On 29 October in DR position LAT 41°12.0'N, LONG 50°18.9'W, you take an ex-meridian observation of the Sun's lower limb, near upper transit. The chronometer time of the sight is 03h 21m 12s, and the chronometer error is 01m 50s slow. The sextant altitude (hs) is 34°54.2'. The index error is 2.0' on the arc, and your height of eye is 45 feet. What is the latitude at meridian transit?
• Ex-meridian (near-meridian) sun sight method for latitude • Correcting sextant altitude: index error, dip, and altitude corrections from the Nautical Almanac • Using the Sun’s declination and the formula that relates latitude, declination, and meridian altitude for LAN-type sights
• After applying all corrections to get Ho, think: if this were an exact meridian passage, how is latitude related to Ho and the Sun’s declination when the Sun is on your meridian and on the same side of the equator as you? • For an ex-meridian sight (a little before or after meridian transit), what small correction do you apply to the meridian altitude based on hour angle and the change of declination? • Compare your computed latitude with the DR latitude: does the result make sense for a small ex‑meridian correction, or is it unrealistically far away?
• Be sure you apply index error with the correct sign ("on the arc" vs "off the arc") and convert height of eye in feet to dip in minutes correctly. • Confirm you use the correct declination and its rate of change (d value) for the exact time of sight from the Nautical Almanac, adjusted by chronometer error. • Before picking an option, check whether the latitude should end up slightly north or south of the DR latitude, based on the Sun’s position relative to you and the sign of the ex‑meridian correction.
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