Table for the Duration of Sunset

Abstract

THE subjoined table was made thus:— From Table VI. in the American Nautical Almanac, for each date and latitude indicated, the hour of sunset on the meridian of Greenwich is taken and corrected for equation of time, giving an hour-angle precise within 1m. or 15′ (as both local mean time and equation of time are rounded off to the nearest minute). From latitude, declination, and this hour-angle the semi-duration of sunset in arc minutes is computed by the differential formula, (1) dP₁ = cos h dh/cos ø δ sin P₁, in which P₁= hour-angle, h = altitude of sun's centre, ø = latitude, δ=declination, and dh= sun's semidiameter. As the hour-angle found from the Nautical Almanac is for the end of sunset, it is corrected by subtracting this approximate semi-duration, and the final value in mean time seconds is found by (2) dP = 8 cos h dh/cos ø cos δ sin P, in which all sines and cosines refer to mid-sunset, declination and equation of time being constant within 1/10° or 1m.