= SOLVED EXAMPLES mean lunar days and ghatis elapsed at sunrise (Sun's equation of the centre)/12 (Moon's equation of the centre)/12, 217 where the signs are chosen appropriately. Lunar months and years are discarded as they are not required. To obtain the Sun's mean longitude from the Sun's true longitude derived from the midday shadow of the gnomon: 5. Subtract the longitude of the Sun's apogee from the Sun's true longitude derived from the midday shadow (of the gnomon) and (then treating the remainder as the Sun's mean anomaly) calculate the Sun's equation of the centre. Apply that (equation of the centre) to the Sun's true longitude con- trarily to the usual law for its subtraction and addition. (Treating this result as the mean longitude of the Sun, calculate the Sun's equation of the centre afresh and apply that to the Sun's true longitude as before.) Repeat the same process again and again (until two successive results agree to minutes). Thus is obtained the mean longitude of the Sun.¹ The method used here is evidently the method of successive approximations. To find the arc corresponding to a given Rsine : 6. From the given Rsine subtract in serial order (as many tabulated Rsine-differences as possible): multiply the number of the Rsine-differences subtracted by 225. Then multiply the residue (of the given Rsine) by 225 and divide by the current Rsine-difference. Add this result to the pre- vious one. Thus is obtained the arc (corresponding to the given Rsine in terms of minutes).³ 1 This rule occurs also in. BrSp.Si, xiv. 28; iii. 61-62; Siśi, I, ii. 45. 2 i.e., the tabulated Rsine-difference which is next to those sub- tracted. 8 This rule is found also in SūSi, ii. 33; BrSpSi, ii. 11; ŚIDVţ, I, ii. 13; SiSe, iii. 16; ȘiŚi, I, ii. 11(ii)-12(i).
