Increments and corrections: the Sun's GHA and Dec, worked
1The lesson in plain words
Take hourly GHA and Dec. Add the time increment to GHA, add or subtract the d correction, then use longitude to find LHA.
The tinted pages
The Increments and Corrections tables, on tinted pages near the back, have one table for each minute, 0m to 59m. Each lists, second by second, the GHA increment for the Sun and planets (15° an hour exactly), Aries (15°02.46′ an hour) and the Moon (14°19.0′ an hour). Beside them, the v or d corrections give the extra for a given v or d at that minute.
Worked: the time
26 November 2026, morning, DR 21°05′N 027°20′W. Sun lower limb observed at deck watch 10-14-38. The watch was checked against GNSS: 12 s fast. UT = 10h 14m 38s − 12 s = 10h 14m 26s, still 26 November. With ZD +2 the ship's clock read about 0814.
Worked: GHA
GHA at 10h from the daily page: 333°11.2′. Increment for 14m 26s, from the 14m table, Sun and planets column: 3°36.5′. Check: 14 min × 15′ = 3°30.0′, plus 26 s × 15″ = 6.5′. GHA = 333°11.2′ + 3°36.5′ = 336°47.7′.
Worked: Dec
Dec at 10h: S 20°58.5′; at 11h S 20°59.0′, so the S magnitude is increasing: add. d = 0.5. The 14m table's v or d column gives 0.1′ for d 0.5. Dec = S 20°58.6′. Enter 26 November 2026, 10:14:26 UT in USNO's celestial-navigation service: GHA 336°47.6′, Dec S 20°58.6′. The GHA differs by only 0.1′.
Worked: LHA
LHA = GHA − west longitude = 336°47.7′ − 27°20.0′ = 309°27.7′. It is over 180°, so the Sun is east of you, as it should be in the morning. DR latitude, Dec and LHA are the inputs to sight reduction (Celestial: sight reduction).
2Step by step
Sun's GHA, Dec and LHA for a sight
- 1
Correct the watch time to UT and check the date.
The almanac is in UT; a wrong hour or day ruins the sight.
- 2
Take GHA and Dec for the whole hour from the daily page.
The page gives them only on the hour.
- 3
Add the increment for the minutes and seconds, Sun column.
The tinted table for that minute gives it second by second.
- 4
Apply the d correction to Dec, with the sign from the trend.
Dec changes up to about 1′ an hour.
- 5
Find LHA: add east longitude, subtract west, keep within 0–360°.
Sight reduction needs the angle from your own meridian.
3Key data
- Sun and planet increment
- 15° an hour: 15′ a minute, 15″ a second
- Aries increment
- 15°02.46′ an hour
- Moon increment
- 14°19.0′ an hour, plus v
4Key points
- 1
Whole hour from the daily page, minutes and seconds from the increments.
- 2
Use the column for your body: Sun and planets, Aries or Moon.
- 3
Apply d from the v or d column, sign from the trend.
- 4
LHA over 180° means the body is east of you: morning for the Sun.
5Frequent mistakes
Wrong: Use the Aries column for the Sun's increment.
Right: Aries runs 15°02.46′ an hour; the Sun and planets column uses 15° an hour. The difference grows to about 1.2′ by the 30th minute.
Wrong: Apply the d correction for the whole hour.
Right: Take it from the table for the minutes past the hour; at 14 minutes, d 0.5 gives only 0.1′.
6Practice case & exam keys
Same day, 26 November 2026, a sight at 13h 38m 00s UT, DR longitude 027°45.0′W. Daily page at 13h: GHA 18°10.6′, Dec S 20°59.9′, d 0.5, S magnitude increasing. A crew member gets a negative LHA and changes to adding west longitude. Is that justified? Give the corrected results.
Show the answer
Increment 38m 00s = 9°30.0′, so GHA = 18°10.6′ + 9°30.0′ = 27°40.6′. d correction at 38m for d 0.5: 0.3′, added: Dec S 21°00.2′. LHA = 27°40.6′ − 27°45.0′ = −0°04.4′, plus 360° = 359°55.6′. Reject that change: subtract west longitude, then add 360° to wrap the negative result. The Sun is just east of your meridian, approximately local noon.
Exam keys
- GHA = hourly GHA + increment (Sun/planets 15°/h; Aries 15°02.46′/h; Moon 14°19.0′/h + v).
- Dec = hourly Dec ± d correction for the minutes; sign from the trend.
- LHA = GHA + E long − W long, within 0–360°.
Finish this unit
When you've read it, answer three questions. Get all three right to finish the unit; opening the page alone doesn't count.
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