Adjustable errors and index error
1The lesson in plain words
Check the mirrors in order: perpendicularity, side error, index error. Index error is usually measured and allowed for, not adjusted away each time.
Three adjustable errors
Check them in this order, because each adjustment can upset the next: perpendicularity, the index mirror square to the frame; side error, the horizon mirror square to the frame; then index error, the two mirrors parallel when the reading is zero. Errors you cannot adjust, such as small faults in the arc, appear on the maker's certificate.
Perpendicularity
Set the arm near the middle of the arc. Hold the sextant flat, arc away from you, and look obliquely into the index mirror. The arc you see reflected and the real arc beside it should form one unbroken line. If the reflection looks raised or lowered, adjust the index mirror with its screw, as the maker's instructions show.
Side error
Set the reading near zero and look at a star. Turn the drum to move the reflected image past the direct image. If it passes beside the direct image instead of through it, there is side error. Adjust the horizon mirror as the maker instructs.
Index error
With the reading at zero, the real and reflected horizons should form one straight line. Usually they do not quite. Turn the drum until they do and read the index error (IE). A reading above zero is on the arc. Below zero, it is off the arc: read the drum backwards, 60′ − drum reading, so a drum reading of 58.2′ means 1.8′ off the arc.
Applying it
Index correction (IC) has the opposite sign to the error: on the arc, subtract; off the arc, add. Measure IE before each set of sights.
Sun method
With shades in place, view the Sun and its reflected image. Turn the drum until opposite limbs (edges) just touch, once on each side of zero. Use positive angular magnitudes in minutes; convert the off-arc drum reading first. IE = (on − off) ÷ 2; positive means on the arc. Check (on + off) ÷ 4 against the almanac's semi-diameter (SD), half the Sun's angular diameter. Repeat the contacts to check that IE is repeatable.
2Key data
- Order of checks
- Perpendicularity, side error, then index error
- Index error
- Reading when the mirrors are parallel: on or off the arc
- Index correction
- On the arc subtract; off the arc add
- Off-arc reading
- 60′ − drum reading: 58.2′ → 1.8′ off the arc
- Sun method
- IE = (on − off) ÷ 2; check (on + off) ÷ 4 = SD
- Spanish terms
- Error de perpendicularidad, error lateral, error de índice
3Key points
- 1
Adjust in order: perpendicularity, side error, index error.
- 2
IE on the arc: subtract; off the arc: add.
- 3
Off the arc, read the drum backwards: 60′ − reading.
- 4
Sun method: IE = (on − off) ÷ 2, checked against SD.
- 5
Measure IE before every set of sights.
4Frequent mistakes
Wrong: Index error on the arc is added to the sextant altitude.
Right: On the arc the sextant reads too high: subtract it. Add only an off-the-arc error.
Wrong: A drum reading of 58.2′ off the arc means an error of 58.2′.
Right: Off the arc the drum is read backwards: 60′ − 58.2′ = 1.8′ off the arc.
5Practice case & exam keys
Before a noon sight you measure the Sun's diameter: 33.6′ on the arc and 30.4′ off the arc. The almanac gives SD 16.0′. Find the index error and index correction, and say whether the readings are trustworthy.
Show the answer
IE = (33.6 − 30.4) ÷ 2 = 1.6′, positive, so on the arc; index correction −1.6′. Check: (33.6 + 30.4) ÷ 4 = 16.0′, which matches the almanac SD. The pair passes this consistency check, but that does not prove IE is correct. Repeat the contacts to check that IE is repeatable.
Exam keys
- Adjust in order: perpendicularity, side error, index error.
- Index correction: on the arc −, off the arc +.
- Off-arc reading: 60′ − drum reading.
- Sun method: IE = (on − off) ÷ 2; (on + off) ÷ 4 = SD.
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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