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

IV. 21 IV. THREE PROBLEMS 91 The gnomon should be twelve units in length, not necessarily digits; no harm will result, pro- vided all measurements are given in the same units. The circle also can be of any desired diameter, not exactly four gnomons in length. We are not sure whether the word for ‘four’ occurs at all in the text, it is so corrupt in that part. We can only say it cannot be śaṅkvaṅgula as corrected by TS; the letters are so different. Finding the directions in the manner described is explained thus: The North is directed towards the north pole of the earth. Corresponding to this is the celestial north pole, (from which we can find the north, if we can only observe it correctly, and therefrom the other directions). At mid-day the Sun is on the meridian, and at equal times before and after, its altitudes and directions are equal, provided its declination does not change. As the Sun’s position is thus symmetrical, before and after noon, with the meridian as the line of symmetry, the gnomonic shadow is symmetrical with the north-south line (which corresponds to the meridian) as the line of symmetry. Therefore if two gnomonic shadows, one in the morning and one in the evening, of equal lengths, are marked on a horizontal surface, the bisector of the angle between the two shadows is the line of symmetry, and therefore the north-south line. From this the east-west line, which is its perpendicular bisector, is drawn. The circle, asked to be drawn, serves the purpose of marking the equal shadows. By the same symmetry, the ends of the shadows are at equal distances from the east-west line, and so the line drawn between them is also east-west, being parallel to the east-west line drawn. Therefore the author asks us to draw the east-west line formed by joining the two points first, and proceed. We have said that the Sun’s declination must be the same, i.e. does not change during the interval. But actually it changes. So if we do the work at a time of the year when the change in declination is very little, then the directions found will be nearly accurate. This happens near the solstices, and there- fore the work should be done when the sun is near the solstices. Methods to find the directions accu- rately even when the declinations are changing rapidly, are given by writers like Vaṭeśvara, Parameśvara etc., and also explained by Govindasvāmin in his commentary on the Mahābhāskarīya, III.1. [छायातः अक्षानयनम्] विषुवद्दिन [सममध्य] छायावर्गात् सवेदकृतुरूपात् | मूलेन शतं विंशं विषुवच्छायाहतं छिन्द्यात् || २० || लब्धं विषुवज्जीवा चाप [म] तोऽक्षोऽ [थवैव] मिष्टदिने | मेषाद्यपक्रमयुतस्तुलादिषु विवर्जितः स्वाक्षः || २१ || Latitude from Shadow 20. Measure the mid-day shadow on the day when the Sun is at the equinoxes (the equinoctial shadow), square it, add 144, and find the square root. By this divide the product of the shadow into 120. 21. The result is the sine of the latitude of the place, called Viṣuvajjīvā (or Viṣuvajyā). Its arc is the latitude. Or, do this work on any day and get the arc. If the Sun is in the six signs from sāyana-Meṣa, i.e. if the Sun’s declination is north, add the declination to the arc, the latitude is got. If the Sun is in the six