________________
June, 1888.]
JACOBIS TABLES FOR HINDU DATES.
159
Instead of starting from this epoch and add. PART IV.-THE CONSTRUOTION OF
ing the increase of these quantities for the time TABLES 5 to 11.
elapsed between the epoch and the given date, As stated above, my Tables are those of M.
as would be more in accordance with the practice Largetean, adapted to the doctrines and elements
of the Hindus, we start from the 1st January of Hindu astronomy, especially those of the
of the corresponding year of the 19th century, Súrya-Siddhanta. The inaccuracy of the
for the hundred years of which the value of elements of Hindu astronomy becomes percep
a. b. c. had to be calculated. Suppose the cortible in calculations for long intervals of
rect value of a. b. c, for the corresponding year time; but, if the interval of time is only a
to be known, the same for the given year can be few years, the result of the Hindu calculation
found, by subtracting the increase of a. b. c. for may be considered correct for all practical
the complete elapsed centuries. But to conpurposes. Therefore Table 7, which gives the
vert the subtractive increase into an additive increase of a. b. c. for the 366 days of the year,
quantity, we subtract the increase from 1, and could be adopted from the original Tables,
add the remaind er. This remainder is entered
in Table 6 as a. b. c. In the way thus explained, without any change beyond omitting two
the a. b. c. for the 1st January of any year columns not wanted, and adding one, w., for
can be found. finding the weekday. But Tables 5 and 6 had
For any other date, we
add to the a. b. c. for the 1st January the to be entirely recalculated. I shall explain how this was effected, in order to show that my
increase up to the given day as registered in
Table 7. Tables must yield correct results.
According to the rules just laid down, we The epoch of Hindu astronomy is the begin.
will now calculate the a. b. c. for the beginning ning of the Kaliyuga ; according to the Súrya
of the Kaliyuge, the amount of which quanSiddhanta, at midnight, at Lanka, of the 17th.
tities has been specified above according to the 18th February, Old Style, B.C. 3102. As the
Súrya-Siddhanta. civil day is usually reckoned to begin with
The corresponding year of B.C. 3102 (besunrise at Lanka, the beginning of the Kali
ginning of the Kaliyaga) is A.D. 1899, the yuga according to the Súrya-Siddhanta may be
interval being 5000 years. Adding to the a.of stated as B.C. 3102, 17th February, Old Style,
Kaliyuga 0, the increase of a. in 5000 Julian 18 hours, Lanka time. (According to the Arya
years, we get the a. for A.D. 1899, 17th Febru. Siddhanta, the Yoga began 6 hours later, or on
ary, 18 hours, Old Style, or 1st March, 18 the 18th February, 0 hour, Lanka time.) At that
hours, New Style. Our Tables serve, howepoch, according to the Súrya-Siddhanta, the
ever, for the inverse problem; thus, we start mean moon and sun were in the initial point of
from a. for A.D. 1899, and add to this, a. for the Hindu zodiac; the longitude of the moon's
5000 years, and a. for the 1st March, and a. for perigee was 9 signs; and the sun's perigee was
18 hours. The two last positions are equal to practically at the same place as at present, i.e.
the increase of a. for 59.75 days. Now we 257° 17' of the initial point of the Hindu zodiac.
have the proportion :--As the synodical revoAccordingly a. or the difference of the mean
lution of the moon in a Yuga is to the increase longitudes of the sun and the moon, was nil.
of 4, in 5000 years, so the days in a Yuga are But we must subtract the constant quantity
to the days in 5000 years; vis.200-5 by which the difference of the longitude
58408438 61842-65629 of the sun and the moon is diminished, in BOTO&BO OT
1 677917828 order that the equations of b. and c. may be in 5000 Julian years. always additive, and not additive in some Hence, increase in 1000 years is 12368-58126, cases, and subtractive in others.
and increase in 100 years is 1236.853126. In Hence, a. was 10000 - 200-5=9799.5. the same way the increase of a. in 59.75 days
b. or the moon's mean anomaly, was 90° will be found to be 2.023326. 0-250 of the circle, or in my notation 250.
Now rejecting complete revolutions, and subc. or the sun's mean anomaly, was 102° 52', tracting the fraction from 1, the remainder is or in my notation 285-8.
to be used as a. for 5000 years, viz. 3437.2 ; a.
increase of a = 1826250 * 58493338
