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COMPUTATION OF DATES.
439
of the Hindus contain 1,461,035 days, they are equal to 40 centuries of Julian years plus 35 days. Therefore 4000 K.Y. began on 18th February + 35 days = 26th March. The same date will be yielded by the tables if the 3rd Vaisakha or beginning of the mean solar year of 4000 K. Y. is calculated. We may also test the Julian date by calculating the ahargana, or civil days from the commencement of the Kaliyuga, by tables VI, VII, VIII, and adding 588,465, the result being the corresponding day of the Julian period, which can readily be converted into the corresponding day of the Julian Calendar by the usual tables.
67. Construction of the Special Tables XIII-XXI.-The Special Tables are based on the mean solar year, and not on the artificial year introduced in the General Tables. It is evident that. Cor.' must denote the same interval of time in both sets of tables, but with a contrary sign, because in the General Tables, the artificial year being given,' Cor.' serves to find the end of the solar year, and in the Special Tables the solar year being given, it serves to find the end of the artificial year, i.e. the interval between the end of the solar year and the beginning of the next preceding or following sunrise at Lanka.
68. To caloulate a given Tithi.- As a Tithi is equal to the time required by the sun and moon to increase their distance by 12° of longitude, we require the following data : (1) the true longitude of the moon, (2) the true longitude of the sun. According to Hindu astronomy, true long. ( = mean long. ( + equation of the els centre; and true long. O = mean long. O equation of the O's centre. The equations of the sun and moon's centres depend on their mean anomalies. Now we have the equations : true distance (-O=true long. ( - true long. = mean long. ( - mean long. O equation equation o. The mean long. ( - mean long. ois equal to the place of the moon in her synodical revolution. Hence it follows that the tables must enable us to calculate accurately
(1) the synodical motion of the moon, (2) the anomalistic motion of the moon,
(5) the anomalistic motion of the sun. Besides this we require tables furnishing the equation for (2) and (3).
69. The synodical motion of the moon (Tables XIII to XIX) in one solar year is evidently equal to the synodical revolutions of the moon in a yuga divided by the number of solar years in a yuga. The moon's synodical revolutions in a yuga are, in the Saiva Siddhanta and Arya Siddhanta 53,433,336;" and Arya Siddhanta 53,433,334; Brahma Siddhanta 53,483,330. Dividing these figures by 4,320,000 and multiplying by 860', we find the mean synodical motion in degrees for one solar year, viz. Sürya and Árya Siddhanta-rejecting complete revolutions or multiples of 360°,=132° 46' 40'8" in 100 solar years : 317° 48', &c.
As the mean distance of the sun and moon at the beginning of the Kaliyuga was 0° (the longitude of both being supposed to have been 0°), the mean distance ( at 3000 K.Y. was 174o as given in column headed Distance'(- of Table XIII. From these data the value of the distance for centuries and for odd years can easily be computed ; in a similar way the corresponding values for the other Siddhántas have been computed.
a The Julian dato advanced by one day after each century of 36,626 days, but remains the same after a century of 36,526.
4 Hence the wypodical period of the S. &.in. = 1,677,917,828 d. + 63,439,386 r. = 29-53068795 days.-J.B.
