2?
- TRUE LONGITUDES OF THE PLANETS [ CH. n
A rule for finding the Moon's true daily motion (known as jhabkukti) : 11-13. From the (mean daily) motion of the (Moon's) mean anomaly subtract the preceding or succeeding arc (of the current element of the arc, i.e., the elementary arc 1 containing the Moon) (according as the Moon is in the odd or even anom- alistic quadrant). (Then) take (the tabulated Rsine-differences) on the basis of the (residue in) minutes of the (mean daily) mo- tion of the Moon's mean anomaly, starting from the current Rsine-difference reversely and directly in the odd and even anom- alistic quadrants respectively. The results (i.e., the Rsine-dif- ferences) corresponding to the fractions of the first and last elementary arcs should be determined by proportion (and added to the sum of the previous Rsine-differences). The Rsine-dif- ference (corresponding to the daily motion of the Moon's mean anomaly) thus obtained multiplied by the (Moon's tabulated) epicycle and divided by 80 should be subtracted from or added to the Moon's mean daily motion as before (in the case of the Sun, i.e , according as the Moon's anomaly is in the half-orbit commencing with the sign Capricorn or in that commencing with the sign Cancer). This is known as (the Moon's) true (daily motion). 2 The commentator Paramesvara explains the above method as follows: "From the mean (longitude) of the Moon subtracting its apogee, (then) obtaining the (corresponding) bkuja, (then) reducing that to minutes of arc, (then) dividing that by 225, (then) setting down separately the preceding portion of the current elementary arc as also the succeeding one, (then), the (anomalistic) quadrant being odd, having multiplied the preceding portion of the current element of the arc by the current Rsine-difference and divided by 225 and taken (down) the resulting Rsinc-difTerence, subtract the preced- ing portion of the current elementary arc from the (daily) motion of the Moon's mean anomaly. Then, having divided that remainder by 225, add to the Rsine-difference obtained before as many(tabulated)Rsine-difTerences, 1 The twenty-four divisions of a quadrant, each equal to 225' t the Rsine-differences of which have been tabulated by Aryabhata I, are called "elements of arc", or "elementary arcs". 2 Cf. MBh, iv. 15-17.
