Kuṭṭākāra

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, (5.1)<math display='block'> <mrow> <msub> <mi>A</mi> <mi>m</mi> </msub> <mo>=</mo><mi>M</mi><mo>&#x2212;</mo><mn>12</mn><mi>S</mi><mo>,</mo> </mrow> </math>$${A_m} = M - 12S,$$ 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 (5.2)<math display='block'> <mrow> <msub> <mi>A</mi> <mi>d</mi> </msub> <mo>=</mo><mn>30</mn><mi>M</mi><mo>&#x2212;</mo><mi>D</mi><mo>,</mo> </mrow> </math>$${A_d} = 30M - D,$$ 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 (5.3)<math display='block'> <mrow> <msub> <mi>a</mi> <mi>m</mi> </msub> <mo>=</mo><mfrac> <mrow> <mrow><mo>(</mo> <mrow> <mn>12</mn><mi>s</mi><mo>+</mo><mi>m</mi> </mrow> <mo>)</mo></mrow><msub> <mi>A</mi> <mi>m</mi> </msub> </mrow> <mrow> <mn>12</mn><mi>S</mi> </mrow> </mfrac> <mo>,</mo> </mrow> </math>$${a_m} = \frac{{\left( {12s + m}\right){A_m}}}{{12S}},$$ 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 (5.4)<math display='block'> <mrow> <msub> <mi>a</mi> <mi>d</mi> </msub> <mo>=</mo><mfrac> <mrow> <mrow><mo>[</mo> <mrow> <mn>30</mn><mrow><mo>(</mo> <mrow> <mn>12</mn><mi>s</mi><mo>+</mo><mi>m</mi><mo>+</mo><msub> <mi>a</mi> <mi>m</mi> </msub> </mrow> <mo>)</mo></mrow><mo>+</mo><mi>d</mi> </mrow> <mo>]</mo></mrow><msub> <mi>A</mi> <mi>d</mi> </msub> </mrow> <mrow> <mn>30</mn><mi>M</mi> </mrow> </mfrac> <mo>.</mo> </mrow> </math>$${a_d} = \frac{{\left[ {30\left( {12s + m + {a_m}} \right) + d} \right]{A_d}}}{{30M}}.$$