Sychronizing Months and Seasons

Sychronizing Months and Seasons
The religious calendar of the Hindus, as of many other faiths over the world, is lunar and is based on the Tithis or lunar days. If the lunar months are allowed to recede progressively, [this is allowed in the Islamic calendar] the seasonal festivals of any particular lunar month will get divorced from their association of their correct seasons. For the lunar months to move through all the solar months and to come back to their original position it may take about 321 years. In other words, the religious festivals will harmonize with the seasons once in about 321 years only. Therefore, there arose a need to synchronize the religious calendar with the calendar of seasons, mainly to prevent this problem of shift of festival days. It is only to avert this contingency the occasional introduction of inter-calary months in the lunar calendar was devisedby our ancients. When this recession of about 11 days per year gets accumulated to 30 days or one month, an inter-calary month is inserted in the lunar calendar to bring it back to its original position in relation to the seasons. Such extra months can come at regular intervals after every 32 and 33 solar months, alternately, to maintain the balance. This procedure was in vogue in the early period of Siddhantic astronomy. However, later the method adopted is different and is the determined on the basis of true motions of the Sun and the Moon.

The ancient Hindu concept of computation of time stems from the Mahayuga. In a Mahayuga there are 4,320,000 years, which contain 51,840,000 solar months or Souramasas and 53,433,336 lunar months or Chandramasas. So in a Mahayuga there will be 1,593,336 inter-calary or Adhikamasas in the lunar calendar. The pattern of occurence of the solar and lunar months can be expressed mathematically,as a continuous fraction based on the fact there are 33 lunar months for 32 solar months.

But the problem does not stop with this. For 423 solar months there will be 436 luner months, an additive of 13. If we take 1692 solar months or exactly 141 years, we get 52 additive months. On the basis of one per 32 years, the additive month must be 53 for 1696 years. It can be seen that an increase of 4 solar months has brought in another lunar month. So also for 1920 solar months only 59 Adhikamasas occur. As per the normal rules this must be be 60. Therefore, one month has to be reduced to make it 59. That is why the need to identify a Kshayamasas or surpressed month arises to offset the excess. This is done by just ignoring a count of a lunar month. Kshayamasas occur generally once in 141 years and again after 19 years, more frequently though they are possible in other intervals of 46, 65, 76 and 122 years.