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No. 10.]
THE SIDDHANTA-SIROMANI.
On this basis then, viz. the exact amount of increase of a, b, c, in 4200 K. Y. years, has been calculated the increase per civil day (Table LIV A), per hour, minute and second (Table LIV B), per year and per century (heading of Table LIV A), according to the Siddhanta-Siromaṇi. The valuation of increase of a differs from that of the Sürya-Siddhanta by about 2 units in a century. Note that a common century consists of 36,526 days, a defective century of 36,525 days. In the 4,200 years concerned there were 37 common and 5 defective centuries. The whole period consisted of 1,534,087 civil days.
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To assist in the calculation the yearly increases of a, b, c given, from year to year, in Prof. Jacobi's Special Tables (above, Vol. I, Tables XVI, XIX) were also referred to. It would have been easier had these contained decimals of seconds.
Tables LV, LVI. Equations of the centre, moon and sun.
275. The values of a, b, c at any moment, which fix the positions of mean moos and mean sun, having been found by use of Tables LIV A and B, the tithi, or the position of the true moon with reference to the true sun, is ascertained by applying the equations of moon (eqn. b) aud sun (egn. c) to the value of a. Tables LV, LVI give these equations in closer detail than heretofore (compare Tables VI, VII," Indian Calendar "), enabling great accuracy to be obtained. They can be used as a close approximation for any Siddhanta, but are specially prepared as Tables exact for the Siddhanta-Siromani.
Each equation (col. 3) is the exact value (the value, that is, to be used in our system of work), in 10,000ths of the circle, of the equation of the mean anomaly angle stated on either side of it in cols. 2a, 2b. Col. 1 gives the number of the base-equation, that is to say, the serial number of the equation of each of the 24 base-angles of anom.; each such angle separated from the next by 3° 45', the whole forming the quadrant of 90°. Each section of 3° 45' is divided into five equal parts, the whole forming a group within the limits of which, following universal Hindu practice, the equation is computed by the fixed value of the sine of the base-angle. In 10,000ths of the circle 3° 45'-10-416, and one-fifth of this is 2.083. The difference, col. 4, is the difference between the equations of each of the five parts of the group.
When examining a date, Tables VI, VII of the Indian Calendar may be used for obtaining approximate results, or the new Tables may be used with whole numbers only. The latter for a sort of eye-Table. Absolute accuracy, or very close approximation, can be obtained by using the decimals as a whole or in part. Thus
(Rule) Take the difference between the value of anom., (b or c), found in work for a date, and the nearest to it, greater or less, in cols. 2a, 2b of Table LV or LVI. Multiply this difference by the group-difference (col. 4), and divide the quotient by 2-083. Add, or subtract, the result to, or from, the next equation. This gives the exact value of equation b or c. For an approximation use only one or two decimals, and instead of dividing by 2-083 divide by 2 or by
2.1.
The amount of " Equation b" or "Equation e" is a compound of the actual equation for the given anom. and the greatest equation (which is the actual equation for anom. 90°). The first half of each of the equation-Tables LV and LVI concerns the quantity of anom. 0° to 180°, or, in 1,000ths of circle, 0 to 500. Here the tabulated" equation " (Table LV) is the moon's greatest equation plus the actual equation of the given anom. The tabulated" equation b" in the second half of Table LV deals with the moon's anom. 180° to 360° or, in 1,000ths of circle, 500 to 1000; and the tabulated equation is the greatest equation minus the actual equation of the given anom. In the first half of Table LVI (for sun's anom. 0° to 180°, or, in 1,000ths of
