123: The author takes up now the Hindu eccentric theory. Here the mean Sun (or Moon) is supposed to move on a circle centred at the earth called the concentric (kakṣāvṛtta), whereas the true Sun (or Moon) is supposed to move on another equal circle called the eccentric (pratimaṇḍala) with the same angular velocity as the mean Sun (or Moon) has. The centre of the eccentric is supposed to be deviated from the Earth towards the Sun's (or Moon's) apogee by an amount equal to the Rsine of the Sun's (or Moon's) greatest equation of the centre. TRUE DISTANCE OF THE SUN OR MOON In Fig. 13, the circle UMNY centred at E, the Earth, is the concentric and the circle U₁T₁L centred at C is the eccentric for the Sun. When the mean Sun is at U, the true Sun is at U₁(the apogee). Subsequently, when the mean Sun is at M, the true Sun is at T₁. Since the mean Sun and the true Sun have the same angular velocity relative to the apogee, the line MT, will always be parallel to the apse line EU. Let XY be perpendicular to EU through E, and T₂B perpendicular to XY. Then in the triangle T,BE, right- angled at B, we have BE=MA=Rsin (arc MU), and T₂B T₂M + MB = EC+ Rsin (arc MX), where the arc MX is the koți and EC is the Rsine of the greatest equation of the centre for the Sun. = L X U1 W U K A N Fig.13. 8 Y Had the length EC been cqual to the radius of the Sun's true epicycle for the mean sun at M,T,E would have been the Sun's true distance, but EC corresponds to the radius of the Sun's tabulated epicycle, which is mean and not true, therefore T₁ is not the true position of the Sun and likewise T,E is not the true distance of the Sun. The true distance is determined as follows: Join T,C and let it intersect the concentric at S. Produce MT₁ and ES to meet at T. Then MT denotes the true distance between the centres of the concentric and the eccentric, T the position of the true Sun, and ET the true distance of the sun.
