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No. 15.]
THE BRAHMA-SIDDHANTA: MEAN SYSTEM.
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samkrānti was 6228-4770. We select sucb a value of a in col. 3 of that Table as, added to the former, makes a value between 0 and 333-3, the limits of the tithi fukla l; and note the interval of days, and the week-day resulting by addition of the given week-day (col. 2) to the week-day of mean Měsha-sankranti. Here the selected value of a is 3904:6243, since 6228-4770+ 3904-6243=133-1013. The interval of days is 18 (col. 1). The week-day corresponding to the day Chaitra sukla 1 is (0+3 =) 3. The result is the same as obtained by the former process.
All the entries in the general Table XC, cols. 19-23, can be proved in this way.
To find the exact phase of the mean moon, i.e. the mean tithi-index a, on any day of any year, or at any particular moment of any day, it is only necessary to add to the value of a given in col. 23 of Table XC for the first day of the luni-solar year the amount of increase of a during the intervening whole days, hours, etc., given in Tables LIVA and B (above, Vol. XV).
The purnimänta system of lunar months. 327. The amanta lunar month begins at the moment of new moon, the purnimänta month at the moment of full moon a fortnight earlier; so that the fortnight (sukla) between new moon and full moon bears the same month-name by both systems, while the fortnight (krishna) between full moon and new moon bears, in the pūrnimānta system, the name of the lunar month next after that which it bears in the amānta system. The sukla fortnight of the first lunar month, for instance, belongs to Chaitra by both systems. The following krishna fortnight, however, belongs to Chaitra by the amānta system, but to Vaisakha by the pūrnimānta system.
This should always be borne in mind when examining dates of inscriptions, especially in earlier years. For references to already published explanations see $ 322 above, and for a Table of corresponding fortnights aud lunar months see Indian Calendar, Table II, Part I.
The mean moon's nakshatra. 328. The note on this subject already given ( 308) in dealing with calculation by the First Arya-Siddhanta mean system (above, Vol. XVI) applies equally to the Bruhma-Siddhänta mean system. It is unnecessary to repeat it.
Tables LXXX and LXXXI, fixing the sun's mean longitude for every day of the mean solar year according to the First Arya-Siddhanta, may safely be used for general calculation by the Brahma-Siddhanta, since the difference between the two authorities in their estimates of the length of the year only amounts to 21 seconds. But in any exceptionally close case the exact value, at mean sunrise of any day in the year, of, or the sun's mean longitude, can be found by multiplying the sun's mean motion in one day (Table XLIII, Vol. XIV above). by the number of days' interval between the day on which mean Měsha-sankranti occurred and the given day. The sun's mean motion in one day by the Brahma-Siddhanta is 59m 8-172655, or in 10,000ths of circle 27.377875426.
The Rule for work is as follows. (i) Find, as above, value of "a" at menn sunrise of given day. (ii) Note number of whole days intervening between the day of mean Mosha-sankranti (Table XC below, col. 18, figure in brackets) and the given day. Turn to Table LXXX and note the increase of sun's mean long., "", during that interval. Deduct from this, by Table LXXXI, the increase of long during the hours and minutes stated in col. 17 of Table Xc. The result is the sun's mean long., 8, at mean sunrise of given day. (iii) Add to a. This *, the reqnired index of the mean nakshatra, or the mean moon's place in the heavens at that moment. Table LXVIII above, or Table VIII, Indian Calendar, will shew in which nakshatra the mean moon stood at the time.
In yenurument by 10,000ths of circle the total difference in 365 days is 0:0X666, by which amount the Bralna-Siddhanta is the greater.
