112 TRUB LONGITUDE OF A PLANET Initially, when the mean Sun is at U, the true Sun is at U₁. Subsequ- ently, when the mean Sun is at M, the true Sun is at T₁, such that MT, is parallel to EU. Since both the mean Sun and the true Sun have the same angular velocity relative to the apogee, the line MT, will always be parallel to EU. According to the Hindu astronomers, the tabulated (manda) epicycles are the mean epicycles (i.e., the epicycles corresponding to the mean dis- tances of the planets) whereas the true epicycles (on which the planets are supposed to move) are those which correspond to their true distances.¹ That is to say, the point T₁ in the above figure is not the position of the true Sun. According to the Hindu theory the true epicycle and the true position of the Sun, when the mean Sun is at M, are obtained as follows: Let C be a point in EU such that EC-UU₁. Join CT₁ and let it intersect the deferent at S. Produce ES and MT, to meet at T. Then MT is the radius of the true epicycle at M and T the true position of the Sun. Obviously, the epicycle varies from point to point. If denote the first point of Aries. Then Sun's mean longitude = arc TUM, and Sun's true longitude-arc TUS. The difference between the two, i.e., arc SM, is the Sun's equation of the centre. Let MA be perpendicular to EU and T,B, and SB be perpendi- culars to EM or EM produced. T₂B₁ is called bahuphala or bhujaphala and B₂M is called kotiphala. The triangles B₂MT₁ and MAE are similar. T₂B₁ T₁M MA EM' or, T₁B₁, i.e., Sun's bahuphala - T,MX MA EM Therefore, radius of Sun's mean epicycle )× Rsin (arc MU) R (Sun's tabulated epicycle) x Rsin (bahu due to the Sun's mean anomaly). 80 ¹ See BrSpSi, xxi. 29; Sise, xvi. 24; Sisi, II, v. 36-37. Also see Bhas- kara II's comm. on Siśi, II, v. 36-37; and the extract from the Adityapra- tāpa-siddhanta quoted by Amarāja in his comm. on KK, page 33.
