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

240 PAÑCASIDDHĀNTIKĀ XI.6 The explanation of all this has already been given. The author does not go beyond this in his graphical representation. The corrections of the text to agree with the ideas intended to be conveyed, are easily understood. [कलानामङ्गुलीकरणम्] लिप्ताद्वयेन हरिजे त्रयेण (मेषूरणे) ऽङ्गुलं भवति । अनुपातोऽन्तर [सं]स्थे कर्तव्यो दृष्टियुक्तार्थम् ॥ ६ ॥ Conversion of minutes into angles 6. So that the graphical representation may appear as the eclipse is seen actually, the minutes of arc are to be converted into digits, at 2' per digit when the Moon is near the horizon, and at 3' per digit when it is on the tenth sign, i.e. meridian, and proportionately in between. The proportion is as follows: In the fifteen nāḍikās (roughly) when the Moon rises from the horizon to the meridian, or falls from the meridian to the horizon, there is an increase of one minute of arc from 2' to 3', or decrease of one minute of arc from 3' to 2'; what is it at a given time? The number of minutes thus obtained is to be represented by one digit in the graphical represen- tation. At this rate the minutes of latitude etc. are to be converted into digits. In the example, for the hour angle of ten nāḍis, we have the rate per digit, (3 − 10/15) = 2 1/3 minutes, i.e. three digits per seven minutes. The following is the explanation of the conversion formula: The Sun and the Moon appear to be larger at the horizon, and to become smaller and smaller as they proceed to the meridian and near the zenith. This is an optical illusion, and really the size is practically the same, as can be proved by measurement, taking photographs etc. We shall not explain the phenomenon here as it is outside the pale of astronomy proper. But we must mention that the explanation given in some works like the Siddhāntaśekhara in wrong. Our author has taken that the magnification at the horizon is one and a half times that at the zenith, (practically the meridian in our latitudes) and the increase in size is proportionate to the hour angle, though this may not be strictly true. He also thinks that the orbs, which are nearly 32', appear to be about 11 digits near the zenith, and about 16 digits at the horizon. Hence his rule, two minutes per digit at the horizon, and three on the meridian. With the possibility of different people giving the actual estimate of size differently, what the author says must be taken as only approxi- mate. Therefore no harm will ensue by taking the meridian for the zenith, or by taking the mean value of the maximum hour angle, viz., 15 nāḍikas, in finding the proportion, especially in our latitudes. 6b. A. सेषूरणंगुल 1. Col. A.B. अवर्णनात्येकादशोध्यायः | c. A. तरःस्थे; B. तरस्थे [इति पञ्चसिद्धान्तिकायां वराहमिहिरविरचितायां C. इत्यनुवर्णनं नामैकादशोध्यायः | d. B. भुक्तार्थिः अनुवर्णनं नाम एकादशोऽध्यायः ]¹ D. अ [नु] वर्णनमेकादशोध्यायः | Thus ends Chapter Eleven entitled ‘Eclipse Diagram’ in the Pañcasiddhāntikā composed by Varāhamihira