THE EQUALIZATION OF EPOCHS
A considerable importance attaches to the proper understanding of
Epochs, so that when a statement is made in terms of one Epoch we should
be able to refer it at once to another with which we are familiar. There
are several astronomical Epochs of this nature which are frequently used
and ought to be known. Those who are interested in tracing the astral
cause of events often find themselves debarred from research through
ignorance regarding the data employed. Much of this trouble can be
overcome by the determination and equalization of Epochs.
Ptolemy, to whom we are indebted for a great number of scientific
statements in addition to his astronomical observations and those of
Hipparchus which he has preserved to us, makes use of two important
Epochs. The first is that of Nabonasser. The first year of his reign was
in the year 747 B.C., and the month Thoth began on the 26th February in
that year. Hence Nab. 1, Thoth 1 constitutes an Epoch equivalent to Feb.
26, 747 B.C. But this latter is the secular date and the astronomical is
one less, namely, 746 B.C. The reason for this is that the secular date
A.D. 1 passes directly to the year 1 B.C., when counting backwards,
whereas the astronomical account makes A.D. 1 refer back to A.D. 0, and
then to 1 B.C. Hence all dates _before_ the Christian Era are given in
secular accounts as one year more than the astronomical. Now as to the
Egyptian months used by Ptolemy. These were—
1. Thoth February.
2. Paophi March.
3. Athyr April.
4. Choiac May.
5. Tybi June.
6. Mechir July.
7. Phamenoth August.
8. Pharmuthi September.
9. Pachon October.
10. Payni November.
11. Epiphi December.
12. Mesori January.
Each month contained thirty days, and there were five days at the end of
the year which they called the Epagomene. The year began at noon on the
first of Thoth.
Another Epoch used by Ptolemy, and frequently referred to by the Greeks,
is that of Calippus. The Calippic Period was invented by the man whose
name it bears and dates to the year 330 B.C. It is a period of 76 years,
which is four times 19, and was designed to bring the new and full moons
to the same date of the solar year.
The Olympiads were in use among the Greeks, and began in the year 776
B.C., on the 1st July (O.S.). Each Olympiad consists of four years, and
in marking a date the number of the Olympiad and the year of that
Olympiad are given. Thus the first of Calippus would fall in the third
year of the 112th Olympiad. The astronomical years equivalent to these
are, for the Olympiads 775 B.C., and for the Calippic Period 329 B.C.
The Kali Yuga is an Indian Epoch which began at the New Moon of February
3102 B.C.—Feb. 5th. The Epoch of Salivahana in use among the Dravidians
of India is the year A.D. 78.
The Chinese Cycle of years began in the year 2696 B.C. (astronomical),
at the New Moon of February, the Sun being then half-way between the
Solstice and the Equinox.
But even when we have the Epochs equalized there are difficulties
depending from this determination of Epoch. This is particularly the
case with the Indian calendarics. They have in India a solar year
divided into solar months, and a lunar year which is divided into lunar
months. Thus the first of Mesham is that point of time when the Sun
enters the first point of the constellation Mesham. This is about the
12th April. But the first of As’wini is the day of New Moon in the
constellation As’wini, and this, of course, is a variable date,
depending on the position of the New Moon in relation to the first point
of Mesham.
But whatever may be the date given in terms of the Indian Calendar,
before we can apply it we have to know in what relations our zodiac
stand to theirs. They have a fixed point from which they make their
calculations. This is _Zeta Piscium_, which marks the beginning of the
constellations, and it corresponds with the first of Mesham, or the
Sun’s ingress to the constellation Aries. We, on the other hand, count
from the Vernal Equinox, the point at which the Sun crosses the Equator
in the spring. This point, in relation to the fixed constellations, is
continually shifting westward at the rate of about 50´´ per year, and
this is what is known as the precession of the Equinoxes.
The point we have to make is the relation of the Equinox to the first
point of Mesham. The difference is what is called Ayanámsha. The
difficulty in the matter of calculation has been—(_a_) the exact rate of
precession during past centuries, which has only been determined in
comparatively recent years, and (_b_) the unsatisfactory condition of
Indian astronomical data. But these latter, with the advance of more
exact methods in modern centres of Indian learning, have been
considerably improved, and it is now justifiably possible to attempt an
equalization of the two astronomical Epochs.
Very much depends on this, for it is quite impossible to study the
Indian astrological literature without being able to refer their
quantities to terms of our modern Western ephemerides or astronomical
tables. When, for instance, the Indian books say that a certain yoga or
conjunctions of planets in Kumbha means a particular thing, or has a
particular signification, they mean the constellation Aquarius, and it
will depend on the relations of this constellation to our corresponding
sign Aquarius, as to what we are to understand. Also in the
determination of the various periods depending on the Moon’s longitude
at an Epoch, such as that of birth, we have to convert the Moon’s
longitude into terms of our zodiac before we can apply their
interpretations, or synchronize the periods with our own calendar. I
have therefore agitated for a long time past for a thorough examination
of the matter, and in despair of collaboration in other directions I
applied to Dr. V. V. Ramanan of Madras, one of the most distinguished
pandits of Southern India, and found in him a most useful and able
exponent of ancient Indian learning.
The first attempt at a determination of the Epoch or point of time when
the Equinox coincided with the first point of Mesham was from a
comparison of the length of the solar year as given in the
_Suryasiddhanta_ and the value given in the best European works. It is
seen that the Indian year is longer than the European estimate by 3 min.
20·4 sec.
Now it is said that the Sun entered the sign Mesham in the year 1900 at
30 ghatikas 50 vighatikas after sunrise at Ujjain, on the 12th April.
This equals 12th April, at 1 hr. 31 min. 28 sec. p.m., Greenwich mean
time. The Sun’s longitude was then 22° 11´ 4´´ from the Vernal Equinox,
and this divided by the mean rate of precession yields 1594 years, which
taken from 1900 gives A.D. 306 as the Epoch. Let us check this result.
We have seen that the Indian year is estimated at 3 min. 20·4 sec. more
than the European. If then we multiply this amount by 1594, the number
of years since the Epoch, we shall have 3 days 16 hrs. 45 min. 37·6 sec.
as the total increment. The Sun in this time moves at a mean rate 3° 38´
43´´, and as this amount represents the excess of the Indian solar year
over the European during 1594 years, we should take it from 22° 11´ 4´´
in order to obtain the true difference in longitude between the Vernal
Equinox and Mesham 0° in the year 1900. This leaves 18° 33´ 21´´, which,
being divided by the mean rate of precession 50·1´´, gives 1335 years.
Allowing for the difference of the Sun’s anomaly and the consequent
increase of longitude, we should make the longitude 19° 4´ 7´´ and the
Epoch 1372 years, which would give the year A.D. 528, as compared with
A.D. 306 by the former calculation.
This clearly shows that there is some miscalculation in the Ujjain
estimate of the Sun’s ingress, and I am confirmed in this by a note from
Dr. Ramanan in which he says that “According to Bhaskaracharya in his
_Graha-ganitádhyáya_, the Vernal Equinox of Kali Yuga 3628 (A.D. 527),
coincided with the starting-point of the Hindu ecliptic.” He adds that
“the so-called fixed Indian Zodiac is not thought to be really fixed,
but is subject to a slow motion of about 8´´ per year eastwards. The
zero point of Indian longitude is thus subject to a slight annual
displacement, and this motion is a practical postulate of Hindu
Siddhántas.”
But so far we have based all our calculations on estimates made from the
Hindu Siddhánta and not from modern observations. Necessarily correct
evaluations made from the same source would work out to the same
figures, and it is therefore important that we should again check the
results by reference to modern sources.
In the Panchángam for Kumbakonam 1912 it is stated that the Sun enters
Vrishabham (constellation Taurus) on 13th May at 36 gh. 5 vigh. after
sunrise.
Sunrise at Kumbakonam, Lat. 11° North, on this date—
Tan. log. of 11 degs. 9·28865 For lat. 51° 30´ 0·09939
Sun’s decl. 6 a.m., 18.18 9·51946 9·51946
———————— ———————
Sine log., 3° 41´ 18·80811 Sine log., 24° 34´ 9·61885
less 3° 41´
———————
20° 53´
4
—————————
83m. 32s.—1h. 23m. 32s.
This represents the difference of sunrise due to latitude. That is to
say, a place in 11° North latitude, and on the same meridian as
Greenwich, would have its sunrise 1 hr. 24 min. later than Greenwich on
the 13th May, 1912. Now the sunrise on this date at Greenwich was at 4
hrs. 13 min. a.m., and therefore at Kumbakonam the sunrise would be at 5
hrs. 37 min. a.m.
The longitude of Kumbakonam is 5 hrs. 18 min. east of Greenwich, and the
equivalent Greenwich time of sunrise at Kumbakonam will be G.M.T., 0 hr.
19 min. a.m.
The Sun’s longitude at this time according to the Greenwich ephemeris is
1s. 21° 51´ 57´´, which we may call Taurus 21° 52´. This, therefore,
represents the Indian estimate of the present value of Ayanámsha.
The mean rate of Equinoctial Precession for the past eighteen centuries
being 50·1´´ per year, we must divide 21° 52´ by this amount of
precession to obtain the year of coincidence. The result is 1571 years,
which, being taken from the present year 1912, gives the year A.D. 341
as that in which the two zodiacs coincided. But by taking the actual
precession for 1912 and the increment for _t_ years where _t_ equals
1571 - 62, or 1509 years, we have the actual precession as equal to 50´´
per year nearly, and 21° 52´ divided by 50´´ is 1574, the years to be
taken from 1912, which gives the year A.D. 338. According to our
estimate of the rate of precession, therefore, the Epoch will vary
between A.D. 338 and 341. In round numbers, therefore, we may regard the
year A.D. 340 as that of the coincidence of the zodiacs, and the number
of years since elapsed multiplied by the mean rate of 50·1´´ will give
the increment known as Ayanámsha for any date since the Epoch.
But I find an entry in the Ephemeris of Kumbakonam to this effect.
“Mean amount of precession at commencement of K.Y. 5014 (A.D. 1912), 22°
27´ 20´´. Rate of precession, 50·26´´.”
Now if we divide the above amount of precession by the rate we shall get
1612 years, which would give the Epoch A.D. 300, whereas, as we have
seen, other data in the Ephemeris lead us to the year A.D. 340. Now I
have checked the Kumbakonam Ephemeris, and find that so far as the Solar
ingresses are concerned they agree with the Nautical Almanac, and there
would therefore appear to be no reasonable doubt that if the true amount
of precession is here given, the true Epoch for the coincidence of the
zodiacs has been found. But I am advised by Dr. V. V. Ramanan that there
is an increment not generally recognized by either the Indian or
European astronomers, but which is nevertheless an essential part of the
calculation. It is that of the progression of the asterisms or
constellations from west to east, along the order of the signs at the
rate of 8´´ per year, to which I have already referred in an extract
from one of his valuable letters. If, therefore, we add this 8´´ to the
annual precession 50·1´´, we shall have 58·1´´ as the total precession
of the Equinoxes on the first point of As’wini, and then if we further
divide the amount of precession for the year 1912 as given in the
Panchángam, namely, 22° 27´ 20´´ by 58·1´´, we shall get 1390 years,
which taken from 1912 yields the year of coincidence A.D. 521.
From various sources, therefore, we have the years A.D. 300, 306, 338,
527, 528 and 521. The former dates take account only of the precession
of the Equinoxes on a fixed zodiac, whereas the latter take into account
also a direct motion of this so-called “fixed” zodiac which amounts to
8´´ per year, and which has to be applied to the precession. It is
further to be observed that the Epochs 338 and 306, variously derived
above, are unified by the adoption of 58·1´´ as the total annual
precession of the Equinoxes on the first point of As’wini. It needs but
quotation of authority for this increment of 8´´ in order to establish
the date of zodiacal coincidence beyond disputation, at all events
within the limits of a very few years.
The above questions have an historical interest. Varahamihira, who
mentions the coincidence of the solstices with the cardinal
constellations Makaram and Katakam as having taken place in his day, has
not been finally placed by the chronologists. Astronomical notes made by
him have chiefly been used for this purpose, and the writing of his book
the _Brihat-samhita_, in which the above note occurs, is on these
grounds fixed at A.D. 505.
But then we have to remember that Mihira speaks only in general terms
when he refers to the coincidence of the zodiacs. He had no instruments
which would have enabled him to make a close observation, but he could
make certain approximations from the meridian transit of some of the
chief stars in the constellations. We have no reason, therefore, to
expect more than an approximate agreement of the date of Mihira with
that of the true coincidence of the zodiacs. The _Graha Laghava_, which
is in general use in India, gives this latter as A.D. 522 or 444 Shaka.
The Shaka Epoch is known to be A.D. 78. Dr. V. V. Ramanan gives reasons
for accepting the year A.D. 525. In the present state of the controversy
I see no reason against this Epoch.