SUN'S TRUE LONGITUDE UNDER THE ECCENTRIC THEORY 125 Obviously, the sequences {n} and {H} are convergent. The former converges to MT and the latter to ET. It will be noticed that the convergence is rapid, so that the third or fourth approximation will give the required distance correct to the minute. In practice, the process is repeated until two successive approximations agree to minutes.¹ The process of finding the true distance of the Moon is similar. It may be added that the position and distance of the Sun or Moon derived from the eccentric theory are the same as derived from the epicy- clic theory. A rule for the determination of the Sun's true longitude (for mean sunrise at the svaniraksa place) under the eccentric theory: 21-23. Multiply the radius by the Rsine of the bhuja (due to the Sun's mean anomaly) and divide (the product) by the (Sun's true) distance. Add the arc corresponding to that (re- sult) to the longitude of the (Sun's) own apogee depending on the anomalistic quadrant (occupied by the Sun) (as follows): (When the Sun is in the first anomalistic quadrant, add) that are itself, (when the Sun is in the second anomalistic quad- rant, add) half a circle (i.e., 180°) as diminished by that arc, (when the Sun is in the third anomalistic quadrant, add) half a circle as increased by that arc, and (when the Sun is in the fourth anomalistic quadrant, add) a circle as diminished by that arc: the result is the true longitude of the Sun (for mean sunrise at the place where the local meridian intersects the equator).² This is stated to be the determination (of the Sun's true longitude) under the eccentric theory. The greatest equation ¹ In the above discussion we have assumed that the Sun is in the first anomalistic quadrant as shown in the figure. When the Sun is in the other quadrants, the process is similar. This rule occurs also in BrSpSi, xiv. 17-18 and Sise, iii. 52.
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