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
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