On 24 September your 1841 zone time DR...

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Question 1 of 2066636eea28f7522a1c51ad93

On 24 September your 1841 zone time DR position is LONG 129°34.5' E. At that time you observe Polaris with a sextant altitude (hs) of 25°20.8'. The chronometer time of the sight is 09h 38m 12s, and the chronometer error is 03m 12s slow. The index error is 4.3' off the arc, and the height of eye is 52 feet (15.9 meters). What is your latitude by Polaris?

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🔍 Key Concepts

• Polaris latitude formula for mid‑northern latitudes (approximate latitude ≈ corrected altitude of Polaris with small corrections) • Proper sextant altitude corrections: index correction, height of eye (dip), and atmospheric refraction to get Ho (observed altitude) • Daily Polaris corrections from nautical tables (correction for date and longitude)

💭 Think About

• First, convert the sextant altitude (hs) to apparent altitude and then to Ho step by step. Are you applying the index correction with the correct sign for an error "off the arc"? • After you find Ho, think about how Polaris’ altitude relates to your latitude in the Northern Hemisphere. Is your latitude slightly greater or slightly less than Ho for this date and longitude? • How does the date (24 September) and your longitude in the western or eastern hemisphere affect the small Polaris correction from the tables?

✅ Before You Answer

• Be sure the index error sign is handled correctly: off the arc vs. on the arc gives opposite signs for the index correction. • Confirm you have applied dip (height of eye) with the correct sign (it is always subtracted from the sextant altitude). • After all corrections, check that your final latitude makes sense: it should be close to the corrected Polaris altitude, with only a small adjustment (less than a degree).

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