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

V. 7 V. PAULISA MOON'S CUSPS 145 Now, we shall show why this elevation is always on the northern limb. As mentioned several times before, when latitude is used in the rules given, it is always north latitude that the author means. As seen from north latitudes, the circles on the stellar sphere are all bent towards the south above the horizon. Therefore the hypotenuse also is inclined south, the angle of inclination being equal to the latitude, the hypotenuse being small and taken as a straight line. By this inclination south, the line joining the tips of the horns, which is perpendicular to the Hypotenuse is elevated in the north and depressed in the south, the angle of elevation being equal to the latitude. This elevation, measured on the rim in aṅgulas is, as we have shown, twice the latitude divided by fifteen. In the matter of the addition or subtraction of the difference of declination and the Moon's latitude, we have said that the author has in view only the visibility in the west in the evening, for then alone is the statement correct. Perhaps the author thinks that this is enough, because the ele- vation of the horn at evening appearance alone is observed anxiously by people, as an omen of good or evil. Or the author thinks that the readers themselves will understand the reversal of addi- tion and subtraction for the morning appearance, by analogy with what was done before in the case of visibility. It must also be noted that the object here is only to represent the orb of the Moon as it appears, and the Hypotenuse, Bhuja and Koṭi are given to serve this end. Therefore it would not matter if these are represented on a different scale from that on which the Moon is given, as for instance an aṅgula per degree here. (On this scale the Moon will have to be represented by a dia- meter of a half-aṅgula.) There is a view that the elevation of the horns should be observed when the orb of the Moon is on the horizon. In that case, the Sun will be below the horizon, and the question of the difference in scale will not arise at all. So, these are the steps in the work:- i. The elevation of the horn due to latitude in aṅgulas = latitude in degrees × 2 ÷ 15. ii. Illumination or digit of illumination in aṅgulas = the difference in longitude in degrees ÷ 12. iii. Koṭi in aṅgulas = diff. in declination in degrees ± latitude in degrees. (For evening in the west, if the Moon's latitude and ayana are of like direction, addition, and if of different directions, sub- traction. For morning in the east, reverse the addition and subtraction). iv. Hypotenuse = aṅgulas equal in number to difference in longitude. v. Bhuja in aṅgulas = √(Hypotenuse² – Koṭ i²). vi. See fig. 5, below. On the surface on which the phenomenon is to be represented draw a hori- zontal line and mark the north and south sides on both ends. Mark the point S on it to represent the Sun. Mark a point A on the horizontal line on the side in which the Moon is situated, (this is known when finding the Koṭi) such that SA = Koṭi. From A draw a perpendicular upwards equal to the Bhuja and at the end mark M, the centre of the Moon. MS is the Hypotenuse. With M as centre draw the orb of the Moon having a diameter of 15 aṅgulas. At M draw a diameter BC perpen- dicular to the Hypotenuse. From the northern end the diameter, say C, measure the aṅgulas of ele- vation due to the latitude of the place, along the rim, and mark the point D. Draw the diameter DME. D and E are the tips of the horns. On the lower semicircle caused by DE, mark its mid-point, F. Draw the radius FM. On this mark a point G, such that FG = the aṅgulas of illumination. Draw the arc DGE by the well-known method of making a circle pass through 3 points. This is the upper limit of the illumination. The figure of the Moon is now as it will be seen in the sky. The horizon is between the Sun and the Moon, parallel to the original horizontal line. It must be remembered that