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

IX. 15 IX. SAURA-SIDDHĀNTA — SOLAR ECLIPSE 213 (b) The Bhuja or Sun's anomaly in example 5 is rā. 1-14-44.3. The current interval, 12th, is 5' 44". ∴ by (A ii), the daily change in Eq.C. = 5' 44" × .29 = 1' .7. By (A iii), the true motion = 59'.1 - 1'.7 = 57'.4, (subtraction since anomaly is between rā. 9 and 3). Example 9. For the noon of example 8, find the Moon's radius vector. By (C), the radius vector required = 120' × 790'.6 ÷ 729'.1 = 130'.1. The following is the explanation of the rules: The true motion during any interval between two moments is the difference between the true longitudes of the moments. The shorter this interval, the more accurate is the motion. In the rule, all factors excepting the sine of anomaly are constants. Therefore the accuracy of the motion depends on the sine of anomaly only. In the case of the Moon, the motion of the anomaly being rapid, there is significant difference in the sine from time to time even within the day, for four or even five sine intervals pass in a day, with the result that the motion is got differently for different times. So the motion has got to be found for shorter periods like the yāma in the day, and this is the motion for the time being. For every 225' of anomaly there is one sine interval. So, during the time for which the anomaly interval is current, the change in sine Eq.C. is caused by the corresponding sine interval current. Therefore, the change in sine Eq.C. is got by multiplying the current sine interval by the degrees of epicycle, and dividing by 360, for the period covered by the corresponding anomaly interval of 225'. From the change in sine Eq.C. the change in Eq.C. is got in minutes (by multiplying by 3438 and dividing by 120, as we have done). This change is for the time to which the current 225' interval of anomaly corresponds. It is converted into the change per day by multiplying by the daily motion of anomaly in minutes and dividing by 225. This is applied to the mean daily motion to get the daily rate. Now, we know that the Eq.C. is zero when the anomaly is zero, that it is negative and increases numerically in the first quadrant of anomaly, i.e. upto 3 rāśis, then decreases numerically, still being negative, to the end of the second quadrant, i.e. upto 6 rāśis where the value becomes zero again, then in the third quadrant it is positive and increases to a maximum at 9 rāśis and then decreases in the fourth quadrant to zero at the end of 12 rāśis or zero. From this it can be seen that the Eq.C. goes on decreasing as the anomaly passes from 9 rāśis to 3 rāśis i.e. the change is negative or subtrac- tive, and goes on increasing as the anomaly passes from 3 rāśis to 9 rāśis, i.e. the change is positive or additive, as instructed by the text. No harm will ensue from the instruction to multiply and divide the sine interval first and then reduce it to the epicycle, since the sine is small. It is to be noted well that the motion per day found is not actually the motion in the day, but only the rate during the short interval or moment taken in the day. That is why the motion for the day is given by a separate rule, for the Moon. In the case of the Sun there is no distinction between the two, since the daily motion of the anomaly is small. The rule for the radius vector has been explained already when dealing with the Romaka. [रविचन्द्रकक्षे] 'मुनिकृतगुणेन्द्रिय'घ्नः स्फुटकर्णः 'खकृत' भाजितोऽर्कस्य | '(स्वरवसु) मुनीन्द्रविषया' भानोः 'खकृतर्तु [व] सुगुणाः' शशिनः |