Page 709 - Lokmanya Tilak Samagra (khand 2)

CRITICISM AND SUGGESTIONS. 61
in R. 10 ( Y. 15) we multiply the number ofparvans by 11, and
then dividing the result by 124 ( the total number of amshas in
a Nak~hatra) take the excess (without omitting quarters) to repre-
sent the Nak .hatra-amshas at the end of a parvan. The rule had,
however, to be given somewhere in the Vedanga, and the second
half of the verse gives it to us in plain words. When the parvan
amshas so calculated are equal to 3 I, - and this happens only
once in a Yuga, viz. at the end of the 93rd parvan, - a civil day
( anycthemeron )is to be abandoned or omitted from our reckon-
ing. In short, it is an extra or leap or intercalary day. This is the
plain meaning of the verse; and the following explanation will
disclose the importance and the necessity of this correction in the
Vedanga calender. The idea of omitting a day is not a new device
of the Vedanga Jyoti~ha. As shown by me elsewhere, it is the basis
of the Utsarginam ayanam, and is expressly mentioned in the
Taittirtya SaQlhita VII. 5. 7.1. In the case of yearly sacrificial sattras
like the Gavam ayanam, the vi~huvat or the central day was also
always omitted in counting the 360 days of the sacrificial year.
The astronomical elements on which the Vedanga rules are
based, represent only the mean ( ~~~ ) motions of the Sun
and the Moon. But the Sun's or the Moons' actual ( ~ )
position in the celestial sphere is not generally the mean, but a
few degree in advance or behind it. Besides this, the Vedanga mean
motions themselves are again not exact but only approximately
correct. The Sun does not complete exactly five revolutions in a
Yuga of 1830 days; nor is the number of lunar pakshas therein
exactly equal to 124, as the Vedanga assumes it to be. At the rate
of five revolutions per Yuga of five years, a solar siderial year
becomes, according to the Vedanga, exactly equal to 366 days,
whereas according to modern more accurate observations the
same contains 365.25636 .... ( or roughly 365! ) days. This yearly
error would amount to about one lunar month in 39.7, or, in
round numbers, 40 years altering the Sun's position amongst the
fixed stars by a month in advance. It is impossible that this
could not have been noticed; and the late Mr. Kri,hpashastri
Go~bole thought the error was probably corrected by omitting
one intercalary month in 40 years, that is once in 8 Yugas; while
Mr. Dikshit believed that 35, instead of 38, intercalary months were
inserted in 95 years, that is, in 19 Yugas. But whatever the method
adopted might be, it was not necessary to speak of it in a book,