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

162 PAÑCASIDDHĀNTIKĀ VI.8 From verse 3, giving the general duration, we see that the sum of the semi-diameters of Shadow and Moon is 55'. Here we see that their difference is 21'. Hence, (55' + 21') = 76', is the diameter of the Shadow according to this Siddhānta, and 55' − 21' = 34', is the diameter of the Moon, giving the semi-diameters as 38' and 17' respectively. By a strange confusion of ideas TS and NP have concluded here that when Moon ~ Rāhu is less than 10°, there must be a total eclipse. (vide the Sanskrit com. p. 33, and English translation, p. 44, NP, Pt. II, p. 53). We have shown that for a total eclipse to occur the difference must be less than 5°. It is easy to see which is correct. If the difference is greater than 5°, the number under the radix becomes negative, and no real root can be obtained. For e.g. if we take 7°; as the difference, according to TS there must be total obscuration. But using it in the formula, we get, 21 × √{(5 − 7){10 − (5 − 7)} 4/5 = 21 √− 96/5 = 21 × 4 √− 6/5, which does not give a real value. Their error is due to their confusing in their work, the 21 minutes, sine of 10°, as 21 minutes, latitude to be got for 10° difference. Further the postulation by TS of a maximum latitude of 240' in this context is unwarranted. True, from the above a latitude of 55' for 13° difference, and 21' for 5° difference will follow, if the correct formula, with the sine of (Moon ~ Rāhu) is used, instead of the degree of difference. But nowhere in Hindu astronomy is 240' given, and the Vāsiṣṭha does not give the latitude at all. So when the Vāsiṣṭha wants the latitude to be used in V. 3, we have got to use only the Paulīśa formula, and the reading gives 280', which TS have translated tacitly as 270'. 280', if taken, will give 63' and 24' for differences 13° and 5°, and 270' will give 61' and 23', instead of 55' and 21', both of which are unsupported by the context. This is the reason why we changed the reading to mean 380', instead of 280', and, following the instructions strictly, gave the rule, latitude = 380' × difference in degrees/90, getting 55' and 21' for differences of 13° and 5°. This is also in keeping with the practice of the Paulīśa, which usually uses for proportion the degrees in the place of sines. [स्पर्शमोक्षदिशौ] स्थितिदलविमर्ददलयोर्विशेष(के तमः) सकलमत्तीन्दुम् । प्रग्रहणमोक्षशशिराहुविवरभागैश्च दिग् वाच्या ॥ ६ ॥ विक्षेपविपर्ययात्सान्तरीयभागे (कृ)ते त्रयोदशधा । परिधौ प्राक्प्रभृतीन्दोर्ग्रहणा(शां)शे वदेत् पर्व ॥ ७ ॥ शशिपरिधिदला(र्ध)ग्रे खेन्द्वन्तरभागसंगुणे (चा)क्षे । ‘खखरूपाष्ट’ हृते प्राग्वल(नं) वामं च्युते सव्यम् ॥ ८ ॥ Direction of the eclipse 6. During the interval from the time of first contact to the beginning of totality, Rāhu (i.e. darkness), swallows the Moon completely. The directions of the points of first and last contacts are to be calculated from the Moon ~ Rāhu of those times. 7. Divide the semi-orb of the Moon situated opposite to the direction of latitude into 13 parts, by straight lines parallel to the east-west diameter, at