________________
160
THE INDIAN ANTIQUARY.
(JUNE, 1888.
for 1000 years, viz. 4687-4; a, for 100 years, The remaining operations are the same as viz. 1468-7.
with a." Our calculation will be as follows:
For determining c. we say :-As the anomaA.D. 1899 ... 6129
listic revolutions of the sun in the Kalpa is to
the increase of c. in 5000 years, so the days in 5000 years ...3437-2
the Kalpa are to the days in 5000 years; viz.59.75 days.....233.26
increase of c. in 5000 Julian years =
18262500 x 4319990613_4999-8796. Kaliyuga 0... 9799.45
1577917828000 The difference from 9799.5 being smaller
Hence the increase in 1000 years is 999.9759; than can be expressed in my Tables, the cal- in 100 years, 99.9976 ; in 59-75 days, 0.1636 culation has proved that the a. for A.D. 1899 is and c. for 5000 years is 1204 ; for 1000 years, correctly given.
21:1; and for 100 years, 2-4. From the a. of A.D. 1899 the a. for the re- Therefore, as above :- C. maining years of the 19th century was found
A.D. 1899 ........ 18 by subtracting the increase of a. for the interval between A.D. 1899 and the particular years,
5000 years ......... 120-4 rejecting the fraction, or counting it as 1,
59.75 days ......... 1636 according as it was less or greater than a half. The a. in Table 6 was found as stated above.
Kaliyuga 0 285-8 But, for 3 and more centuries, the increase of a. for 12 complete days, 4064, is to be added on Accordingly c. for A.D. 1899, viz. 2, is too account of the difference between the Old and large by only 0.2. the New Style : e.g. 10 cent. = 4687 + 4064 Tables 9 and 10 are calculated according to = 8751.16
the rules of the Surya-Siddhanta, on which we In an analogous manner was found the b. of need not enter here. Tables 5 and 6. The proportion holds :As the anomalistic months in the Yuga are to the increase of b. in 5000 years, so the days in
Possible Error. the Yuga are to the days in 5000 years; vis. 1826250 x 3726513366277-5056
As in the Tables fractions are neglected or increase of b. = 1 increase o . 1577917828
counted as 1, according as they are less ot in 5000 Julian years.
larger than , the absolute error in every Hence the increase in 1000 years is 13255.5011; quantity may amount to # 0-5. Usually the in 100 years, 1325-5501; and in 59.75 days, plus and the minus of the different figures will 2.1684. And b. for 5000 years is 494.4; for compensate for each other; but in extreme 1000 years, 498:9; and for 100 years, 449.9. cases the neglected fractions may sum up to Therefore, as above :
+ 2.5 or 3.5, according as five or seven A.D. 1899 ......... 5872
figures are summed up to find A., and the
error in time will be 10 or 14 minutes respec. 5000 years ......... 494 4
tively. In the same way, the error in the sums 59-79 days ......... 168-4
of b. and c. may mount up to + 1.5 or + 2.5,
according as three or five figures are summed Kaliyuga 0 250.0
up. Bat the effect of these errors on the
equations of b. and c., and through them on A., Accordingly b. for A.D. 1899 is 587-2. But, as
is not the same, but can be ascertained, in the fraction is smaller than $, we roject it.
every case; generally, it is very small.
b.
** In the way indicated Table 6 may easily be extended beyond the limits I have chosen, which were selected because the calendar now in use was not introduced before that time.
11 Some centuries ago a blja or correction was introduced, by which the b. of Table 5 would be diminished by 5. This correction should be applied in dates of the last three or four centuries.
