________________
No. 10.)
THE SIDDHANTA-SIROMANI.
171
5° 2' 7"-366068, which is the correct equation of the moon's centre when his mean anom, is 90°. Worked in the other way, a 224th part of 76-78 is 0-342768, and this added to 76.78 gives the Bame result, yiz. 77.122768.
It is advisable here to state the Hindu rule for finding the sine of any ungle, viz. :-Ascertain the number of minutes contained in the given arc. Divide these by 225' (= 3° 45'). The quotient is the serial number of the preceding base-sine as given in Table LIX, col. 1. Multiply the remainder by the difference between the preceding and succeeding base-sines (col. 4) and divide by 225. Add the result to the preceding base-sine. Thus with arc 24° or 1440. 1440° 225 yields quotient 6, remainder 90. 6 is the serial number of the sine of 22° 30' (col. 1). The difference between the base-sine No. 6 and base-sine No. 7 is (col. 4) 205.90 x 205 = 18450, and this divided by 325 = 82, with no remainder. The preceding base-sine, No. 6, is 1915', and this plus 82 = 1397'. 1397' is the sine of 24°.
283. The equation-Table for the moon's centre given below (Table LIX) is practically the same as that of Prof. Jacobi's Table XXIV A (Vol. I, p. 458, above); but in the former decimal points are given which are omitted in the latter. We agree also in our equation-Tables for the aan (mine in Table XLVII, Vol. XIV above, his in Table XXIV B, Vol. I, p. 459). But there seems to be some mistake in the figures entered by him, stated in parts of the circle, in his equivalent Table of the equations of the sun's centre given in Vol. XI above (Table XII, p. 169, col." A 10 ") for differences in consecutive equations. For instance the equation for anom. 221° 15' is 1° 26' 3.72 (base-equation No. 11) and for anom. 225' is 1° 32' 17:28 (base-equation No. 11). Difference 6' 13":56. There is a difference of 225' in the anomalies, and 6' 13:56 - 225 gives the difference per minute of anom, as 10.66. In this we both agree.
Now 6' 13-56, in 10,000ths of the cirole, is 2-8824, or, with two decimals only, 2.88, but Prof. Jacobi in Vol. XI quotes - 2.78” as the figure. It stands between his “arg. o" 1146 and 1250, which are the equivalents in his notation of the anom, angles corresponding to 221° 15 and 2250 - serial numbers 11 and 12 in the equation-Table.
One-fifth of 2-8824 = 0.5765, and this is the entry given in col. 4 of Table LVI below, as the group-difference for all anom. angles between those of the serial numbers 11 and 12.
I venture to suggest the following amendments to all the entries in Prof. Jacobi's col. "A 10," reading from top to bottom of his Table XII (Vol. XI) :For 3-75 read 3.95 For 3-26 read 3-36
For 1.83 read 186 3.85 3.94
3:07 3.22
► 153 . 163 3.75 3.90 2.88 3.06
1.34 , 1.39 3.65 3085 2-78 , 288
1.15 1.14 , 378
2-71
0-86 , 0-90 3.56 , 3-69 2.40
0-58 085 3.46 3.61
2.212 :30
, 0-380 39 3.36 3.50
2.02 2.09
► 0-100 12 These differences stand in regular progression. It is possible that the Professor's first entry " 3.75" is a printer's error for 3.95; but even so our agreement is only in that one out of 24 entries.
3-65
2.59
2-51
• Table LX. Working Table for computation of dates. 284. Table LX is the principal working Table by which the tithi, lunar and solar month and day, nakshatra and yoga given in an inscription-date based on the Siddhanta-Siromani
Y 2
