6 $t¢g-Siddhant be repeated, until the declinations of the two bodies come to be the same. By this proups are scertained the longitudes of the sun and moon nt the time when their declinations are equal. Its method may be briety explained as follows. At ahe midnight assumed as the starting-point of the whole neulation there is found to be a certain difference in he two tteelinations : we desire to determine how fas the paths of the two luminaries xmust be traced forw४rd or backward, in order that thnt difference may be removed; and this must be offected by means of a series of approximations. We commence our calculation with the moon, as being bhe body of more rapid motionBy a proportion bhe inverse of bha Upon which the rule for (teriving the declination from the longitude {i. 28) is founded, we ascertain at what longitude the moon would have the sun's actual declina tion, and at what longitude she would have her own actual declination, 15 corrected by hor latitude the difference between the two results is a measure of the atmount of motion id longitude, forward or backward, by which she would gain on loke the difference of declination, if the sun remained stationary and her own latitude unchanged. Since, howeve is not the case, we are compelled to calculate the corresponding motion of the sun, and also the moon's labitude in her new position; and in order to the latter, we must correct the place of the Hotle also for its retrograde motion during the interval. The motions of the sum and node are found by the following proportion : as the poon's daily motion is to that of the Sun, or to that of the bode, so is the correction pplied to the moon's place to that which must be upplied to the place of the sun, or to that of ahe new set of positions in longitude having thus been found, the declinations are again to be calculated, and the same approximative process repeated and so on, until the desired degree of accuracy is attained. The text permits us to apply, as the correction for the place of the moon, either the whole of the hulf of the difference of longitude found as the result of the first proportion it is upe8sential, of course, in a proces of the tentative character, what amount we 0BBurme as that of the first ७orrection, provided those which we apply to th2 places of he sun and node be made to correspond with it: and there may be caseE in which we Bhould be conducted more directly to the inal result of the proces by talking only half of the difference. 12. The aspect (pitc) is at the time of equality of declina tions; if, then, the moon's longitude, as thus increased or diminish. ed, be less than her longitude at midnight, the aspect i8 past: if greater, it is to come
