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No. 10.)
THE SIDDHANTA-SIROMANI.
175
By Tablo LVI we see that the equation for anom. values between 145.83 and 147.916 lies between 12-4786 and 12.0181; the difference between them being 0-4605. For rule of work see $ 275 above.
Approximation. A glance at Table LVI shows that eqn. o must be 12 and a small fraction.
Oloser work. The difference between 146-3 and the next figure of Arg. in the Table (col. a), viz. 147.9, is 1.6. The group-difference (col. 4) is 0.4605. Call this 0:5. The invariable difference betwoon successive entries of arc ("Arg."') is 2.083. Call this 2. 1.6 x 0:5 =0.8. This divided by 2 is 0-4. Add this to the equation stated for Arg. 1479, viz. 12:0. Result 12.4.
Stall closer work. The actual anom. difference (147.916-146-3264) is 1.5902. This multiplied by the group-difference, 0 4605=0.7323. This divided by 2.088 is 0-8515. And this, added to 12-0181 (the equation of anom. 147-916), gives us the exact equation of anom. 146-3264 as 12:3696.
Example 4. To find the tithi current at mean sunrise of any oivil day, or at any moment of
that day. Rule. Take the European date, serial number of the day (in braokete measured from Jan. 1st of the A.D. year) and a, b, c of Chaitra sukls 1 of the luni-solar year, from cols. 19 to 25 of Table LX. Find the interval of days to the given day and add to the a, b, c of Chaitra sukla 1 the a, b, c for that number of days given in Table LIV A. This gives the a, b, c of sunrise on the given day.
Por subsequent hours, minutes and seconds add the a, b, c given in Table LIV B.
Find egn. b and egn. c from Tables LV and LVI, and add them to the a already found. The result is the tithi-index; with which find the current tithi in Table VIII, Indian Oalendar.
Example 5. Calculation for intercalated (adhika) and suppressed (kshaya) lunar months.
This is the same as in work by the Indian Calendar or Indian Chronography, but the lengths of the solar months, their collective duration, week-days and a, b, c must be taken from Table LVIII below when working by the Siddh.- Siromani. In a very close case uge may be made of Table LVIII D. But even so, in work for the tithi, or for intercalations and suppressions of months, the correction in the value of a need alone be taken into account, since the change in the tithi-index, t, is governed by the value of eqn. b and eqn.c, not of b and c; and the difference in these equations is infinitesimal.
Bsample 6. An example is here given of work by the Tables in a very close case, viz. the interoslation of a lunar month in K. Y. 4850 expired, A.D. 1749-50.
In that year, acoording to the Sarya-Siddhanta Bh&drapada was the added month. Was it so according to the Siddhanta-Siromani ?
In that year (Table LX, cols. 13-17) true Masha-Barkránti oocurred on Tuesday 28 March A.D. 1749, at 56 46m 57. after mean sunrise. First must be ascertained the position of mean moon and mean sun at that moment, individually and relatively, i.e. the values of a, b, c. For this process see example 1.
