76 SA SB = Rsin a. Rsin (given time in asus asc. diff.) × day-radius LSBA and SAB DIRECTION, PLACE AND TIME 90º-, 90°, where a is the Sun's altitude, and the latitude of the place. Therefore, we have Rsin a = Hence the rule. = SBX Rcos R radius Rsin a = S A Fig. 7 An approximate rule for finding the Sun's altitude: 21. Multiply "the upright due to the instantaneous meridian-ecliptic point" by the Rsine of the degrees intervening between the Sun and the rising point of the ecliptic and then divide (the product) by the radius: the result is the Rsine of the Sun's true altitude. The square root of the difference between the squares of that and the radius is the Rsine of the Sun's zenith distance. 1 See the next stánza. "The upright due to the meridian-ecliptic point" is the Rsine of the altitude of the meridian-ecliptic point. Therefore, the rule stated above may be expressed as + earthsine, Rsin x Rsin (L- -S). R B 2 where a is the Sun's altitude, the altitude of the meridian-ecliptic point, L the longitude of the rising point of the ecliptic, S the longitude of the Sun, and R the radius of the celestial sphere (= 3438'). The rising point of the ecliptic is that point of the ecliptic which lies on the eastern horizon. This formula is approximate, because the distance between the rising point of the ecliptic and the meridian-ecliptic point is not always exactly equal to 90° as assumed there.
