पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

214 PAÑCASIDDHĀNTIKĀ IX. 15 Kakṣā of the Sun and the Moon 15. The Sun's radius vector multiplied by 5347 and divided by 40 is called its kakṣā. The Moon's radius vector multiplied by 10 is its kakṣā. It is to be noted that the kakṣa obtained here, depending as it does on the radius vector is also for the moment taken and its neighbourhood. We can also derive it directly from the daily rate of motion obtained from verses 3-14, above. Thus: (a) The Sun's kakṣā = Sun's radius vector × 5347/40 = (120 × 59.13 ÷ Sun's daily rate of motion) × 5347/40 = 9,48,558 ÷ Sun's daily rate of motion. (b) The Moon's kakṣā = Moon's radius vector × 10 = (120 × 790.56 ÷ Moon's daily rate of motion) × 10 = 9,48,680 ÷ Moon's daily rate of motion. Example 10. Pudukkottai (Lat. 10° 24′), on a particular day, new moon falls at nā. 20-40 after sunrise. At that moment, the longitude of the sun = the longitude of the Moon = rā. 2-0-0. The Rāhu-head, at that time is rā. 7-29-24. The Sun's rate of motion for the time is 57' per day and the Moon's 810'. The daytime is nā. 31- 20. Compute the solar eclipse occurring. For this, the kakṣā is found first: (a) The Sun's Kakṣā for the time = 9,48,558 ÷ 57 = 16,641 (b) The Moon's for the time = 9,48,680 ÷ 810 = 1171.2 The author does not use the word kakṣā here in its usual sense of orbit, but for the actual distance reduced by some factor, for the orbit is constant, while what we get here is a quantity varying with the rate of motion. Since only the proportion of the distances of the Sun and the Moon from the earth is significant, the reduction will not cause any error. That is why, the word yojana giving the measure of distance, is not used here. Now, the mean kakṣā, derived from the mean radius vector, 120', is for the Sun, 120 × 5347 ÷ 40 = 16,041. For the Moon it is 120 × 10 = 1200. These obviously are the respective reduced mean dis- tances from the earth. In the Original Saura the Sun's orbit is given as 6,89,358 yojanas, and the Moon's 51,566 yojanas, as we learn from the Ārdharātrika system etc. Since the mean distances are proportionate to the orbits etc, if the Moon's orbit, 51,566, is reduced to 1200 as here, the Sun's orbit, by the same factor, must be reduced to, 6,89,358 × 1200 ÷ 51566 = 16,042. This agrees very closely with 16,041 got above. The difference of one may be due to giving the multiplier correct to the nearest whole number, as 5347. Further, the orbits, which is the same for our present purpose as saying distances, are inversely proportionate to the yuga cycles given in the Śāstras. Therefore, from the Saura cycles of Sun and Moon in I. 14, by the proportion 1,80,000:24,06,389 :: 1200: x, we get 16,042 for x, the Sun's reduced mean distance, when the Moon's is 1200. This agreement is the justification for our correcting the reading drighna into digghna. But TS correct it into gnighna. Also, they correct khaṛ into khārka though there is the alternate reading khakṛta fitting correctly in the rule and adopted by us. By their corrections the Sun's mean kakṣā will be 5347 and the Moon's 360. Thus the Sun's kakṣā becomes, 5347/360 ( = 14.85) times the 15a. A. स्पुट b. A. खऋभाजितो; C. खार्कभाजितो B3. Has an unnecessary gap after c. B. कक्ष्येति. A. करणों; B. कर्णे कर्णः; B1.2. do not have it. d. A.B. द्रिघ्नः; C. मिघ्नः