Sextant altitude and noon latitude

How it works

Ho = Hs + index correction − dip − refraction ± semi-diameter + parallax. Index error on the arc is subtracted, off the arc added. Dip ≈ 1.76 √h minutes. Refraction by Bennett's formula for standard conditions (about 5′ at 10°, 1′ at 45°). The sun's semi-diameter is about 16′ (15.8′ in July, 16.3′ in January): add it for the lower limb, subtract for the upper. Parallax adds about 0.1′.

At noon, the zenith distance z = 90° − Ho is named opposite to the sun's bearing (sun bearing south → z north). Latitude = z ± declination: same names add, different names subtract. Example: Ho 40° 00′ with the sun south at the equinox gives 50° N. The declination comes from almanac formulas (about 0.01°) for the date and the DR longitude.