44
ALBERUNTS INDIA.
Application
of the rule
to the
gaugeyear.
Rule for
the same
purpose
given by
Ya'kub Ibn
Tarik.
Explanation
of the latter
method.
Page 225.
our gaugeyear are 720,635,951,963. This number is
given, and what we want to find is, how many Indian
years and months are equal to this sum of days.
Firstj we multiply the number by 55,739, and divide
the prod uct by 3,506,481. The quotient is 11,45 5,2 24,5 7 5
iXnardtra days.
We add this number to the civil days. The sum is
732,091,176,538 lunar days. We multiply them by
5 311, and divide the product by 178,111. The quotient
is the number of ctdhimdsct days, viz. 21,829,849,018.
We subtract them from the lunar days and get
the remainder of 710,261,327,520, i.e. partial solar
days. We divide these by 30 and get the quotient of
23,675,377,584, i.e. solar months. Dividing them by
12, we get Indian years, viz. 1,972,948,132, the same
number of years of which our gaugedate consists, as we
have already mentioned in a previous passage.
Yakub Ibn Tarik has a note to the same effect:
" Multiply the given civil days by the universal lunar
days and divide the product by the universal civil
days. Write down the quotient in two different places.
In the one place multiply the number by the universal
adhimdsct days and divide the product by the universal
lunar days. The quotient gives the adhimdsa months.
Multiply them by 30 and subtract the product from
the number in the other place. The remainder is the
number of partial solar days. You further reduce them
to months and years."
The rationale of this calculation is the following:—
We have already mentioned that the given number of
days are the difference between the lunar days and
their unctrdtra, as the universal civil days are the dif¬
ference between the universal lunar days and their
universal Unardtrct. These two measures stand in a
constant relation to each other. Therefore we get the
partial lunar days which are marked in two different
places. Now, these are equal to the sum of the solar
