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

158 PAÑCASIDDHĀNTIKĀ VI.4 equal. As the three lines of latitude are perpendicular to the ecliptic, △ M₁ AS, and △ M₂ BS, are equal and right angled at A and B. Therefore AS = SB = √(sum of semi-diameters)² − latitude² = √55² − lat², where AS or SB are the difference of the Moon's longitude at first or last contacts from its longitude at new moon, and measured in minutes of arc. As the motion of S is the same as that of the Sun, the time taken by the longitude to move from A to S or from S to B = the minutes of difference ÷ the difference of the motions of the Sun and the Moon in minutes = √55² − lat² × 60 ÷ difference of daily motion in minutes, in nāḍīs. Therefore the total time in nāḍīs from A to B (this is the uncorrected whole duration) = 2 × 60 × √55² − lat² ÷ the difference of daily motions in minutes. But actually the latitudes at the first and last contacts differ enough from that of the full moon to justify the use of their exact value. So each should be used separately, and the half-duration before full moon, and that after full moon should be found. Using the latitudes of these times again, if necessary, they should be found again. Certain Karaṇas (manuals) like the Vākyakaraṇa apply a certain correction in the place of this repetition of work. This correction depends upon the Moon ~ Rāhu at full moon, like the correction in stanza 4, given by the author for correcting the duration, and therefore it is possible that the correction for the difference in latitude has been included in that correction. But as the correction given is rough, we cannot analyse it and find out whether the author has done so or not. Let us now consider the rationale of the correction in stanza 4. We have already hinted that this is to compensate for using the latitude got in III.31 from uncorrected Rāhu, instead of that from corrected Rāhu, which is to be used in our work here. [Diagram: Fig. VI. 3] M1 R M is the orbit without correction for Rāhu. M1′ R′ M′ is the orbit with correction for Rāhu. Fig. VI. 3 In Fig. 3, R is the uncorrected position of Rāhu, and R′ is its corrected position. The distance between them is 1° 36′, given in stanza 2. When the Moon is greater than Rāhu, (M, M′) then its uncorrected latitude is MB, and the corrected latitude is M′B, greater by M′M. This is case I. When the Moon is less than Rāhu (M₁, M₁′), then the uncorrected latitude is M₁A, and the corrected latitude is M₁′A, less by M₁′ M₁. This is case II. In case I, if the uncorrected latitude, which is less, is used in the work, √55² − lat² will be greater than what it should be, and the duration should be lessened by a correction. Therefore it is said that the correction is subtractive when the Moon is greater than Rāhu. In case II, since the uncorrected latitude is greater, √55² − lat² will be less than what it should be, and so it is said that the correction is additive if the Moon is less than Rāhu, i.e. if Rāhu is greater. The Fig. is for Rāhu-Head. It can be seen that at Rāhu-Tail too the same holds.