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Octant
Brief description
An octant (also known as a reflecting quadrant) is a celestial navigation instrument that measures the angular altitude of the sun, moon, or stars above the sea horizon. Invented independently around 1730 by John Hadley in England and Thomas Godfrey in Pennsylvania, the octant introduced the revolutionary principle of double reflection. Its 45-degree mechanical arc (an eighth of a full circle) measures angular separations up to 90 degrees, allowing mariners to determine their geographical latitude accurately even aboard a rolling ship without the sight alignment errors inherent in earlier instruments.
Use / Function
- Latitude Determination: Measuring noon solar altitude or the height of Polaris to compute exact navigational latitude at sea.
- Lunar and Celestial Sighting: Observing the angular distances of stars or celestial bodies relative to visible planetary horizons.
- Coastal Navigation: Measuring horizontal angles between recognized coastal landmarks, headlands, and lighthouses for position fixing.
- Scale: Essential shipboard navigation equipment for exploratory, commercial, and naval vessels.
Operating principle
- Law of Reflection: When a ray of light strikes a plane mirror, the angle of reflection equals the angle of incidence.
- Double Reflection Angular Doubling: When a beam of light undergoes two successive reflections in the same plane by mirrors inclined at an angle $\theta$, the total angular deviation of the light beam is exactly $2\theta$.
- Horizon and Index Mirrors: Light from the horizon passes directly through the transparent half of a split horizon glass into the observer’s sighting telescope or pinhole. Light from the celestial target strikes an adjustable index mirror mounted on a pivoted index arm, reflects onto the silvered half of the horizon glass, and reaches the eye.
- Coincidence Alignment: The navigator rotates the index arm until the reflected celestial body appears to rest directly on the visible horizon line.
- Direct Arc Reading: Because the reflected angle is doubled, each degree on the 45-degree limb corresponds to two degrees of celestial elevation, allowing direct measurement from 0 to 90 degrees.
How to create it
- Frame Fabrication: Cut and construct a sturdy triangular frame with a curved 45-degree arc limb from seasoned mahogany, ebony, brass, or stable hardwood.
- Mount the Pivot and Index Arm: Attach a rigid brass index arm pivoted at the geometric apex of the arc, extending across the graduated limb.
- Position the Index Mirror: Mount a flat silvered glass mirror precisely perpendicular to the plane of the frame directly over the pivot center.
- Position the Horizon Glass: Mount a split mirror (half silvered, half clear glass) on the frame parallel to the index mirror when the index arm is set to zero degrees.
- Calibrate the Arc: Accurately scribe angular divisions along the arc limb using precision dividers, numbering each half-degree as a full degree (0° to 90°).
- Add Sight Vane and Dark Filters: Affix a pinhole sight vane or low-power sighting tube, and attach hinged colored glass shades between the mirrors to protect the observer’s eyes during solar observations.
Materials needed
- Essential: Well-seasoned Wood (such as ebony, rosewood, or mahogany) or cast Metal (brass) for the rigid frame; flat optical Glass for the index mirror and split horizon mirror.
- Tools: Scribing compass/dividers, jeweler’s saw, protractor, small brass screws, files, polishing stones.
- Substitutes: Polished speculum metal or silvered plate glass for mirrors; bone or ivory inlays for scribe lines on wooden limbs.
Variants and improvements
- Hadley’s Reflecting Quadrant: The original wooden-framed instrument with pinhole sight and tinted sun filters.
- Back-Observation Octant: Included an auxiliary mirror system enabling observers to sight the horizon behind them when the horizon beneath the sun was obscured by haze or land.
- Navigational Sextant: Expanded the arc from 45 degrees (one-eighth circle) to 60 degrees (one-sixth circle), enabling angular measurements up to 120 degrees necessary for lunar distance longitude calculations.
- Brass Vernier Octant: Replaced diagonal scales and pinholes with brass vernier scales and magnifying sighting telescopes for sub-arcminute precision.
Limits and risks
- Index Error: Any deviation from perfect parallelism between mirrors at the zero mark introduces a systematic angle offset that must be measured and corrected before every observation.
- Retinal Damage: Sighting the sun directly without properly aligned dark tinted filters will cause permanent eye damage or blindness.
- Horizon Obscuration: Dependent on a sharp, clear natural sea horizon; unusable in fog, dense haze, or on dark nights without an artificial horizon trough.