Luni-solar calendar, Kali Ahargana and Julian days

Abstract

The paper computes the elements of luni-solar calendar, like saura months, lunar months, intercalary months, omitted tithis, and gives general rules for computing ahargana from different epochs. The later ahargana rules agree very well with that of the Kali ahargana which started counting of days from the Kali epoch. The use of Kali ahargana (KA) for recording time of important events was quite popular and became the part of India's history and culture. Since ahargana is nothing but collection of civil days, it has corresponding agreement with number of Julian days, and as such the system of conversion from one to another has also been included and clarified with the help of tables and examples. This will show that the popularity of KA was based on a strong mathematical foundation, even though the major objective of KA rule was to calculate the mean planetary positions.