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

30 PAÑCASIDDHĀNTIKĀ II.6 (a) (Usually called the Mūla-dhruva or Kṣepa) is the mean Moon at a point of time 1936 days before the Epoch, when the Moon's apogee and the mean Moon exactly coincided according to this Siddhānta. This is given as śaśi-muni-navayamāś ca rāśyādyāḥ, i.e. 1ʳ 7° 29ʹ. (b) is the mean motion during whole numbers of cycles of 3031 days from the point of time 1936 before Epoch, each cycle equal to 110 anomalistic revolutions of the Moon. This (b) is found by multiplying the mean motion per cycle (110 revolutions, 11 rāśis, 7 degrees, 32 minutes) by the number of cycles, called ghanas, obtained as quotient, by dividing the Days from Epoch plus 1936, by 3031. As full revolutions can be neglected, it is enough if we multiply the ghanas by 11 rāśis 7 degrees 32 minutes, which may be done as ghanas × 2ʹ + ghanas × 11ʳ 7° 30ʹ. Ghanas × 2 is given by dviguṇaghanāḥ kalāḥ (yojyāḥ). Because 16 ghanas × 11ʳ 7°30ʹ equals 15 full revolutions, it is enough if we divide out the ghanas by 16 and take the remainder alone for multiplication (for we shall be neglecting only full revolutions), which we are asked to do by ghanaṣoḍaśāhṛta-śeṣam. As 11ʳ 7° 30ʹ is ¾ rāśi less than a full revolution, we can multiply the remaining ghanas by ¾ rāśi and take this as subtractive, which we are instructed to do by projjhyādhas triguṇitaṁ caturbhaktam bhādi (rāśyādi.) Thus b is disposed of. (c) is the mean motion during the subsequent full anomalistic revolutions called gatis, which form the quotient got by dividing the remaining days by the anomalistic period, 248/9 days, (i.e. multi- plying the days left over by 9 and dividing by 248). For each gati the mean motion is 1 revolution and 184 9/10 minutes (which can be obtained by dividing the motion per ghana, viz. 110 rev. 11ʳ 7° 32ʹ by the number of gatis in a ghana, viz. 3031 × 9/248). Hence the rule to multiply the gatis by 185ʹ and deduct minutes equal to 1/10 of the gatis. This is given by viṣayadhṛtayo gatighnā gatīkāṣṭhām- śonitāḥ kalāḥ yojyāḥ. (d) What are now left of the days are ninths of days called padas (and these obviously would be less than 248). The mean motion per pada is 1 degree 27 209/248 minutes, and so padas × 1° 27 209ʹ/248 should be added to complete the mean motion till t. Of this, the Siddhānta asks us to add 1° per pada first, which is given by śeṣapadasamāṁśāmśāḥ (yojyāḥ). This forms d. (e) The residue 27 209/248 minutes per pada, forming (e), is combined with the equation of the centre (ii) and given by the two formulae of II.6. If the padas contain a half-gati (i.e. 124 padas) the value of (d) + (e) + (ii) for the half-gati part is combined together and given as 180° 4ʹ. This is got as follows. As the half-gati is equal to 124 padas, d = 124°. (e) + (ii) given by the first formula of II.6 is: {1094 + 5(124 − 1)} 124/63 = 3364ʹ = 56° 4ʹ; 124° + 56° 4ʹ = 180° 4ʹ = 6 rāśis 4 minutes, which is given by gatyardhe bhagaṇārdham deyam liptācatuṣkasaṁyuktam and which instruction has so much puzzled TS. But, of course, this is incorrect and the defect lies in the equation of the centre- part of the formulae in II.6, which give zero-value for the equation of the centre not at 124 padas, but at 133 padas, as we shall show presently. We shall first explain II.6 by showing how the formulae here combine the residual mean motion, viz. padas × 27 209/248 minutes (= e) with what is identifiable with the equation of the centre (= ii). The equation of the centre of the Vāsiṣṭha is peculiar. Usually in the Siddhāntas the equation of the centre varies as the sine of the anomaly, and therefore is zero at zero degree anomaly, going to a minimum at 90°, again rising to zero at 180°, then going to a maximum at 270°, and then falling to 0 to 360°, i.e. zero°. Thus it is negative in the first two quadrants and positive in the third and fourth quadrants and of the form, '−a sin θ, where 'a' is the maximum or minimum numerical