Before GPS, crossing oceans required knowing both latitude (north–south) and longitude (east–west). Two instruments made this possible:
Measures the angle between a celestial body (sun, moon, star, planet) and the horizon. At local noon, the sun's altitude yields latitude directly (with almanac corrections). At night, Polaris's altitude ≈ latitude in the Northern Hemisphere. Precision: ~0.1–0.5 nautical miles in skilled hands.
Evolution: Cross-staff → backstaff (Davis quadrant) → octant (45° arc) → sextant (60° arc, 1757, John Bird). The sextant's double-reflection principle (Newton/Hadley) allowed measuring angles up to 120°.
A precision timekeeper that maintains accurate reference time (usually Greenwich Mean Time) despite temperature, humidity, and motion. Compare local noon (sun's highest point) to chronometer time: 1 hour difference = 15° longitude.
Breakthrough: John Harrison's H4 (1761)—a large pocket watch with temperature-compensated balance spring and remontoire—won the Longitude Prize. By 1800, chronometers were standard on Royal Navy ships.
Sextant gives latitude; chronometer + sextant (for local noon) gives longitude. Two lines of position cross = a fix. Dead reckoning (course/speed/time) bridged gaps between celestial sights.
These two tools—angle and time—turned the trackless ocean into a navigable grid, enabling the age of global sail.