THREE POINTS ON THE LOCUS OF THE SHADOW-END 89 To determine at any given time three points lying on the locus of the shadow-end : 42-45. Determine the agrā and sankvagra of the Sun and also the shadow (of the gnomon) for the desired time. Then take the sum of the two agras (i.e., of agra and sankvagra) provided that they are of like direction¹; in the contrary case, take their difference. (This sum or difference is called the bhuja and its direction corresponds to that of the Sun from the prime verti- cal.) By that (sum or difference) multiply the shadow and divide (the product) by the Rsine of the Sun's zenith distance (for that time). Whatever is thus obtained should be laid off from the centre in the contrary direction (i.e., contrary to the direction of the Sun from the prime vertical) within a circle (drawn on level ground and) marked with the directions. Through the fish-figure drawn about the point thus obtained stretch out a thread in the east and west directions (bothways) to a distance. Then take a thread equal in length to the shadow (of the gnomon) and lay it off from the centre obliquely (to meet the other thread). Mark the two points where the end of this thread meets (the other thread stretched out) in the east and west directions. At the end of the midday shadow take a third point. The sum or difference of the agrā and śaḥkvagra² of the Sun denotes the distance of the Sun's projection on the plane of the horizon from the east-west line. This is called the bhuja and its direction is the same as that of the Sun from the prime vertical. This multiplied by the length of the shadow of the gnomon and divided by the Rsine of the Sun's zenith distance gives the distance of the end of the shadow of the gnomon from the east-west line. Suppose, for example, that the sun is towards the south of the prime vertical, and that the end of the shadow of the gnomon is at a distance d from the east-west line. Let the circle in Fig. 10 be the one constructed on level ground with ¹ The agra is north or south according as it is towards the north or south of the east-west line; the sankvagra is always south. 2 For agrā see supra stanzas 37-38, and for sankvagra see infra stanza 54,
