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

212 PAÑCASIDDHĀNTIKĀ IX.14 the previous day’s true Moon from the given day’s true moon. The daily mean motion, multiplied by 120' and divided by the momentary motion per day is the radius vector at the moment. The following is given here:- (A) (i) The daily change in sine Eq.C. for short interval = the interval in the tabular sine of anomaly current × daily motion of mean anomaly × degrees of epicycle ÷ (225 × 360). (ii) The daily change in Eq.C. in minutes of arc = (i) × 3438 ÷ 120. (since the sine is small and there is no difference between sine and arc). It should be noted here that it is possible to simplify the above work, because the daily anomaly and the degrees of epicycle are fixed for each body, and the rest are constants. Only the interval in the tabular sine of anomaly current varies. For instance, the Moon’s daily motion of anomaly is 783'.9, and epicycle 31°. Therefore, the daily change in Eq.C. in minutes of arc = the interval in the tabular sine of anomaly current × 783.9 × 31 × 3438 ÷ (225 × 360 × 120) = described interval × 8.6. For the Sun it is, interval in the tabular sine of anomaly current × 59.1 × 14 × 3438 ÷ (225 × 360 × 120) = interval etc × .29. (ii) The daily rate of true motion for the moment = mean daily motion ± (ii) (additive if anomaly is from rāśis 3 to 9 and subtractive if from 9 to 3.) (B) The true daily motion = the given day’s true longitude – the previous day’s true longitude. (C) The radius vector at the moment = 120 × mean daily motion ÷ the daily rate of true motion for the moment. The sine interval of anomaly used in computing the true Moon or Sun for noon can easily be used to find the daily rate for the noon in question. It is this that should be used for finding the motion during the interval between mean and true noons, as we have done already, and in correcting for longitude. In eclipses also this true daily rate with radius vector, for the moment of syzygies should be used, because this will give the circumstances accurately. This seems to be the author’s idea in giving these here. As for the Sun, there is no distinction either in the rate or radius vector between those for the day or for the moment. This is indicated by making the distinction in the case of the Moon alone, using the expression śaśiviśeṣāt. Example 8. For the Ujjain true noon of examples 5 and 6, find the true motion (a) for the Moon (b) for the Sun. (a) In example 6, the Bhuja, i.e. sin of Moon’s anomaly got is rā.0-24-7.5. Sines being given for every 3 3/4 degrees, the current sine interval is the seventh, equal to 7' 9". ∴ By (A ii), the daily change in Eq.C. = 7' 9" × 8.6 = 61'.5 By (A iii), the true motion for the said noon = 790'.6 – 61'.5 = 729'.1, (subtraction since anomaly is between rā. 9 to 3). 14a-b. A.B.C.D.ज्ञेयाहो b. A.B2. भेंद्की; B1.2. र्भइकी; C.D. रात्रिकी d. B1.2.भक्ति A.B1.2हता:; B3.ऋता: