गुप्त अभिलेख संग्रह (जे. एफ. फ्लीट - गुप्त सम्राटों एवं परवर्ती नरेशों के ऐतिहासिक पाषाण व ताम्रलेख)

THE GUPTA INSCRIPTIONS: APPENDIX II. 153

Add this gh. 52, p. 20, to the ghaṭīs and palas only of (a) the abdapa. The result,
vāra 1, gh. 5, p. 48, shews that the 6th mean tithi of Chaitra ended with gh. 5, p. 48, after
sunrise on the following day, Monday, after the day of the Mêsha-Saṁkrānti, Sunday.
This quantity, vāra 1, gh. 5, p. 48, is called the tithi-bhōga, lit. 'the enjoyment or dura-
tion of the tithi;' and it is the end of the tithi-dhruva, increased by one tithi. It is, of
course, a mean tithi. And it shews that days 1, gh. 5, p. 48, had elapsed, from sunrise on
the day of the Mêsha-Saṁkrānti, up to the end of Chaitra śukla 6 as a mean tithi.
We have now to bring into consideration the number of tithis elapsed up to the
commencement of the given tithi. And, in doing this, we must of course take account of
any intercalary month that there may be, preceding the given tithi, in the given year.
In our example, however, the result in (b) the tithi-śuddhi, is less than nineteen tithis.
And a reference to Table VI. p. 22, — which would enable us to determine the inter-
calary month approximately, if there were one, — shews us that there was, therefore, no in-
tercalary month at all in the given year, Śaka-Saṁvat 406 expired. The explanation of
this, is, that, when the tithi-śuddhi is less than nineteen, it shews that the saṁkrānti in
Chaitra occurred within the first nineteen tithis of that month. And, as, generally, the
solar months are longer than the lunar months, the saṁkrāntis of the sun, i.e. his passage
from one sign of the zodiac into the next, occur continuously later in each successive
lunar month. But, when the saṁkrānti in Chaitra falls within the first nineteen tithis,
no saṁkrānti, up to the end of the year, can go beyond the thirtieth tithi of any lunar
month; and, therefore, no month will be intercalary.
Consequently, from the beginning of Chaitra, up to the commencement of the given
tithi, Âshâḍha śukla 12, there had elapsed only the usual number of one hundred and one
tithis; viz. in the bright fortnight of Chaitra, 15; in Vaiśâkha, 30; in Jyêshtha, 30; and
in Âshâḍha, 15 in the dark fortnight, and 11 in the bright.¹ From this number of tithis,
101, we subtract the tithi-dhruva, 5. And the remainder, 96, is the number of tithis
elapsed from the end of Chaitra śukla 5 up to the end of Âshâḍha śukla 11. But the tithi-
bhōga, which we have already arrived at, is the end of Chaitra śukla 6; and the same
number of tithis, 96, expire from the end of Chaitra śukla 6 up to the end of Âshâḍha śukla
12. Therefore, adding to the tithi-bhōga the solar equivalent, now to be introduced, the
result will bring us to the end of the given tithi, Âshâḍha śukla 12.
Turning to Table III. p 14, we find that the equivalent, in mean solar days, of
96 tithis, is days 94, gh. 17, p. 36. And, adding this to the tithi-bhōga, the result, days
95, gh. 23, p. 24, gives the interval that had elapsed, from sunrise on the day of the Mêsha-
Saṁkrānti up to the end of Âshadha śukla 12 as a mean tithi

¹ We are dealing with a northern date; and that is why the tithis are counted in this way. If we
were dealing with a southern date, the enumeration would be, in Chaitra, 30; in Vaiśâkha, 30:
in Jyêshṭha, 30; and in the bright fortnight of Âshâḍha, 11. The total is the same, 101, since a bright
fortnight is concerned.
20

154 CORPUS INSCRIPTIONUM INDICARUM, VOL. III.
Now, however, we have to determine the spashṭa-tithi, or apparent tithi. For this
purpose, we require the parâkhya-correction, which is to be ascertained through the tithi-
kêndra.
Turning again to Table III. p. 14, we find that the variation in the tithi-kêndra
for 96 tithis is tithis 12, gh. 1, p. 20. Enter this in (c), below tithis 22, gh. 18, p. 35,
which we have already arrived at as the tithi-kêndra at the end of Chaitra śukla 6. Add
the two quantities together; and the result, — excluding 28 tithis, as before, — is tithis 6,
gh. 19, p. 55; which is the tithi-spashṭa-kêndra at the end of the given tithi, Âshâḍha
śukla 12.
With this argument, we turn to Table IV. p. 20, for the parâkhya-correction. In
this Table, the correction is given for tithis and ghaṭîs, at intervals of ten ghaṭîs. Thus,
for the tithi-spashṭa-kêndra, tithis 6, gh. 10, the parâkhya is gh. 24, p. 10; and for tithis
6, gh. 20, it is gh. 24, p. 19. The difference, 9 palas, is shewn in the last column of the
Table, and would serve to calculate the exact parâkhya for the tithi-spashṭa-kêndra. But
here it is sufficiently close for our purposes to take the parâkhya as gh. 24, p. 19.
Under (a) the abdapa, enter this parâkhya below the sum of the tithi-bhôga and the
solar equivalent of 96 tithis, and, — as is indicated by the sign plus at the top of col. 1 in
Table IV., — add it to that sum.
The result, vâras 95, gh. 47, p. 43, gives the number of days, and parts of a day,
that had elapsed, from sunrise on the day of the Mêsha-Saṁkrânti, up to the end of
the apparent Âshâḍha śukla 12. To the days, 95, add 1, the week-day of the Mêsha-
Saṁkrânti. Divide the sum, 96, by 7, and the result is 13 weeks, and 5 days over; which
shews that the current week-day of Âshâḍha śukla 12 was the fifth day in the week; that
is Thursday. The remaining quantities, gh. 47, p. 43, shew the time after sunrise, on
that Thursday, on which the given tithi, Âshâḍha śukla 12, ended.
The Tables in Prof. K. L. Chhatre's book, however, are adapted to the meridian
of Bombay. The ghaṭîs and palas, therefore, of a tithi worked out by the method ex-
hibited above, are for Bombay; and are to be reckoned from mean sunrise at Bombay.
When the tithi is required for any other particular place, the difference of longitude in
time (one degree = ten palas) is to be added or subtracted, according as the place is east
or west of Bombay. In the present instance, as I learned after first working it out, the above
Śaka date was selected in consequence of its being the equivalent of the date, in Gupta-
Saṁvat 165, recorded in the pillar inscription of Budhagupta at Êraṇ in the Central
Provinces. We have therefore now to determine the tithi for Êraṇ itself. The longitude of
Bombay is 72° 51'; and that of Êraṇ is 78° 15'; both east of Greenwich. Êraṇ, therefore
is 5 degrees, 24 minutes, east from Bombay. Adding (5° 24' × 10 =) 54 palas to 47
ghaṭîs and 43 palas, which we have obtained above for Bombay, the tithi at Êraṇ is
gh. 48, p. 37, reckoned from mean sunrise on the same day, Thursday.

THE GUPTA INSCRIPTIONS; APPENDIX II. 155
The above result is sufficient for all practical purposes. But it is further to be noted
that the tithis in our Pañchângs are intended to be given from apparent sunrise. In
practice, however, so much minuteness is not always and everywhere attempted; at least,
in the present day, in the Dekkan. For this reason, it seems, Prof. K. L. Chhatre has
not noticed this point in his method exhibited above. But I will now give the tithi
in question from apparent sunrise at Êraṇ. Without going through the process, which is
rather too complicated to be given in the present paper, I will state only the result,
that the apparent sunrise at Êraṇ, on the day in question, took place gh. 1, p. 56, before
the mean sunrise; the latitude of Êraṇ used in the process, being 24° 5'. Adding, there-
fore, gh. 1, p. 56, to the above result from mean sunrise, we get gh. 50, p. 33, reckoned
from apparent sunrise, as the time at which the given tithi, Âshâḍha śukla 12, ended at
Êraṇ on the Thursday.
Before dismissing this part of the subject, I would point out that the calculation of a
tithi, by the above method, is not of necessity absolutely accurate, according to the pre-
sent absolutely accurate European Tables of the sun and the moon. Absolute accuracy,
in this sense, could be ensured only by working from the actual places or longitudes of the
sun and the moon, to be determined in strict accordance with the method prescribed for
that purpose. The tithi obtained by the method exhibited above, will differ, sometimes by
as much as ten ghaṭîs, from that which would be obtained from the apparent places of the
sun and the moon, actually calculated from Prof. K. L. Chhatre's Tables for the sun
and the moon. The difference, however, at full-moon and new-moon will be very small,
one ghaṭî at the greatest; and it reaches its maximum on the eighth tithi of the
bright and of the dark fortnight. But, in respect of this second possible method of Prof.
K. L. Chhatre, it must be stated that we have nothing to do with it in dealing with Hindu
tithis; for the reason that, with the exception of the phala-saṁskâra, the corrections
introduced by him in finding the apparent longitude of the moon, were not taken into account
by ancient Hindu astronomers.
And, on the other hand, the method exhibited above being in close agreement
with Hindu works, it may be claimed that the tithi obtained by it will differ but very little
from the tithi obtained by the method prescribed in the Sûrya-Siddhânta and other Hindu
works. The difference¹ will amount to five or six ghaṭîs at the utmost; and that in but
very few cases.
In order, however, that no room may be left for doubt, I have also calculated
the tithi in the present example actually by the Âryabhaṭîya or Ârya-Siddhânta of the first
Âryabhaṭa, the Brahma-Siddhânta of Brahmagupta, the Sûrya-Siddhânta, the Siddhânta-
¹ See page 149 above, note 1.
u 2

156 CORPUS INSCRIPTIONUM INDICARUM, VOL. III.
Śirōmaṇi, and the Ârya-Siddhânta of the second Âryabhaṭa.¹ I calculated it first for Ujjain,
i.e. for the Hindu meridian, reckoning from the mean sunrise there; and then turned it
into the tithi for Êraṇ. The longitude of Ujjain is 75° 43' east of Greenwich. I have
also calculated the ghaṭīs and palas from the apparent sunrise at Êraṇ; and all the results
are given in Table VI., on the upper part of page 157 below. From them we see that
the tithi fell on a Thursday,² according to all the authorities.
¹ i.e. the work that is usually called the Laghu-Ârya-Siddhânta.—There are two distinct
and separate works, each bearing the name of Âryabhaṭa as its author. The one published by Dr.
Kern contains one hundred and eighteen verses in the Âryâ metre, and is called Âryabhaṭīya in
general and by the author himself; but it may, and justly so, be called Ârya-Siddhânta; and it is
called so by many Hindu astronomers. The date of this work is Saka-Saṁvat 421 expired (A. D.
499-500). The other, which, I believe, has not yet been printed, contains about six hundred and
twenty-five verses in the Âryâ metre, divided into eighteen chapters. The date of it is not given.
But, from internal evidence, I find that it is later than the Brahma-Siddhânta of Brahmagupta
(Śaka-Saṁvat 550 expired; A.D. 628-29); and there is a reference to it in the Siddhânta-Śirōmaṇi
(Śaka-Saṁvat 1072 expired; A.D. 1150-51). Its date, therefore, lies somewhere between these two
limits. In the first verse of it, the author calls himself Âryabhaṭa; and his work, a Siddhânta, without
Laghu or any other epithet. In a manuscript copy of it, I find that it is named Mahâ-Siddhânta
at the end of some chapters, and Laghu-Ârya-Siddhânta at the end of others. For the sake of dis-
tinction and convenience, it is better to call the authors of these two works, the first and the second
Âryabhaṭa. The numbers of the revolutions of the planets &c. given, as belonging to the Ârya-
Siddhânta, in the Rev. E. Burgess' Translation of the Sûrya-Siddhânta and in some instances
those given by Prinsep (Prinsep's Essays, Vol. II. Useful Tables, n. 153) as belonging to the same
authority, belong really to the second Âryabhaṭa. Probably, when these gentlemen wrote, they had
not themselves seen the Siddhânta of the first Aryabhaṭa Gen. Sir A. Cunningham, also, was not,
it seems, aware of the two different Aryabhaṭas, when he wrote (Indian Eras, p. 88) "according to
Warren the number of days assigned by Âryabhaṭa to a Mahâyuga of 4,320,000 years is 1,577,917,500
in the south of India and 42 more in the MSS. preserved in Bengal." Of these two numbers, the
former belongs to the first, and the latter to the second, Âryabhaṭa.
² [i.e. on a Hindu Thursday.—It must be borne in mind that the Hindu week-day is reckoned, with
the solar day and night, from sunrise to sunrise, as stated at page 146 f. above; but the English week-
day, and the civil date coupled with it, from midnight to midnight. In comparing Hindu and English
dates, the only course is to take mean sunrise and mean midnight (6·0 A.M. and 12·0 P.M. respec-
tively), and to give, as the English equivalent, that week-day, with its civil date, which is actually
running during these eighteen hours, when of course the same week-day is running in India; i.e. the
week-day which is identical for the greater part by both the English and the Hindu reckonings. And,
if the difference in mean time between Greenwich and Ujjain, viz. 5 hours, 2 minutes, 52 seconds
(using the same longitude for Ujjain, 75° 43', taken from Keith Johnston's Atlas, that is used by Mr.
Sh. B. Dikshit for his calculations in this paper and for the Sâyana-Pañchâng) be taken into con-
sideration, of course the week-days of the two places are absolutely identical, except for the space
of 57 minutes, 8 seconds, or 2 ghaṭīs, 22·8 palas, at the end of the Hindu week-day; during that time,
while at Ujjain a Hindu Thursday for instance, is still running, at Greenwich the week-day will be
Friday. Owing to this, there may sometimes be a nominal discrepancy in the resulting English week-
day for a given tithi; but the instances will be few and far between, as very few tithis will be found
to end so late after sunrise; and the discrepancy will be confined mostly to such occurrences as the
heliacal rising of Jupiter (see, for instance, the double dates which it has been necessary to quote at
page 104 ff. above). In the present case, not one of the ending-points of the given tithi falls within
the debatable period; either for Ujjain, or for Êraṇ, which is appreciably to the east of Ujjain.—J. F. F.]

THE GUPTA INSCRIPTIONS; APPENDIX II. 157
TABLE VI.
The Times, after Sunrise, of the ending of a given Tithi.
Śaka-Saṁvat 406 expired = A.D. 484-85 current.
Âshâḍha (June-July); the bright fortnight; the 12th tithi; Suraguruvâra (Thursday).

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THE GUPTA INSCRIPTIONS; APPENDIX III. 161
APPENDIX III.
The Twelve-Year Cycle of Jupiter.
By Shankar Balkrishna Dikshit; Bombay Educational Department.
The names of the saṁvatsaras, or years, of the Twelve-Year Cycle of Jupiter,
are determined in accordance with the following rule in the Bṛihat-Saṁhitâ of Varâhamihira,
adhyâya viii. verse 1, — nakshatrêṇa sah=ôdayam upagachchhati yêna dêvapati-mantrî¹ |
tat-saṁjñaṁ vaktavyaṁ varshaṁ mâsa-kramêṇ=aiva ||, — "with whatever nakshatra
(Jupiter) the counsellor of (Indra) the lord of the gods attains (his) rising, the year is to
be spoken of (as) having the appellation of that (nakshatra), in accordance with the order
of the months."
Here, by the word udaya, 'rising,' we have to understand, not the daily rising of Jupi-
ter, but his heliacal rising. Jupiter becomes invisible for some days before and after
his conjunction with the sun. The sun's daily motion is faster than that of Jupiter. So,
when the sun in his course comes near Jupiter, the latter becomes invisible, on the west
side of the horizon; and he is then said to set. He remains from twenty-five to thirty-one
days in this state of invisibility. And, when he is left behind by the sun, he again becomes
visible, in the east; and then he is said to rise. Generally, in India, when the interval
between the daily settings or risings of the sun and Jupiter amounts to forty-four minutes
¹ The reading that I give, is from an old manuscript in my possession. But the commentator,
Utpala, explains the verse with the reading—nakshatrêṇa sah=ôdayam astaṁ vâ yêna yâti sura-
mantrî,—'with whatever nakshatra (Jupiter) the counsellor of the gods attains (his) rising or setting.'
It is curious that the text, in my manuscript copy, stands as given above. The copyists, however far
they might go wrong in ordinary transcribing, could not, unless intentionally, turn the letters mastaṁ
vâ yêna yâti sura, if they were original at all, into mupagachchhati yêna dêvapati. And Utpala him-
self gives the note—Ṛishiputr-âdibhiḥ udaya-nakshatra-mâsa-samjñâ-kramêṇa varshaṁ jñâtavyam
ity=uktam,—"it is said by Ṛishiputra and others, that the year is to be known according to the
order of the name of the month of the nakshatra of the rising (of Jupiter)." Also, all the other author-
ities, which I find giving the rule of naming the years of the cycle according to the risings of Jupiter,
make each year take its name from only the rising of the planet; not from its setting.—[The reading
in the text above, is the one adopted by Kern, in his edition of the Bṛihat-Saṁhitâ, p. 47. His
translation (Jour. R. As. Soc. N. S. Vol. V. p. 45) is—"each year (during which Jupiter completes a
twelfth part of his revolution) has to bear the name of the lunar mansion in which he rises; the years
follow each other in the same order as the lunar months." Both in his Various Readings, p. 6, and
in the note to his translation, he notices the reading sah=ôdayam astaṁ vâ yêna yâti sura-mantrî.
But he points out that "the comparison of the MSS leaves little doubt that this reading is a correc-
tion, suggested by the remark of Utpala, that, in case the planet should set in one and rise in another
nakshatra, only that name must be taken which agrees with the order of the month.—J. F. F.]

(of time), then the so-called setting or rising of Jupiter, i.e. his heliacal setting or rising,
takes place.
To such a system, as is taught in this verse of Varâhamihira, and by no less than
eleven other authorities, as will be seen further on, or determining the commencement of
a saṁvatsara of the Twelve-Year Cycle, and of naming it, from Jupiter's heliacal-rising,
I would give the name of the heliacal-rising system, in order to distinguish it from
the other system in which the duration and name of a saṁvatsara of the Twelve-Year
Cycle are determined from the particular sign of the zodiac in which Jupiter stands with
reference to his mean longitude, and which latter system, to be mentioned more full,
further on, I would name the mean-sign system.
Now, the years of the Sixty-Year Cycle of Jupiter and of the Twelve-Year Cycle ac-
cording to the mean-sign system, are determined by his mean longitude,¹ which sometimes
differs from his apparent longitude by as much as fifteen degrees. But, as the disappear-
ance or reappearance of Jupiter is no imaginary thing, it is evident that it can be calcu-
lated, and is to be calculated, only according to Jupiter's actual place, that is, his apparent
longitude (or right ascension), and not from his mean longitude. And, consequently, the
beginning of each saṁvatsara of the Twelve-Year Cycle according to the heliacal-rising
system, depends on Jupiter's apparent longitude at the time of his heliacal rising.
One revolution of Jupiter, in the zodiac, is completed in about twelve years; and, in
twelve years, there are twelve revolutions of the sun (that is, of the earth). So that, in
this period of about twelve years, there are only eleven conjunctions of the sun and Jupiter.
Therefore, in twelve years there are only eleven heliacal risings of Jupiter.² The interval
between two risings is generally 399 days. And thus, in each cycle of the heliacal-
rising system, there are only eleven saṁvatsaras in twelve years; the duration
of each being about 400 days, and one saṁvatsara, determined by the circumstances of
the particular cycle, being altogether omitted.
The names of the lunar months are used as the names of the saṁvatsaras of the
Twelve-Year Cycle of Jupiter. And the names of these months are given to the saṁvat-
saras, in accordance with the particular nakshatra in which Jupiter's heliacal rising takes
place. Of the twenty-seven nakshatras, two are assigned to each of nine of the twelve
months; and three to each of the remaining three months. The rule for this is given in
the Bṛihat-Saṁhitā, viii. 2, — varshâṇi Kârttik-âdîny=âgnêyâd bha-dvay-ânuyôgîni ।
kramaśas tri-bhaṁ tu pañchamam upântyam antyaṁ cha yad varsham ॥,—“ the years
Kârttika and others (that follow) combine two nakshatras, from (the nakshatra) belonging

¹ The mean longitude of a heavenly body is the longitude of an imaginary body, of the same
name, conceived to move uniformly with the mean motion of the real body.
² In his note on the Sûrya-Siddhânta, xiv. 17 (see the Rev. E. Burgess' Translation, p 271),
Prof. Whitney says that Jupiter “ would set and rise heliacally twelve times in each revolution, and

THE GUPTA INSCRIPTIONS; APPENDIX III 163
TABLE VIII.
Regulation of the Names of the Saṁvatsaras from the Nakshatras.

164 CORPUS INSCRIPTIONUM INDICARUM, VOL. III.
in Table IX. on page 165 below. And generally, whenever we meet with a nakshatra
spoken of with reference to the place of a heavenly body, that nakshatra is to be taken in
the above sense.
There is, however, a second method of determining the nakshatras with refer-
ence to the places of heavenly bodies. And, though it has now gone almost out of use,
yet it was undoubtedly prevalent to a great extent in early times, and was much made use
of, on important religious occasions at least. The chief feature of it is, that the space
on the ecliptic allotted to each nakshatra is not equal. Fifteen nakshatras are held to
be of an equal average space; but six, of one and a half times the average; and six
others, of only half the average.
One system of unequal spaces, according to this method, is referred to in some of
the verses from the Garga-Saṁhitâ, which are quoted by Utpala in his commentary on the
Bṛihat-Saṁhitâ. The commentary, with the passages quoted in it, runs — tathâ cha
Gargaḥ। Uttarâś cha tath=Âdityaṁ Viśâkhâ .ch=aiva Rôhiṇî। êtâni shaṭ adhyardha-
bhôgâni॥ Paushṇ-Âśvi-Kṛittikâ-Sôma-Tishya-Pitrya-Bhag-âhvayâḥ Sâvitra-Chitr-Ânûrâdhâ
Mûlaṁ Tôyaṁ cha Vaishṇavaṁ Dhanishṭh=Âjaikapâch ch=aiva sama-vargaḥ prakîrtitaḥ।
êtâni pañchadaśa sama-bhôgâni॥ Yâmy-Aindra-Raudra-Vâyavya-Sârpa-Vâruṇa-saṁjñitâḥ।
êtâni shaṭ ardha-bhôgâni॥,—"and so Garga (says), 'the Uttarâs (i.e. Uttarâ-Phalgunî,
Uttarâ-Ashâḍhâ, and Uttarâ-Bhâdrapadâ), and Âditya (Punarvasu), Viśâkhâ, and also
Rôhiṇî;' these six (are) of one-and-a-half times (the average) longitude. '(The naksha-
tras) of which the names are Paushṇa (Rêvatî), Aśvi (Aśvinî), Kṛittikâ, Sôma (Mṛiga),
Tishya (Pushya), Pitrya (Maghâ), and Bhaga (Pûrvâ-Phalgunî), (and also) Sâvitra (Hasta),
Chitrâ, Anûrâdhâ, Mûla, Tôya (Pûrvâ-Ashâḍhâ), and Vaishṇava (Śravaṇa), (and) Dha-
nishṭhâ, and also Ajaikapâd (Pûrvâ-Bhâdrapadâ); (this class of nakshatras) is called the
equal class;' these fifteen (are) of equal (average) longitude. '(The nakshatras) which
have the appellations of Yâmya (Bharaṇî), Aindra (Jyêshṭhâ), Raudra (Ârdrâ), Vâyavya
(Svâti), Sârpa (Âślêshâ), and Vâruṇa (Śatatârakâ);' these six (are) of half (the average)
longitude." In this system, which I would name the Garga system of unequal spaces,
the number of the nakshatras is twenty-seven, as usual. The average space of a nakshatra,
therefore, is 13 degrees, 20 minutes; a one-and-a-half space is 20 degrees; and a half
space is 6 degrees, 40 minutes. The longitudes of the ending-points of all the nakshatras,
according to this system, are given in the last column but one in Table IX. on
page 165 below; and the entries of ½ and 1½ in the sub-column, mark the spaces which
differ from the average space. Nârada and Vasishṭha give this system in the same way
as Garga. It seems to have originated in the fact that the distances between the chief
stars, called yôga-târâ, of the different nakshatras, are not equal. The distance is natur-
ally expected to be 13 degrees, 20 minutes. But, in some cases it is less than 7 degrees;
while in others it is more than 20 degrees. However, be the reason of the system what it
may, there is no doubt that it was extensively in use in ancient times. And, that either it,

THE GUPTA INSCRIPTIONS; APPENDIX III. 165
TABLE IX.
Longitudes of the Ending-points of the Nakshatras.

or the very similar system of the Brahma-Siddhânta, explained below, was still in use, at
least on important occasions, up to A.D. 862, is proved by the Dêôgaḍh inscription of
Bhôjadêva of Kanauj; the results for which, calculated by me, have been exhibited by
Mr. Fleet at page 107 above, note 1.
Another system of unequal spaces is given in the Brahma-Siddhânta,¹ chapter
xiv. verses 45 to 53. In its leading feature, it is the same with Garga's system; but it
differs a little from Garga's, in introducing Abhijit, in addition to the twenty-seven naksha-
tras. The moon's daily mean motion,—13 degrees, 10 minutes, 35 seconds,—is taken as
the average space of a nakshatra. And, as the total of the spaces thus allotted to the
¹ By this name, is to be understood, throughout this paper, the Siddhânta by Brahmagupta

166 CORPUS INSCRIPTIONUM INDICARUM, VOL. III.
usual twenty-seven nakshatras, on a similar arrangement of unequal spaces, amounts to
only 355 degrees, 45 minutes, 45 seconds, the remainder,—4 degrees, 14 minutes, 15 se-
conds,—is allotted to Abhijit, as an additional nakshatra, placed between Uttarâ-Ashâḍhâ
and Śravaṇa. This system, which I would name the Brahma-Siddhânta system of
unequal spaces, is best explained by Bhâskarâchârya,¹ in his Siddhânta-Śirômaṇi,
Part iii., chapter 2 (Grahagaṇitaspashṭâdhikâra), verses 71 to 74. His text, and his own
commentary on it, are as follows, — sthûlaṁ kṛitaṁ bh-ânayanaṁ yad êtaj jyôtirvidâṁ
saṁvyavahâra-hêtôḥ ॥ 71 ॥ Sûkshmaṁ pravakshyê-tha muni-praṇîtaṁ vivâha-yâtr-âdi-
phala-prasiddhyai। adhyardha-bhôgâni shaḍ atra taj-jñâḥ prôchur Viśâkh-Âditibha-
dhruvâṇi॥ 72 ॥ Shaḍ ardha-bhôgâni cha Bhôgi-Rudra-Vât-Ântak-Êndr-âdhipa-Vâruṇâni।
śêshâṇy=ataḥ pañchadaś=aika-bhôgâny=uktô bha-bhôgaḥ śaśi-madhya-bhuktiḥ॥ 73 ॥
Sarv-arksha-bhôg-ônita-chakra-liptâ Vaiśv-âgrataḥ syâd Abhijid-bha-bhôgaḥ। 74 ॥ Com-
mentary.— Iha yan nakshatr-ânayanaṁ kṛitaṁ tat sthûlaṁ lôka-vyavahâr-ârtha-mâtraṁ
kṛitaṁ॥ Atha Puliśa-Vasishṭha-Garg-âdibhir yad vivâha-yâtr-âdau saṁyak-phala-siddhy-
arthaṁ kathitaṁ tat sûkshmaṁ idânîm pravakshyê॥ Tatra shaḍ adhyardha-bhôgâni।
Viśâkhâ Punarvasu Rôhiṇy=Uttarâ-trayam। atha shaḍ ardha-bhôgâni। Âślêsh=Ârdrâ Svâtî
Bharaṇî Jyêshṭhâ Śatabhishak। êbhyaḥ śêshâṇi pañchadaś=aika-bhôgâni॥ Bhôga-pramâ-
ṇaṁ tu śaśi-madhya-bhuktiḥ 790 35। adhyardha-bhôgaḥ 1185 52½। ardha-bhôgaḥ 395
17½॥ Sarv-arksha-bhôgair ûnitânâṁ chakra-kalânâṁ yach chhêshaṁ sô=Bhijid-bhôgaḥ
254 15॥ Translation.—"This bringing out of nakshatras (i.e. the method of finding
nakshatras, with their ghaṭîs and palas) which has been made (in the preceding verses),
(is) rough, (and is only) for the practical purposes of astrologers. Now I will explain the
accurate (method) taught by [Puliśa, Vasishṭha, Garga, and other] sages, for the purpose
of securing [good] results in the case of a marriage, a journey, &c. On this point, those
who are versed in that (branch of the science) say, that six (nakshatras) have (each) a
space which is one-and-a-half (times of the average space); (viz.) Viśâkhâ, Aditibha
(Punarvasu), and the dhruvas (Rôhiṇî, Uttarâ-Phalgunî, Uttarâ-Ashâḍhâ, and Uttarâ-Bhâ-
drapadâ). And six have a half space (each); (viz.) those the lords of which are Bhôgin,
Rudra, Vâta, Antaka, and Indra, and Vâruṇa [Âślêshâ, Ârdrâ, Svâtî, Bharaṇî, Jyêshṭhâ,
(and) Śatabhishaj (Śatatârakâ)]. The remaining fifteen (nakshatras) have one space
(each). The (average) space of a nakshatra is declared to be the (daily) mean motion
of the moon [790′ 35″(=13° 10′ 35″)]. [A one-and-a-half space (is) 1185′ 52½″(=19° 45′
52½″)]. A half space (is) 395′ 17½″ (=6° 35′ 17½″)]. The space of the nakshatra Abhijit,
(which comes) next after Vaiśva (Uttarâ-Ashâḍhâ), is [the remainder, 254′ 15″ (=4° 14′
15″), of] the minutes of the whole circle, diminished by the spaces of all the (other)
nakshatras." The longitudes of the ending-points of all the nakshatras according to this
system, are given in the last column of Table IX., on page 165 above. And, as before,
¹ The system explained by Bhâskarâchârya, now given, is just the same as that in the Brahma-
Siddhânta. It seems unnecessary, therefore, to give the verses from the Siddhânta itself.

THE GUPTA INSCRIPTIONS; APPENDIX III. 167
TABLE X.
Details of two Twelve-Year Cycles of Jupiter.
Śaka-Saṁvat, expired. English Date. Longitude of Jupiter. Nakshatra. Month and Name of the Saṁvatsara.
deg. min.
1780 Adhika-Jyêshṭha śukla 10 . . . . 7th June, 1858 . . 41° 47' Rôhiṇî . . . . Kârttika
1781 Âshâḍha śukla 14 . . 13th July, 1859 . . 77 2 Punarvasu . . . Pausha
1782 Śrâvaṇa kṛishṇa 13 . 15th August, 1860 . 110 20 Âślêshâ . . . Mâgha
1783 Bhâdrapada śukla 13 . 16th September, 1861 141 38 Uttarâ-Phalgunî . Phâlguna
1784 Âśvina kṛishṇa 9 . . 17th October, 1862 . 171 55 Chitrâ . . . . Chaitra
1785 Kârttika śukla 6 . . 16th November, 1863 201 32 Viśâkha . . . Vaiśâkha
1786 Mârgaśîrsha kṛishṇa 3 . 16th December, 1864 232 3 Mûla . . . . Jyêshṭha
1787 Mâgha śukla 2 . . 18th January, 1866 . 263 48 Uttarâ-Ashâḍhâ . . Âshâḍha
1788 Mâgha kṛishṇa 4 . . 22nd February, 1867 . 298 0 Dhanishṭhâ . . Śrâvaṇa
1790 Chaitra śukla 5 . . 29th March, 1868 . . 334 3 Uttarâ-Bhâdrapadâ Bhâdrapada
1791 Adhika-Vaiśâkha kṛishṇa 10 . . . . 6th May, 1869 . . 10 27 Aśvinî . . . . Âśvina
1792 Jyêshṭha śukla 14 . . 12th June, 1870 . . 46 39 Rôhiṇî . . . . Kârttika
1793 Śrâvaṇa śukla 1 . . 18th July, 1871 . . 81 47 Punarvasu . . . Pausha
1794 Śrâvaṇa kṛishṇa 1 . . 19th August, 1872 . 114 45 Maghâ . . . . Mâgha
1795 Bhâdrapada kṛishṇa 14 20th September, 1873 145 53 Uttarâ-Phalgunî . Phâlguna
1796 Âśvina śukla 11 . . 21st October, 1874 . 175 52 Chitrâ . . . . Chaitra
1797 Kârttika kṛishṇa 8 . 20th November, 1875 205 36 Viśâkhâ . . . Vaiśâkha
1798 Pausha śukla 1 . . 16th December, 1876 235 21 Mûla . . . . Jyêshṭha
1799 Pausha śukla 15 . . 18th January, 1878 . 267 22 Uttarâ-Ashâḍhâ . Âshâḍha
1800 Phâlguna śukla 6 . . 27th February, 1879 . 302 46 Dhanishṭhâ . . Śrâvaṇa
1801 Phâlguna kṛishṇa 10 . 4th April, 1880 . . 339 0 Uttarâ-Bhâdrapadâ Bhâdrapada
1803 Vaiśâkha śukla 12 . . 11th May, 1881 . . 15 30 Bharaṇî . . . Âśvina
the entries of 3/4 and 1 1/6 in the previous sub-column, mark the spaces which differ from the
average space.
Now, the additional nakshatra Abhijit, introduced in this system, is not taken into
account among the nakshatras from which the names of the months are derived.¹ The
question, therefore, occurs,—What name is to be given to the saṁvatsara, when Jupiter
rises in Abhijit? It can be solved thus. Abhijit is considered to be composed of the
last quarter of Uttarâ-Ashâḍhâ, and the first fifteenth part of Śravaṇa. This is stated in
the following verse of Vasishṭha, as quoted in the commentary, called Pîyûshadhârâ, on
the Muhûrta-Chintâmaṇi;— Abhijid-bha-bhôgam êtad Viśvêdêv-ântya-pâdam akhilam
tat | âdya-chatasrô nâḍyô Haribhasya,— “this (is) the longitude of Abhijit; the whole
last quarter of Viśvêdêva (Uttarâ-Ashâḍhâ), (and) the first four ghaṭis (i.e. the fifteenth
part) of Haribha (Śravaṇa).” And other later authorities give the same rule. A quarter
of a nakshatra is 3 degrees, 20 minutes; and a fifteenth part is 53 minutes, 20 seconds;
and the sum of the two amounts to 4 degrees, 13 minutes, 20 seconds In other
words, Abhijit consists of nineteen parts; of which, the first fifteen come from, and
properly belong to, Uttarâ-Ashâḍhâ; and the last four come from, and properly belong to,
Śravaṇa. And the name of the saṁvatsara is to be determined as Âshâḍha or Śravaṇa,
according to the particular part of Abhijit in which Jupiter rises.
As a practical illustration of the application of the rules, I give in Table X.
above, a list, in which the dates of the heliacal risings of Jupiter are shewn for twenty-
¹ See the verse varshâṇi Kârttik-âdîni, &c., at page 162 above.

168 CORPUS INSCRIPTIONUM INDICARUM, VOL. III.
four years, from Śaka-Saṁvat 1780 to 1803 (expired);¹ with Jupiter's apparent longi-
tudes at the time, and his nakshatras determined from those longitudes. The dates
of the risings of Jupiter are taken from ordinary Pañchâṅgs in my possession, printed in
different Presses at various places. The lunar months in which the risings took place, are
all given by the Amânta southern reckoning.² The longitude of Jupiter at each rising, is
calculated from his longitude, given in the Pañchâṅgs, at some stated interval; for
instance, of seven or fifteen days. In naming the nakshatras, the Brahma-Siddhânta
system of unequal spaces, in the last column of Table IX. on page 165 above, is the one
that has been resorted to. In the last column, the months, that is, the names of the
saṁvatsaras which then began, are given. It will be seen, that Mârgaśîrsha is omitted in
each of these two cycles. Other saṁvatsaras also may be omitted, in the same way, ac-
cording to the circumstances of the particular cycle
From this Table X. it will be seen that, from one rising of Jupiter to another, the motion
of the planet amounts to from 30 to 36 degrees. By the systems of unequal spaces, some
months, and the saṁvatsaras which are named from them, have the average space of one
and a half nakshatras; that is, about 20 degrees only; they are Mârgaśîrsha, Mâgha,
Chaitra, and Jyeshṭha; and these are the saṁvatsaras that are most apt to be
omitted. For example, in Śaka-Saṁvat 1780 expired, when Jupiter rose, he was in
Rôhiṇî. The following rising took place in Punarvasu; that is, from the first rising, he
passed entirely through Mṛiga and Ârdrâ, before the next rising occurred. And, therefore,
Mârgaśîrsha was omitted. Again, by these two systems, Śrâvaṇa contains the average
space of two nakshatras; that is, about 26 degrees, 40 minutes; and, therefore, it also is
liable to be omitted. Kârttika, Pausha, Vaiśâkha, Âshâḍha, and Âśvina, contain the
average space of two and a half nakshatras each; that is, about 33 degrees; and will
but rarely be omitted. And Phâlguna and Bhâdrapada, containing not less than 40
degrees each, will never be omitted. So also, by the system of equal spaces, the nine
months that contain two nakshatras each (excluding Abhijit), are sometimes likely to be
omitted. But the remaining three, viz. Phâlguna, Bhâdrapada, and Âśvina, containing
three nakshatras each, will never be omitted.
On the other hand, sometimes it is possible that a saṁvatsara may be repeated.
By either system of unequal spaces, this may happen in respect of Kârttika, Pausha,
Phâlguna, Vaiśâkha, Âshâḍha, Bhâdrapada, and Âśvina; but, by the system of equal
spaces, only in respect of Phâlguna, Bhâdrapada, and Âśvina. And, whenever a
saṁvatsara is repeated, then two saṁvatsaras will be omitted in the same cycle; one, under
ordinary circumstances; and one, on account of the repetition.

¹ Out of these years, in Śaka-Saṁvat 1789 expired, and again in 1802 expired, no heliacal rising
took place.
² See page 148 above, note 1.

THE GUPTA INSCRIPTIONS; APPENDIX III. 169
In the preceding remarks, my object has been to explain concisely the system of the
Twelve-Year Cycle of Jupiter that is based on his heliacal risings; and the three methods
for determining the nakshatra with which the heliacal rising takes place. I have now to
make a few observations of a more general kind; and to introduce the eleven
other authorities of which I have spoken at page 162 above. Before doing so, however,
I must refer more fully to another system, which also has been incidentally mentioned, of
naming the saṁvatsaras of the Twelve-Year Cycle according to Jupiter's passage from one
sign of the zodiac into another, with reference to his mean longitude.
The rule for that which I have named the mean-sign system, is thus given by
Âryabhaṭa in his Ârya-Siddhânta or Âryabhaṭîya, Kâlakriyâpâda, verse 4,—Guru-bhagaṇâ
râśi-guṇâs tv=Âśvayuj-âdyâ Gurôr abdâḥ,—"the revolutions of Jupiter, multiplied by the
signs (twelve), (are) the years of Jupiter, the first of which is Âśvayuja." And it is given,
in very similar words, by Brahmagupta, in his Brahma-Siddhânta, adhyâya xiii. verse 42,—
Guru-varshâṇy=Âśvayujâd dvâdaśa-guṇitâ Gurôr bhagaṇâḥ. In this rule, the revolutions
(bhagaṇa) are meant to be taken from the beginning of the Kalpa, or of a Mahâyuga.
But, for practical purposes, we need not go back so far. One Twelve-Year Cycle is com-
pleted in one revolution. And, therefore, we can determine the saṁvatsara for a given
year, or for any given date in it, by taking Jupiter's signs, including the current sign, of the
current revolution, and counting from Âśvayuja. In this system, the signs are intended to
be taken, and in practice are taken, according to Jupiter's mean longitude. Now, suppose
that on a certain day Jupiter's mean longitude is 9 signs and 12 degrees; i.e. that he is in
the tenth sign. Then, counting from Âśvayuja, we have Âshâḍha, as the current saṁvatsara
for the given day.¹
The names of the saṁvatsaras of the Sixty-Year Cycle also,—according to that
which is usually called the northern system, but which is, in reality, the only truly astrono-

¹ In his treatment of the Twelve-Year Cycle (Indian Eras, p. 26 ff.), Gen. Sir A. Cun-
ningham opens the subject by quoting Kern's translation (see page 161 above, note 1) of the same
verse in the Bṛihat-Saṁhitâ which I use for the same purpose. But, for the rest, he altogether
ignores the force of the reference to Jupiter's rising, and treats the subject as if the heliacal-rising
system, described by me above, did not exist at all. What he has deduced from the verse, is only the
mean-sign system, which the verse does not really refer to at all; and in respect of which he is wrong
in making the saṁvatsaras of both the Twelve-Year and the Sixty-Year Cycle, begin and end with the
luni-solar years. The rules that he applies give, at the best, only the saṁvatsaras of the Twelve-Year
Cycle by the mean-sign system, and of the Sixty-Year Cycle, that are current at the commencement of a
given solar year; they do not provide for the essential point in both the cycles, viz. the determination
of the exact day on which a given saṁvatsara of either cycle commences—I have not had an
opportunity of seeing the writings of Davis and Warren on this subject. But, with all due deference,
I may safely say that the Twelve-Year Cycle by the heliacal-rising system, has hitherto remained
quite unknown to European scholars.—I would take this opportunity of remarking that I can find no
authority for the introduction, in Kern's translation, of the bracketed words "(during which Jupiter
completes a twelfth part of his revolution)." Jupiter completes a twelfth part (râśi) of his revolution
in about three hundred and sixty-one days; while the interval between two of his heliacal risings is
about four hundred days.
A b

mical system of it, and was current, as is shewn by many epigraphical quotations of it,
in Southern India also,—are determined by Jupiter's mean place. And the rule is thus
given in the Sûrya-Siddhânta, i. 55,—dvâdaśa-ghnâ Gurôr yâta-bhagaṇâ vartamânakaiḥ ।
râśibhiḥ sahitâḥ śuddhâḥ shashṭyâ syur Vijay-âdayaḥ ॥,—" the expired revolutions of Jupi-
ter, multiplied by twelve, (then) increased by the current signs (of the current revolution),
(and then) divided by sixty, are (i.e. the remainder is) (the saṁvatsaras counted from)
Vijaya as the first." In fact, the Sixty-Year Cycle, and the Twelve-Year Cycle of the
mean-sign system, are quite identical with regard to the day of the commencement of each
saṁvatsara; and, consequently, with regard also to its duration, which, according to
Jupiter's mear motion as given in the Sûrya-Siddhânta, is 361 days, 1 ghaṭî, 36 palas.
The Twelve-Year Cycle of the mean-sign system, therefore, with regard to its other details,
may be most properly described with the Sixty-Year Cycle, which I shall treat of fully on a
separate occasion. And I have introduced the present brief mention of it, only because
references to it are unavoidable in the following observations.
The eleven authorities for the heliacal-rising system, in addition to the Bṛihat-
Saṁhitâ, of which I have spoken, are as follows;—(1) Parâśara says—Kṛittikâ-
Rôhiṇîsh=ûditê kshuch-chhastr-âgni-vṛishṭi-vyâdhi-prâbalyaṁ ..... Chitrâ-Svâtyôr uditê
nṛipa-sasya-varsha-kshêm-ârôgya-karaḥ.—(2) Garga says—pravâs-ântê sah=arkshêṇa
hy=uditô yuga-pach charêt । tasmât kâlâd ṛiksha-pûrvô Gurôr abdaḥ pravartatê ॥—(3)
Kaśyapa says—saṁvatsara-yugê ch=aiva shashṭy-abdê¹-ṅgirasas sutaḥ । yan-nakshatr-
ôdayaṁ kuryât tat-saṁjñaṁ vatsaraṁ viduḥ ॥—(4) Ṛishiputra says—yasmin tishṭhati
nakshatrê saha yêna pravardhatê । saṁvatsaras sa vijñêyas tan-nakshatr-âbhidhânakaḥ
॥— (5) Also, in the following, Ṛishiputra quotes Vasishṭha and Atri, in addition to
Parâśara, who is separately referred to above,—Tishy-âdika-yugaṁ prâhur Vasishṭh-Âtri-
Parâśarâḥ । Bṛihaspatês tu Saumy-ântaṁ sadâ dvâdaśa-vârshikaṁ ॥ Udêti yasmin mâsê
tu pravâs-ôpagatô=ṅgirâḥ । tasmât saṁvatsaraḥ.—(6) In the Samâsa-Saṁhitâ, a
short work by Varâhamihira, we have²—Gurur udayati nakshatrê yasmin tat-saṁjñitâni
varshâṇi.—(7) Bṛihaspati, as quoted in the Kiraṇâvalî, a commentary by Dâdâbhâî
on the Sûrya-Siddhânta, says—yadâ Gur-ûdayô bhânôr Gurôr abdas tad-âditaḥ.—
(8) In the Nârada-Saṁhitâ, Guruchârâdhyâya, we have—yad-dhishṇy-âbhı uditô Jîvas
tannakshatr-âhva-vatsaraḥ.—(9) In the Muhûrta-Tattva, Guruchâra, verse 7, we have—
dvy-ṛikshô=Gnêḥ Kârttikât try-ṛiksha ishu-ravi-Śivô=bdaḥ sa yên=ôdit=Êjyaḥ.—(10)
In the Jyôtishadarpaṇa, adhyâya v., we have — yasminn abhyuditô Jîvas tan-

¹ From this, it appears that the saṁvatsaras of the Sixty-Year Cycle also, were originally determin-
ed by the heliacal risings of the planet. And corroboration of this is afforded by a verse of Varâhamihira,
quoted further on. The above verse of Kaśyapa, evidently applies to the Twelve-Year Cycle also.
² I have taken this, and the preceding five quotations, from Utpala's commentary on the
Bṛihat-Saṁhitâ.

THE GUPTA INSCRIPTIONS: APPENDIX III. 171
nakshatrasya vatsaraḥ. — It is unnecessary to translate these ten quotations; as the
general purport of all of them is the same; viz. that "a saṁvatsara is to be named
after that nakshatra in which Jupiter attains his rising."—(11) In the remaining au-
thority, the Sûrya-Siddhânta, the rule appears to be a little different from that
of all the other authorities; though the general features are the same. And, for
this reason, though the work is one of the earliest, I have quoted it last. The rule
is given in the verse—Vaiśâkh-âdishu kṛishṇê cha yôgaḥ pañchadaśê tithau l Kârttik-
âdîni varshâṇi Gurôr ast-ôdayât tathâ ll,—"and the years Kârttika and others (that
follow) (are to be named) from the rising, after setting, of Jupiter,¹ according to the occur-
rence (of Kṛittikâ and other nakshatras)² on the fifteenth tithi in the dark fortnight of
Vaiśâkha and other (months that follow)." The application of this rule seems to be
thus:—The years are to be named, according as Kṛittikâ and other nakshatras,—
evidently those in which the sun and the moon stand,—occur on the amâvâsyâ of Vaiśâ-
kha and others, immediately preceding or following³ the day on which Jupiter rises;
that is, on whatever day Jupiter may rise, the nakshatra on either the preceding, or
the following, amâvâsyâ, gives the name to the saṁvatsara. This rule seems to have
been alluded to, though not in the name of the Sûrya-Siddhânta, by Utpala; but it is
rejected by him. It may possibly have been occasionally in use; but it certainly does not
apply to the Gupta records.
Now, all these quotations distinctly refer, in some form or another, to the rising of
Jupiter; which it is impossible to understand as meaning anything but his heliacal-
rising. And, if the rising referred to is the heliacal-rising, then no astronomer can deny
that, in the period of about twelve solar years, there are only eleven conjunctions of Jupiter
¹ I should remark that Raṅganâtha, one of the best commentators on the Sûrya-Siddhânta,
explains this verse with the understanding, into which he seems to have been led by Utpala's com-
ments on the Bṛihat-Saṁhitâ, viii. 1, that ast-ôdayât means "from the setting or rising." He adds,
however, — idânîm udaya-varsha-vyavahârô gaṇakair gaṇyatê,—"at the present time, the practice
of (naming) the year by the rising, is taken into account by astronomers." For the sake of consist-
ency, it is justifiable to translate the expression ast-ôdayât as I have translated it above; and the
use of the compounded base in the singular, supports that translation. I also find that Dâdâbhâî,
in his commentary on the Sûrya-Siddhânta, explains it in the same way; his words being —
tath=âstâd udaya-kâlê Gurôs tad-yukta-nakshatra-saṁjñô Gurôr abdô jñêyaḥ,—"so the year of
Jupiter is to be known as having the appellation of that nakshatra with which he is joined at the
time of (his) rising after setting."—[There can be no doubt that ast-ôdayât is used here in the sense
of "from the rising after setting;" compare such compounds as supt-ôtthita, 'having arisen from
sleep;' lit. 'having slept and then having risen.'—J. F. F.]
² These words, in connection with yôgaḥ, have to be supplied from the preceding verse, in which
the result exhibited in Table VIII. page 163 above, is given.
³ Which of the two, cannot be determined from the context: and I can find no commentator
who has explained the point properly. I myself think that the following amâvâsyâ is intended. But
seems that Utpala, in his allusion to this rule, takes the preceding amâvâsyâ.

• 2b

172 CORPUS INSCRIPTIONUM INDICARUM, VOL. III.
and the sun, and consequently eleven heliacal risings of the planet. And, this fact being
established, the interval of about four hundred days between two successive risings, —the
same period, for the duration of each saṁvatsara,—the omission of one saṁvatsara in
each cycle of twelve years,—and all the other points described by me,—follow of necessity
It will, doubtless, have been noticed that I have not been able to give any quotations
from the first Âryabhaṭa (born A.D. 476) or Brahmagupta (born A.D. 598), in support
of the heliacal-rising system. And it might be sought to base some argument against
its existence, on the grounds that these two early authorities, who moreover may be said to
be the originators of two of the three schools of astronomers in India, are silent about it,
though they do give the mean-sign system. But the facts only prove the early existence
and use of the mean-sign system; which I do not seek to deny. They do not prove, either
that the heliacal-rising system did not exist; or that, having existed, it had gone out of use
in their time. To take another instance, Âryabhaṭa and Brahmagupta give no rule for
finding the saṁvatsaras of the Sixty-Year Cycle; but, to say that this cycle was not
known to either of them, would hardly be sensible. The mean-sign system for the
Twelve-Year Cycle is undoubtedly early. But the heliacal-rising system is earlier still.
Among the authorities quoted above, the Sûrya-Siddhânta¹ is as early a work as the
Âryabhaṭîya, if not earlier. And, that Parâśara, Garga, and Kaśyapa, are earlier than
Âryabhaṭa, cannot be denied. Utpala quotes a verse of Garga, which, with some proposed
emendations, I give as it stands in my manuscript copy,—êvam Âśvayujaṁ ch=aiva Chaitraṁ
ch=aiva Bṛihaspatiḥ | saṁvatsarô(?raṁ) nâma(?śa)yatê saptaitêda (? saptaty-abda)-śatê=
dhikê ||.² This verse seems to refer to the mean-sign system; though I can say nothing
definitely about it, without seeing the context; of which I have not the opportunity at
present. But, supposing that it does refer to the mean-sign system, still it is not un-
favourable to the heliacal-rising system; for the same Utpala also quotes a verse of the
same Garga, given at page 170 above, in which Garga says—"when Jupiter, after dwelling
together (with the sun),³ rises and walks along with a nakshatra, then commences the year
of Jupiter, of which the first part (of the name) is the (name of that) nakshatra."
Not only that the heliacal-rising system is very early, but that it alone is the
original system of the Twelve-Year Cycle, is self-evident. The heliacal rising of Jupiter
is a natural phenomenon. No scientific apparatus is needed for the observation of it; nor are
¹ To say that the Sûrya-Siddhânta is a work of Varâhamihira, is simply a mistake. I cannot
enter iuto this point at present; but would refer any who hold that view, to Varâhamihira's Pañcha-
Siddhântikâ, and to Kern's Preface to his edition of the Bṛihat-Saṁhitâ.
² [Gen. Cunningham also has quoted this verse (Archæol. Surv. Ind. Vol. X. p. 114); and in
such a way, his authority giving nâśyatê, where Mr. Sh. B. Dikshit's MS. gives nâmayatê, as to shew
that, in the second half of it, we certainly have to read nâśayatê saptaty-abda-śatê.—J. F. F.]
³ pravâsantê may be translated by "after having completed his journey;" i.e. having completed
a revolution of some kind or another.

THE GUPTA INSCRIPTIONS ; APPENDIX III. 173
any calculations required.¹ But such is not the case with the passing of Jupiter from one
sign of the zodiac into another. No kind of apparatus can determine Jupiter’s mean longitude.
It is to be found only by calculations, the rules for which must have been established
after observations carried on during a very long time ; to lay down the means of determining
Jupiter's mean yearly or daily motion, is not a thing that can be accomplished in a few
years. It seems, therefore, quite evident that the system of naming the saṁvatsaras after
the nakshatras in which Jupiter rises, i.e. the heliacal-rising system, is the only origi-
nal one.
So much, as regards the antiquity of the heliacal-rising system. Let us now look into its
somewhat later use. Varâhamihira is later than Âryabhaṭa. And his verse with which
I have opened my account of the Twelve-Year Cycle, undoubtedly refers to this system.
So, also, another of his verses, in the Brihat-Saṁhitâ, viii. 27, points to the same thing.
It runs—âdyaṁ Dhanishṭhâṁ samabhiprapannô² Mâghê yad=âyâty=udayaṁ Surêjyaḥ |
¹ The phenomenon, moreover, is one to which much attention has always been paid in India.
Even in the present day, almost all the Hindu Pañchâṅgs give the dates of the heliacal rising and
setting of Jupiter. This is for religious purposes ; since, when Jupiter is invisible, some duties and
ceremonies, such as investiture with the sacred thread, marriage, pilgrimages, &c., are not to be per-
formed ; and the dates in question are necessary, in order to know when he is visible, and when he
ceases to be so. In Pañchâṅgs printed in Mahârâshṭra, the custom of naming the saṁvatsaras after
the months is not in use ; in fact, the Twelve-Year Cycle is now almost unknown to the people at
large of the Dekkan. But in a Pañchâṅg prepared by Jwâlâpati Siddhânti, and printed in the
Jñânasûryôdaya Press at Madras, I find that the author, in the saṁvatsara-phala, after giving the two
saṁvatsaras of the Sixty-Year Cycle, according to the northern and the southern reckoning, goes on
to say—sarvatra Gur-udaya-vaśât (Chaitr)-âbdô grâhyaḥ,—" all over (India) a (certain) year (i.e.
such saṁvatsaras as Chaitra, &c.), which depends on the rising of Jupiter, is to be taken ;" from
which it is evident that some such rising-system, as that described above, is followed in this Pañchâṅg
from Madras. Also, in the Chaṇḍu-Pañchâṅg, prepared for the meridian of Jôdhpur in Mârwâḍ, and
used there and by Mârwâḍîs in other parts of India, the saṁvatsaras are named as Chaitra-Varsha,
Vaiśâkha-Varsha, &c. ; the system adopted in that Pañchâṅg, however, for naming the saṁvatsaras,
is the mean-sign system.
² The reading that I give, is from my manuscript copy. But, s and ś being very liable to confu-
sion, the reading âdyaṁ Dhanishṭh-âṁśam abhiprapannô, which is given in some printed copies, may
also be of some authority. By calculation, however, I find that Jupiter does not always stand just at
the beginning of Dhanishṭhâ, at the time of his rising at the commencement of the Prabhava saṁvat-
sara. And I think, therefore, that the reading which I give, is the author's original reading. I take
âdyaṁ to qualify the word nakshatram understood. And Varâhamihira calls the nakshatra in ques-
tion "the first," because his opinion was, I think, that Dhanishṭhâ was the first nakshatra of the
Sixty-Year Cycle, as it was of the Five-Year Cycle of the Vêdâṅga-Jyautisha [see its verse—svar
âkramêtê sôm-ârkau yadâ sâkaṁ sa-Vâsavau syât tad=âdi-yugaṁ Mâghaḥ,—" when the moon and
the sun, being in (the nakshatra) Vâsava (Dhanishṭhâ), go together in the heavens, then there is the
beginning of the Yuga (and of the month) Mâgha"], which two he intends to reconcile.—[Kern would
seem to have known only the reading âdyaṁ Dhanishṭh-âṁśam. His translation (Jour. R. As. Soc.
N. S. Vol. V. p. 49 f.), which follows also the reading of pravartatê for prapadyatê, is—" when Jupi-
ter, on reaching the first quarter of Dhanishṭhâ, rises in the lunar month of Mâgha, then begins the
first year of the cycle of sixty, named Prabhava, a year salutary to all beings." And he adds the

174 CORPUS INSCRIPTIONUM INDICARUM, VOL. III.
shashṭy-abda-pûrvaḥ Prabhavaḥ sa namnâ prapadyatê bhûta-hitas tad=âbdaḥ ||.—
“when Jupiter, having come to the first (nakshatra) Dhanishṭhâ, attains (his) rising in
(the month) Mâgha, then commences that year, beneficial to beings, which is named
Prabhava, the first of the sixty years.” Now, in eighteen centuries from the beginning
of the Śaka era, the Prabhava saṁvatsara has occurred thirty times. And, by approxi-
mate calculations, I find that Varâhamihira’s assertion, though not quite correct, is
nearly so by the heliacal-rising system. Out of the thirty occasions, Jupiter rose, accord-
ing to the Amânta southern arrangement of the fortnights,¹ twenty-six times in the month
of Mâgha ; three times early in Phâlguna ; and once in Pausha, nearly at the end of
it. And, on many occasions he rose in the Dhanishṭhâ nakshatra ; and on some, in
Śravaṇa. The assertion, however, is not correct for the mean-sign system. According
to that system, at the commencement of the Prabhava saṁvatsara, which always begins
when Jupiter, by his mean longitude, enters Kumbha or Aquarius, he evidently always
stands in the middle of Dhanishṭhâ.² But the Prabhava saṁvatsara may begin, and
as a matter of fact I find by calculation that it has begun, in any of the twelve months ;
as will be shewn when I treat of the Sixty-Year Cycle. It is evident, therefore, that the
verse in question supports the heliacal-rising system. Moreover, the word udaya itself is
used in it. It might be argued that Varâhamihira’s rule (Bṛihat-Saṁhitâ, viii. 22 ;
êk-aikam abdêshu nav-âhatêshu, &c.) for finding the nakshatra of Jupiter, has reference
to his mean longitude ; and, consequently, that it gives the mean-sign system. But it
is absurd to suppose that so learned an astronomer as he, stating the rule that a saṁvatsara
is to be named from the nakshatra in which Jupiter rises, did not know that the nak-
shatra, at the time of his rising, can be determined only from his apparent longitude.
The reason why he gives a rule for finding the mean longitude only, is, in my opinion,
this : — Anyone conversant with Hindu mathematical astronomy, knows how tedious a
task it is to find the mean longitude of a planet from the ahargaṇa, or number of elapsed
days, counted from the beginning of the Kalpa or of a Yuga. But, when once it has been
found, it is much less tedious to calculate, from it, the apparent longitude by the general
rules. So, Varâhamihira, I think, gives a simple rule for finding the mean longitude of
Jupiter on a given day, and leaves to the astronomer the calculation of the apparent longi-
tude. Or, it may also be said, as the difference between the mean and the apparent
longitudes of Jupiter, on the day of his heliacal-rising, is not very much,—sometimes about
five degrees, and sometimes nearly nil, as I have found from several calculations,—
Varâhamihira gives the simple rule for rough practical purposes only ; leaving it to the
note—“cf. Davis, Asiatic Researches, Vol. III. p. 220. The word aṁśa also means ‘degree,’ but is
here rendered by ‘quarter,’ according to Utpala, who explains it by pâda.”—[J. F. F.]
¹ See page 148 above, note 1.
² The sign Kumbha commences in the middle of Dhanishṭhâ, and ends at the end of the third
quarter of Pûrvâ-Bhâdrapadâ.