ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

UNITS OF TIME 297
Addendum : The mean lunar day (madhyama tithi) may,
however, differ from a true lunar day (spaṣṭa tithi) by one, so that
the ahargaṇa obtained by the above process may sometimes be in
excess or defect by one. To test whether the ahargaṇa (obtained
by the above process) is correct, it is divided by seven and the
remainder counted with Friday. If this leads to the day of
calculation, the ahargaṇa is correct; if it leads to the preceding
day, the ahargaṇa is in defect; and if that leads to the succeeding
day, the ahargaṇa is in excess. When the ahargaṇa is found to
be in defect, it is increased by one; when it is found to be in
excess, it is diminished by one. (K.S. Shukla : MBh. p. 4-5)
Example—Calculate the ahargaṇa on October 1,1965.
From Indian Calendar we find that October 1,1965 falls
on Friday. 7th lunar day (tithi) in the light half of the 7th
month Āśvina in the Saka year 1887 (elapsed). Let us proceed
as follows :
Adding 3,179 to 1,887. we get 5,066. (1)
Multiplying this by 12 and adding 6 (i. e. the number
of lunar months elapsed since the beginning of Caitra)
we get 60,798. ... ... (2).
Multiplying this by 1,593,336 and dividing the product
by 51,840,000, we get 1,868 as quotient. (The remainder
is discarded as unnecessary) (3)
Adding this number (i.e. 1,868) to the previous one (i.e.)
60,798) we get 62,666. (4)
Multiplying this by 30 and adding 6 (i.e. the number
of lunar days elapsed since the beginning of the current
month) to the product, we get 1,879,986. (5)
Multiplying this by 25,082,580 and dividing the product
by 1,603,000,080, we get 29,416 as the quotient. (The
remainder is discarded as not necessary). (6)
Subtracting this number (i.e. 29,416) from the previous
one (i.e. 1,879,986) we get 1,850,570. (7)
This is the required ahargaṇa. Since division by 7 leaves