system of Brahmagupta and the Aryabhata's system Intermediate system present day

CD 1st Yugapad a. . . 1,080,000 The divisions of the Yuga in this Krita 1,728,000 a: system are not known 2nd „ ... 1,080,000 Treta 1,296,000 3rd „ ... 1,080,000 Dvapara 864,000 4th ,, ... 1,080,000 Kali 432,000

. o University Library Frankfurt Yuga 4,320,000 Yuga 4,320,000 Yuga ...... 4,320,000 https://www.cambridge.org/core/terms X 72 X 71 X 71 EC >

Manvantar .... a 311,040,000 Manvantar .... a 306,720,000 Manvantar .... a 306,720,000 O X 14 X 14 X 14 a 4,294,080,000 b 15 ' junction-periods '

, on each equal to one Krita .... + 25,920,000 o 14 Feb2018 at20:27:14 Kalpa 4,354,560,000 Kalpa 4,294,080,000 Kalpa 4,320,000,000 Yuga x 1008 Yuga x 994 Yuga x 1000 . , 488 THE KALIYUGA ERA OF B.C. 3102

an intermediate stage in the development of the scheme favoured by him from that presented to us by Aryabhata. The divisions of the Chaturyuga according to this intermediate system are not known. In other respects, the table on p. 487 above presents a comparison of the three schemes.

The settlement of the Hindu system of cosmical periods, first in the form in which it is given by Aryabhata, and finally in the form which it now has, is due to a com- bination of astronomical necessities with the pre-existing popular ideas. And it was in these circumstances that there were developed the features which distinguish the Hindu, from the Greek and Roman systems. The Ages of the Greeks and the Romans had no specific duration: their Golden, Silver, and Brazen Ages included the whole period from " the beginning of years " to the commence- ment of the Iron Age, and were past and done with for ever; and their Iron Age was to last until the end of everything. But the Hindu Ages are of definite lengths, and recur again and again; and the cycle of them constitutes a unit in the measurement of time, with the result that, by means of the initial point assigned to the current Kali age, the beginning of any other age in the life of Brahman, or any other point in his existence, can be determined. The circumstances in which this distinguishing feature was introduced were as follows:— At some time not long before A.D. 400 the Hindus received the principles of the Greek astronomy and astrology, and developed their own application of them.1 Amongst other details, they adopted the idea of a solar year beginning at the vernal equinox as marked for them

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.

by the entrance of the sun into their constellation and sign Mesha, the ram, which answers to our Aries, though it does not coincide with our constellation Aries, and much less with our present astronomical sign Aries.1 And, as that equinox was then occurring in their synodic lunar month Chaitra, they adopted also a lunar year beginning with Chaitra sukla 1, the first day of the bright fortnight of Chaitra, and bound it to that solar year by the system of lunisolar cycles and the intercalation of lunar months. Like other Oriental peoples, and like the Greeks themselves and the Romans, the Hindus had had the system of lunisolar cycles and intercalation from a great antiquity. But, so far, all that they had been concerned with was the harmonizing of the courses of the sun and the moon, and the keeping of a lunar reckoning as closely as possible in agreement with the natural seasons, by those means. Now, however, under the influence of the Greek sciences, they had to compute, both for astronomical and for astrological purposes, the courses of the planets as well as those of the sun and the moon. And to this end they required bases for calculation going far beyond any ordinary lunisolar cycles. In the first place, for laying down their elements in integers and for introducing refinements of them in the 1 The first point of Mesha is the fixed initial point of the Hindu sphere : it is either at, or 10' on the east of, the star £ 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 ( Piscium. The Hindu mean vernal equinox is the time when their mean sun comes to the first point of Mesha. According to the Hindu bases, this was, in B.C. 3102, on 18 February : now, as a result partly of the Hindus 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 Hindu true vernal equinox occurs two days and a few hours earlier, when their true sun comes to the first point of Mesha.

same convenient form, they required a large calculative period of the kind called by the Greeks an exeligmos and by the Romans an annus magnus or inundanus;1 that is, a period of evolution and revolution, in the course of which any given order of things runs through an appointed course and is completed by returning to the state from which it started. And they adopted an exeligmos beginning and ending with a conjunction of the sun, the moon, and the planets, at the first point of Mesha; which conjunction of course involved a new-moon and the vernal equinox.2 The Hindu astronomers themselves may have determined the precise length of time which they assigned to their exeligmos, and the all-important date to which (as will be shown) they referred the last occurrence of this conjunction before their own time. But the suggestion for the particular nature of the conjunction seems plainly

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 Geminos and Ptolemy in the course of his instructive article entitled '' Notes on Hindu Astronomy and the History of our Knowledge of it." 2 This conjunction is usually indicated, perhaps not too clearly, by statements such as that made by Aryabhata in his Kalakriya chapter, verse 11 :—" The Yuga (i.e. the Mahayuga 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 Dasagitikasutra, 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) Mesha and from sunrise on a Wednesday at Lanka. But it is defined in very plain terms in the Sfirya-Siddhdnta, 1. 57. This work purports to have been revealed by the Sun to the great Asura Maya when the Krita age was being superseded by the Treta : and we are here told that:—"At this same end of the Krita age, all the planets, by mean motion, but excepting (their) nodes and apsides, have come to equality (conjunction) at the beginning of Mesha." 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 Krita age, that is, to the beginning of the Treta, comes also at the beginning of the Kaliyuga.

to have been obtained from Greek or other1 sources: a passage found by Professor Jacobi in the De Die Natali of Censorinus (A.D. 238) tells us thus:-—-" There is also the year, which Aristotle [B.C. 384-322] calls maximus rather than magnus, which the orbs of th'e sun, the moon, and the five wandering stars bring to an end when they are all together carried back to that same sign in which they once were at one and the same time; and of which year the midwinter is a cataclysm which our people call a deluge, and the summer is a conflagration which is a burning of the world: for in these alternate times the world is perceived to be turned now into fire, now into water."1 • Whatever may be the origin of the idea of this conjunction, the Hindu astronomers adopted it. And, as regards one of the details of their system, it was necessary, in view of the number of the heavenly bodies concerned, that the exeligmos to be used in connexion with it should be a very long one, to admit of assigning a sufficiently great number of revolutions to the sun, the moon, and the planets, to bring them all together again at the end of it, and at the same time to state those numbers as integers without the inconvenience of fractions. Now, the Hindus have sometimes used the Kalpa as an exeligmos. But that was laid out and adopted expressly with the same objeet of avoiding the introduction of fractions in making refinements in the elements.2 The more general exeligmos has 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 thi* 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 opinibri that it is infinite and cannot ever complete itself." ' 2 An example may be given, to make the meaning clear. For the planet Jupiter, Aryabhata had 364,224 revolutions in the Yuga, giving

been the Yuga, Mahayuga, or Chaturyuga of 4,320,000 years. And this was the earlier exeligmos of the two, and was nominally the exeligmos of Aryabhata. But, except in the case of the apsis and node of the moon, all the figures for the principal elements, taken for that period by him and his successors, are exactly divisible by four. And it is recognizable from this that the true original Hindu exeligmos was the quarter of that period, namely, Aryabhata's Yugapada of 1,080,000 years, with the conjunction recurring at the beginning of each Yugapada.1

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 V'uga as the exeligmos, he would have had to state the number1 of revolutions, i taken by him, as 364,226if lr0-: but, using the Kalpa, he was able to put it aa 364,226,455. , (Further, the Surya-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. 1 Before the publication of Kern's edition of the Aryabhatlya in 1874, Aryabhata was known only from quotations from him in other Hindu "Works ; and even in those quotations he was confused with the author of the later work, the Arya-Siddhanta : the real Aryabhata, 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 Yugapada might be substituted for the Yuga for purposes of calculation : see the Surya-Siddhanta, trans., p. 160f. The reason for the precise length of the Hindu exeligmos in either form, Yuga or YTugapada, does not come within the scope of this article : it'has been much debated, but is still a matter of conjecture, and seems ljkely 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), 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, Yugapada ; and in the second place, that it is tolerably certain that the Hindus 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

As regards another detail, the Hindu astronomers found that they required also a specific date to which they could refer the conjunction or some fairly recent recurrence of it, so that they could state the positions of the heavenly bodies for any desired times. And, applying themselves to this detail, and working, let us say (simply taking a convenient year at any time more or less near the real period) in A.D. 399, they found, whether by calculations of their own or from some extraneous hint,1 that the said conjunction had occurred exactly 35 centuries previously. There was not, indeed, really such a conjunction, or even a close approximation to it: nor, apparently, is it even

precession at 54" and 1' simply because these rates gave periods which go without fractions into the period of their exehgmoi. 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 Hindu exeligmos, either the shorter one, the Yugapada, 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 Hindu divisions of time, 21,600 nadis or ghatls, 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 yojauas 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. 1 The Kaliyuga era was known to the Arabian astronomers as the Era of the Deluge: see Alberum's Chronology of Ancient Nations, trans. Sachau, p. 29 ; also the Aln i Akbarl, trans. Jarrett, vol. 2, p. 22. It is not impossible that some tradition about the Flood, obtained from the Greeks or the Romans, may have indicated to the Hindus the period in which, in a general way, they should look for the date of the great conjunction.

the case that the sun was actually at the first point of Mesha at the moment arrived at.1 But there was an approach to such a conjunction, which was turned into an actual conjunction by using the mean instead of the true positions of the sun, the moon, and the planets, and by taking liberties with some of them.2 And, partly from the reckoning which has come down to us, partly from the statements of details in the astronomical books, we know that the moment assigned to the assumed conjunction was according to one school mean sunrise at Lanka-Ujjain on Friday, 18 February, B.C. 3102, and according to another school the preceding midnight.3

1 It cannot be said safely, off-hand, as has been said, that no such conjunction ever did or ever will occur : as Alberuni observed (see his Chronology of Ancient Nations, trans. Sachau, p. 30), 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. 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 Hindu books : of those three, the Art/a-Siddhdnta 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 Mesha ; Venus and Jupiter were 2° 52' 48" west of that point ; and Mercury was 8° 38' 24" west of it: see SuryaSiddhdnta, 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 mid Chronologische Tafeln (1908). 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. 3 Aryabhata belonged to the sunrise school: the midnight school is represented by the original Surya-Siddhdnta, which existed before the time of Varahamihira (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) :—"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, Bhattotpala 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

This difference, however, is only a technical point of detail for purposes of calculation: all the Hindu books agree that the civil day runs from sunrise: and for all purposes of chronology the period beginning with this conjunction runs from the sunrise on the Friday. For the rest, the case is as follows. To suit the pre- existing notions about the Ages, which involved the understanding that the Kali age had already begun, the Hindus took the moment of the conjunction, fixed in B.C. 3102 as stated above, as the initial point, not of the Yuga, but of the last Yugapada or quarter Yuga, which accordingly became the Kali age. Further effect was given to the same notions by redistributing the period of 4,320,000 years into the unequal Krita, Treta, Dvapara, and Kali ages, in the proportion of 4, 3, 2, and 1 tenths. And the result was the peculiar position which marks the beginning of the Kali age as the pivot of the whole system of Hindu cosmical periods : namely, the conjunction taken as the starting-point of the entire Yuga now recurs, as originally, at the beginning of each Kali age; in a Dvapara age, it does not occur at all; in a Treta age, it occurs twice, at the beginning and at 216,000 years before the end ;1 and in a Krita age, in spite of that age being always the first and the best of the ages, it occurs, not at its beginning, but after the lapse of 648,000 years from its beginning. We may add, however, that though the Krita age was thus at first left without any particular occurrence to mark its arrival, the deficiency was subsequently supplied. The next Krita age, and of course each Krita age after it,

a day : see the Brihat-Sarhhita, ed. Vizianagram Sanskrit Series, vol. 1, p. 32. 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 Yugapada, 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.

is to be attended by a conjunction of the sun, the moon, the planet Jupiter, and the nakshatra Tishya, perhaps better known as Pushya, which is part of the constellation and sign Karka, the crab (Cancer).1 But it must be noted that every Krita age, like all the other cosmical periods, must begin at the vernal equinox: and such a conjunction as this one can only happen shortly after the Hindu summer solstice ; it is only at that time of the year that the sun is in Karka. 1 See, e.g., the Vtiyu-Parana, 99. 413 :— Yada chandras=cha suryaszcha tatha Tishya-Brihaspati I eka-rasau bhavishyanti tada Kritayugam bhavet || 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 Puranas it should be. The Brahmdnda, however, has the verse, 74. 225, word for word the same. The Vishnu, 4. 24. 30, has the first half of the verse in the same words: its second half runs :— eka-rasau sameshyanti bhavishyati tatah Kritam. The Bhdgavata, 12. 2. 24, follows the Vishnu, except that its \&stpada runs :— tada bhavati tat=Kritam. The verse is found also in an interpolated passage in the Mahdbhdrata, 3, Vanaparvan, § 190. 13099 : here it agrees with the Vishnu and the Bhdgavata, except that the last pdda runs :— pravartsyati tada Kritam. 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. (To be concluded in the next number.)