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EPIGRAPHIA INDICA
(VOL. XVII.
Tables LXXVIII and LXXIX, with Table LXXIII above (under heading a), which gives the value of a at the beginning of each year of the Kaliyuga century, enable us to find the value of a at mean sunrise of the civil day Chaitra enkla 1 at the beginning of each lani-solar year. Tables LXXVIII and LXXIII yield the value of a at mean sunrise of the day on which mean Měsha-sankranti occurred; and Table LXXIX enables, by addition, the a for the interval of days between that day and the day Chaitra kakla 1 to be ascertained. [The same can be found by subtracting from the sum of the values obtained from Tables LXXVIII and LXXIII (col. a) the value for those intervening days given in Table LXIV above (see Example 1).]
The use of Tables LXXX and LXXXI is explained above ($ 308). They correspond, mutatis mutandia, with Tables XLVIII A, XLIX above used in calculation for the sun's true longitude.
310. The century-Table LXXVIII requires some further explanation. Its object is to determine the mean moon's phase, a, at mean sunrise of the opening civil day of each Kaliyuga century, i.e. the day on which mean Mēgha-samkranti occurred at some time later on that day. Reference to Table LXXVI shews that this opening day occurred at the beginnings of centuries 36 and 37 K.Y. on a Sunday, and in centuries 38 to 45 on a Saturday. From Table I, Indian Calendar, by adding the sodhya interval (above, $ 306, viii) to the date and time there given for the moment of true Mésha-sama krinti, we find that in centuries 46 to 48 it fell on a Friday. In the mean system, therefore, centuries 37 and 45 were defective centuries, while the rest were common.
Table LXXVIII corresponds to Table LXXII above, which concerns true solar years, and by the true system, i.e. calculation by the movements of true sun, the only defective century w& bentury 42. This accounts for the difference between the two Tables.
It has been shewn above ($ 299, i) that the actual value of a at mean sunrise of Sunday, 21 March A.D. 499, on which day, 6 hours later, occurred the moment of mean Měsha-sankranti (mean sun at 0°) at the beginning of Kaliyuga century 36, was, in notation in 10,000ths of the circle, 7715-352496330. The values of a for later century-beginnipgs are found by addition to this of the century increases of a, common and detective ng required.
EXAMPLES Haample 1. To find the European day, week-day, and phase of mean moon, .e. the mean tithi-indez a (which = t, the index) at mean sunrise of the first civil day of the luni-solar year; that is to say, of the day called "Chaitra Sukla 1" of the year in question,
[This example is given in order to enable any student to verify the entries in Table LXXVI, cols. 19-23, For ordinary date work the entries themselves afford all information.]
The mean new moon which marks the astronomical beginning of any mean lunar year is the new moon at the end of the lunar month Phålguna of the previous year. The moment of its occurrence is always earlier than the moment in the current year of mean Mésha-samkrinti, the beginning of the mean solar year. The civil day next following the moment of the initial mean new moon of the year is called "Chaitra sukla 1," that tithi being current at mean sunrise of that civil day. Our tabular calculations being for mean sunrise, the value of a in Table LXXVI, col. 23, must always be between 0 and 333-3, the last being the limit of the tithi.
To find its value for any year we must first calculate the value of a at mean sunrise on the day of occurrence of mean Mēsha-sankranti from Tables LXXVIII and LXXIII (above) under heading a.
This done there are two processes by which the mean sunrise value of a on the day Chaitra sukla 1 can be obtained. One is to use Table LXIV, which, by deducting from the a of mean Měsha-samkrānti-day mean sunrise (already found) the next lower value of a in the Table as given for the first 30 days, yields at once the interval of days between Chaitra sukla 1 and
