VSS. 2-4- (i)] MERIDIA-ECLIPTIC POINT 75 the true semi-duration of the day. If the geocentric conjunction of the Sun and Moon occurs in the forenoon, subtract the time of geocentric conjunction (in asus) from the true semi-duration of the day (in asus); and if the geocentric conjunction occurs in the afternoon, then from the time of geocentric, conjunc- tion (in asus) subtract the (true) semi-duration of the "day (in asus) : in both the cases the remainder denotes the asus between the times of geocentric con- junction and midday." Sankaranarayana has given the full method for finding the tropical (sayana) longitude of the meridian ecliptic point for the time of geocentric con- junction of the Sun and Moon when the geocentric conjunction occurs in the afternoon. He writes : "When the geocentric conjunction of the Sun and Moon occurs in the afternoon, then the semi-duration of the day is subtracted from the time of geocentric conjunction and thus is obtained the difference in asus between the times of geocentric conjunction and midday; the result is set down at some place; from these asus of the difference between the times of geocentric conjunction and midday are then subtracted the asus which are obtained by proportion from the untraversed portion in minutes of arc of the sign occupied by the Sun or Moon at the time of geocentric conjunction and the right ascension of the sign (i.e., the asus of the right ascension of the un- traversed portion of the Sun's sign); the untraversed portion of the Sun's sign is then added to the Sun's tropical (sayana) longitude for the time of geocen- tric conjunction; from the remaining asus are then subtracted in serial order the right ascensions of as many signs as possible and these signs are added to the Sun's longitude; finally, adding the degrees, minutes, etc., obtained on multiplying the remaining asus by 30 and dividing by the right ascension of the next sign is obtained the tropical (sayana) longitude of the meridian ecliptic point." Sankaranarayana further says, "How is the longitude of meridian ecliptic point to be obtained when the traversed or untraversed part of the Sun s sign, while being subtractive, is less than the asus intervening Between the time of geocentric conjunction of the Sun and Moon, falling near noon, and the time of midday ? There, the difference, in asus, between the times of g cocen * tric conjunction and midday is itself multiplied by 30 and divided by the right ascension o f the sign occupied by the Sun : the quotient subtracted from or added to the Sun's longitude according as the time of geocentric conjunction occurs in the forenoon or afternoon gives (the longitude of) the meridian ecliptic point." It may be pointed out that in the above determination of the meridian ecliptic point, use is to be made of the Sun's tropical longitude, because the signs of the zodiac, whose right ascensions are made use of in the obove pro- cess, are tropical (sayana). The resulting longitude of the meridian ecliptic point is also tropical.
