The Astronomical Observatories of Jai Singh c7.41

c7.41

20. The central part of the disc consists of a projection of a sphere and a table of sines.² These are illustrated in figure 22, where the quadrant OAB forms the table of sines. The arc AB is divided into degrees, and, from every point of division lines are drawn perpendicular to OA. The radius OB is divided into 60 equal parts, and lines are drawn parallel to OA. In the diagram sin 40° reads 39°, i.e., 39/60 or ·65, but the instrument itself is more accurate than this. The radius OD is divided into sixty equal parts, and, through each point of division, circles, also passing through the points A and C, are drawn. These arcs are orthogonal projections of great circles inclined to the meridian C¹A¹ of the sphere ABCD. For example, the arc passing through the division numbered 50 represents a circle on the sphere inclined to the meridian at an angle φ, such that sin φ = 50/60 (= ·835). Now the arc 50 in the quadrant CB touches the horizontal line 50 which cuts the arc BA at 56½, therefore φ = 56½ [actually sin 56½ = ·8339].