Kuṭṭākāra

Abstract

The following is the method of computing ahargaṇa A, the number of civil days elapsed since the beginning of Kaliyuga by using the rule of three twice. Let s be the number of solar years elapsed since the beginning of Kaliyuga, m the number of lunar months elapsed since the beginning of current solar year and d the number of civil days elapsed in the current month. Let S be the number of solar years in a yuga, which is also yuga-bhagaṇa or the number of revolutions of the Sun in a yuga. If M the number of lunar months in a yuga (which is also the difference between the yuga-bhagaṇa-s of the moon and the Sun), then,

$${A_m} = M - 12S,$$

((5.1))

is the number of adhimāsa-s, intercalary months in a yuga, which correspond to 12 S solar months in a yuga. Similarly, if D is the number of civil days in a yuga, then

$${A_d} = 30M - D,$$

((5.2))

is the avamadina, the number of omitted lunar days in a yuga, corresponding to 30 M lunar days in a yuga. Now, by rule of three, the number of elapsed intercalary months a _m corresponding to 12s + m elapsed solar months, is given by

$${a_m} = \frac{{\left( {12s + m}\right){A_m}}}{{12S}},$$

((5.3))

Thus the number of elapsed lunar months is 12 s + m + a _m and the number of elapsed lunar days is 30(12 s + m + a _m ) + d. The number of elapsed omitted lunar days a _d , corresponding to the above number of lunar days, can now be obtained by rule of three as

$${a_d} = \frac{{\left[ {30\left( {12s + m + {a_m}} \right) + d} \right]{A_d}}}{{30M}}.$$

((5.4))