CHAPTERXXIITHE 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 747B.C., and the month Thoth began on the 26th February in that year. Hence Nab. 1, Thoth 1 constitutes an Epoch equivalent toFeb.26, 747B.C.But this latter is the secular date and the astronomical is one less, namely, 746B.C.The reason for this is that the secular dateA.D.1 passesdirectly to the year 1B.C., when counting backwards, whereas the astronomical account makesA.D.1 refer back toA.D.0, and then to 1B.C.Hence all datesbeforethe 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—
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 330B.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 776B.C., on the1stJuly (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 the112thOlympiad.The astronomical years equivalent to these are, for the Olympiads 775B.C., and for the Calippic Period 329B.C.
The Kali Yuga is an Indian Epoch which began at the New Moon of February 3102B.C.—Feb.5th. The Epoch of Salivahana in use among the Dravidians of India is the yearA.D.78.
The Chinese Cycle of years began in the year 2696B.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 the12thApril. 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 isZeta 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, suchas 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 theSuryasiddhantaand the value given in the best European works. It is seen that the Indian year is longer than the European estimate by 3min.20·4sec.
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 the12thApril. This equals12thApril, at 1hr.31min.28sec.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 givesA.D.306 as the Epoch. Let us check this result.
We have seen that the Indian year is estimated at 3min.20·4sec.more than the European. If then we multiply this amount by 1594, the number of years since the Epoch, we shall have 3 days 16hrs.45min.37·6sec.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 yearA.D.528, as compared withA.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 hisGraha-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) on13thMay 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´ 0·09939Sun’s decl. 6 a.m., 18.18 9·51946 9·51946———————— ———————Sine log., 3° 41´ 18·80811 Sine log., 24° 34´ 9·61885less 3° 41´———————20° 53´4—————————83m. 32s.—1h. 23m. 32s.
Sunrise at Kumbakonam, Lat. 11° North, on this date—Tan. log. of 11 degs. 9·28865 For lat. 51° 30´ 0·09939Sun’s decl. 6 a.m., 18.18 9·51946 9·51946———————— ———————Sine log., 3° 41´ 18·80811 Sine log., 24° 34´ 9·61885less 3° 41´———————20° 53´4—————————83m. 32s.—1h. 23m. 32s.
Sunrise at Kumbakonam, Lat. 11° North, on this date—Tan. log. of 11 degs. 9·28865 For lat. 51° 30´ 0·09939Sun’s decl. 6 a.m., 18.18 9·51946 9·51946———————— ———————Sine log., 3° 41´ 18·80811 Sine log., 24° 34´ 9·61885less 3° 41´———————20° 53´4—————————83m. 32s.—1h. 23m. 32s.
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 1hr.24min.later than Greenwich on the13thMay, 1912. Now the sunrise on this date at Greenwich was at 4hrs.13min.a.m., and therefore at Kumbakonam the sunrise would be at 5hrs.37min.a.m.
The longitude of Kumbakonam is 5hrs.18min.east of Greenwich, and the equivalent Greenwich time of sunrise at Kumbakonam will beG.M.T., 0hr.19min.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 toobtain the year of coincidence. The result is 1571 years, which, being taken from the present year 1912, gives the yearA.D.341 as that in which the two zodiacs coincided. But by taking the actual precession for 1912 and the increment fortyears wheretequals 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 yearA.D.338. According to our estimate of the rate of precession, therefore, the Epoch will vary betweenA.D.338 and 341. In round numbers, therefore, we may regard the yearA.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 ofK.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 EpochA.D.300, whereas, as we have seen, other data in the Ephemeris lead us to the yearA.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 thecoincidence 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 coincidenceA.D.521.
From various sources, therefore, we have the yearsA.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 theBrihat-samhita, in which the above note occurs, is on these grounds fixed atA.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. TheGraha Laghava, which is in general use in India, gives this latter asA.D.522 or 444 Shaka.
The Shaka Epoch is known to beA.D.78. Dr.V. V.Ramanan gives reasons for accepting the yearA.D.525. In the present state of the controversy I see no reason against this Epoch.