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

164 PAÑCASIDDHĀNTIKĀ VI.8 In all the three figures, M, M₁, M₂, M' represent the centres of the Moon, and S, S₁, S₂, the centres of the Shadow. S' is the point of contact. R is Rāhu. In fig. 5a, R M₂ is part of the Moon's orbit, and RS₂ is part of the ecliptic. In position S₂ which is the limit for the occurrence of an eclipse, MS₂ = 13°, and M₂S₂ is the latitude, equal to 55', = the sum of the semi-diameters, i.e., M₂S' + S'S₂. S', the point of contact, is seen 90° from the east point, directed towards the north from the ecliptic, i.e. at the north point of the Shadow, but at the south point with reference to the Moon. In position S, the Moon is at the node, Rāhu, and (Moon ~ Rāhu) is 0°. Clearly, S', the first point of contact, is at the east point. In position S, between the above two, it is seen that S', the first point of contact, makes an angle P M₁ S₁ with the east point, on the south, with reference to the Moon. It may be seen that the sine of the angle is proportionate to PS₁, the latitude, which itself is propor- tionate to (Moon ~ Rāhu) as we have shown. Thus, at any intermediate position, the point of con- tact makes an angle with the east, whose sine is proportionate to Moon ~ Rāhu. Hence the rule to divide the Moon's half opposite to the direction of the latitude into 13 parts by parallel lines at equal intervals, and take the point of contact of that line which corresponds to the degrees, Moon ~ Rāhu. This is shown clearly in fig. 5c. Here P' S', the sine of the angle P'MS', which is the direction, is seen proportionate to PS, the latitude, which is proportionate to Moon ~ Rāhu. The figure is for Moon ~ Rāhu equal to 7°. Fig. 5b is intended to show both the first and last points of contact, and because of the increase (or decrease) of the latitude during the interval, there is an increase (or decrease) in the angle. In the figure, the angle of first contact, P'MS', corresponds to the latitude MA and is smaller; the angle of last contact, P'M'S' corresponds to the greater latitude M'B, and is greater. It is also to be noted that the last contact is at the western part of the Moon, the Moon now being east of the Shadow. The directions mentioned above are with reference to the ecliptic, taking it as east-west, (neglecting the angle of inclination of the Moon's orbit). But the directions have to be given as seen by the observer. For this, two corrections have to be applied, one to convert it with reference to the east- west of the equator, called Āyana-valana, and the other to correct it for the east-west of the place. depending on the latitude of the place, called the Ākṣavalana. Both these have been mentioned and explained in connection with the observation of the first appearance of the moon given in Chap V. The author here gives the Ākṣavalana alone following the original Siddhānta, neglecting the other one, though that is not negligible. Even in this, he takes into consideration only the northern hemis- phere. There the celestial equator is inclined south. An observer facing east looking at a body on the celestial equator sees the east point bent northward, and the west point bent southward. Simi- larly, an observer facing a body west, sees the east point bent south, and the west point bent north.