36 if the epicycle (in the beginning of the current quadrant) is greater, subtract the (above) result from it. Then is obtained the corrected epicycle. If this correction is not made, the motion (of the planet) would be like the jumping of a frog . From chapter I, starm2as 19-21, we know that the planets Mars, Mercury, Jupiter, Venus, and Saturn have two types of epicycles, manda and 31gra, which vary in size from place to place. Their values for the beginnings of odd and even quadrants were tabulated in those starm2as. The above rule gives their values for any other place of the orbit Let ८ and 3 be the values of the epicycles (numda or 3ghra) of a planet for the beginnings of odd and even quadrants respectively. Then (i) if the planet be in the first anomalistic १uadrant, say at P, and its amounaly be 8, (P-८)x Rsin 0 epicycle at P=८ + when ८. < 3, 3 + ८ - 3) x Rsin 6 and (ii) if the planet be in the second anomalistic guadrant, say at 2, and its anomaly be 90°++; ( 8 epicycle at 9=Bि when ८ < P, when ०८ >P, d-B ) x Rversin whern d. > B. Similarly in the third and fourth anomalistic quadrants. A rule relating to the calculation of the true (geocentric) long: tudes of the superior planets, Mars,Jupiter, and Saturn 33-37(i). Having added half the bahu4lhala due to the mand०८ (apbgce) t0 or subtracted that from the mean longi tude of the planet as before, the result should be subtracted from (the longitude of) the ॐgthr0c0 : that (difference) is called the ॐgrak०7dra. From that obtain the balu4hala : (and) having multiplied that by the radius, divide (the product) by the (3ghra)karta. Half the arc corresponding to the result obtained should be added or subtracted according as the 5ःghrakendra is in the half-orbit beginning with Aries or in that beginning with
