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

108 PAÑCASIDDHĀNTIKĀ IV. 33 Fig. IV. 12 In this figure of the sky-sphere, Z is the zenith, and NP is the north pole. D₁D₁, DD, etc. are four diurnal circles, on which four positions of the sun, S₁, S, etc are indicated. D₂M₂D₂ is a part of the unmaṇḍala, visible. In all the diurnal circles, the Sun S₁ etc. rising at D₁ etc. moving westward, moves a little south, little by little, until it reaches the meridian point M₁ etc., where the ‘southing’ is equal to the latitude, N NP, and then proceeds to move westward, moving north little by little, setting in the west at a point having the same amplitude as the rising point, (assuming that the declination does not change). On the two equinoxes, the Sun rises due east (D₂) and sets due west (D₂) southing on the meridian by ZM₂ (= N NP = latitude), and thus is always south of the prime vertical. So, when the declination is south, the diurnal circle (D₃D₃) is always south of the prime vertical and so the Sun (S₃) never touches the prime vertical. Even when the declination S₁S₂ (= M₁M₂)is greater than the latitude (ZM₂) then the Sun is always north of the prime vertical, the diurnal circle D₁S₁;M₁D₁ being north of it. It is this that was referred to by us as the case not mentioned by the author, viz. the case of the declination being north, but still not crossing the prime vertical, the case that is possible in the southern part of India. There is only one case left, that of the Sun’s declination being north, but less than the latitude, (e.g. the Sun moving on the diurnal circle D U S MD), in which alone the Sun crosses the prime vertical as at S. The time by which the Sun rising at D describes the part of the diurnal circle, DS, is to be found. Here there are two parts, the time from D to U which is the half-cara, and the time from U to S, i.e. the time after crossing the unmaṇḍala, which alone, we have said, has been mentioned explicitly by the author, and for which alone the rules of computation have been given by him. That is why we have said that the two times should be combined to get the time after sunrise. Of these, the method for computing the half-cara has been explained already. Therefore we shall explain the second part alone. The time to move from U to S in the diurnal circle is clearly the time to move from D₂ to S₂ on the celestial equator, and given by the arc D₂ S₂ which is to be got by solving the spherical triangle