Page 703 - Lokmanya Tilak Samagra (khand 2)

CRITICISM AND SUGGESTIONS 55

Sun's entry into the last Nak~hatra and the end of a parvan or tithi.
According to the usual method of the Vedanga we expect to find
two verses dealing with the subject - one for the parvan and
the other for the tithi calculation. But in the present case onerule
is sufficient for both these purposes. The Sun takes 13~ days to
traverse a Nak~hatra of 124 amshas; or, in other words, the Sun
moves through 9 NakQhatra-amshas in a single tit hi ( R. 24, Y. 42 ).
Therefore the Nak!!hatra-amshas of the sun divided by 9 will
at once give the tithi-periods elapsed since his first entry into the
said Nak~hatra. I use the words tithi-periods advisedly. For a tithi
does not generally begin with the Sun's entry into a Nak~Jhatra;
and all that we are entitled to say is that the quotient obtained
by dividing the solar amshas by 9, represents periods of time,
each of which is equal in length to a tithi. But it is not convenient
to measure time, in this case, by such tithi-periods. We have to
convert them into days. This can be done as follows :- We know
from the Vedanga that whereas a day contains 124 amshas, a
tithi contains only 122; or that one tithi is equal to one day minus
2 daily amshas. Therefore, the above mentioned tithi periods
will be equal to as many days minus daily amshas equal to double
the number of the said tithi-periods. Expressed algebraically, if
n be the number of amshas traversed by the Sun at a particular
time, then n/9 is the number of the tithi periods elap ed between
the sun's entry into the akQhatra and the time in question: and
that n/9 tithis are = n/9 days - 2nf9 ( daily) amshas. For example
the Sun's NakiJhatra amshas at the end of the 11th parvan are 121·
therefore the time elapsed between his entry into the last parvan
NakiJhatra and the end of the said parvan is = 121/9 = 13~ tithi-
periods or 13~ civil days minus 26~ ( daily ) amshas. Or we may
proceed to calculate in a slightly different way. We know that
the sun traverses 124 amshas ( one Nak~Jhatra) in 13~ days. There-
fore, by a simple rule of three we can directly obtain the time, in
days, required by the Sun to traverse 121 amshas. The result is
the same in either case. B and S both agree that, in one form or
another, this rule is contained in the following verse :-
~~~~)r~:l
~ ~~~ ifilWT ~Tiit ~~a~ II Y. 26.
But they differ widely in their detailed explanations. B takes ~
to mean the whole quotient including the remainder, though the