सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

33 elapsed tithis, integral or fractional (x + 12y)° will be the longitude of the Moon. If, however, we consider y only as the integral number of the elapsed tithis, we will have obtained the Moon’s position from the formula (x + 12 y)° at the ending moment of the tithi on the previous day. The time in between this ending moment of the tithi and the Sun-rise of the day concerned is known as Avama- Sesha, since the Avama-days or Kshayāhas are the differ- ence of days between the number of tithis in a given period and the number of civil days during the same period. In other words, the excess of a civil day over a tithi which falls short of it, is the part of a civil day that contributes towards the number of Kshayāhās in a given period. Thus we have to compute the increase in the Moon's longitude during the aforesaid Avama-Sesha to obtain his longitude at the Sun-rise of the day concern- ed. But this Avama-Sesha is of the form F { (t × K) / T } where ‘ t ’ is the number of elapsed tithis upto the Sun-rise of the day concerned K the number of Kshayāhas in a Kalpa, T is the number of tithis in a Kalpa and F { (t × K) / T } signifies the fractional part called Avama-Sesha, the integral quotient having given the number of elapsed Kshayāhas. Hence writing F { (t × K) / T } as R / T where R is the remainder obtained by dividing (t × K) by T, the Avama-Sesha is of the form R / T. This Avama-Sesha being mean solar. it has to be rendered luni-Solar, which process is known as चान्द्रीकरणम्. The rule of three used in this behalf is ‘ If for C civil days we have T tithis of the Kalpa, what shall we have for R" / T ? The answer is (R / T) × (T / C) = R / C. This then is the balance fractional part of a tithi that is there in between the end of the elapsed tithi and the Sun-rise of the day concerned. This part of a tithi is to be multiplied by 5