Semi-Arc

SEH-mee-ark

Definition

A semi-arc is half of the path a planet travels across your local sky in a day or a night. Its diurnal semi-arc runs from where it rises to its highest point overhead (or from that point down to where it sets); its nocturnal semi-arc is the matching half-path below the horizon. The length depends on the planet's declination — how far north or south of the celestial equator it sits — and on your latitude. At the equinoxes, anywhere, and on the equator all year, the day and night semi-arcs each come to exactly 90 degrees.

In Tradition

In the Renaissance-Latin tradition of primary directions — Regiomontanus, Placidus, Morinus — the semi-arc is the basic measuring stick for counting time in proportion. Because the sky's daily turning carries each planet across its own personal arc, not a fixed 180-degree band, the semi-arc gives the local hour-unit: divide it by six and you get one "seasonal hour." Placidean primary directions are worked out by counting these proportional semi-arcs.

In Practice

You calculate a birth planet's diurnal semi-arc from its right ascension, its declination, and your latitude, using standard spherical-trigonometry formulae or modern software. The semi-arc then becomes the yardstick for the significator's arc of direction: the Placidean method expresses that arc as a fraction of the significator's own semi-arc, rather than as a plain difference in right ascension. The Regiomontanan method instead measures against the prime vertical, the great circle running overhead through due east and west; the Morinus method measures against the celestial equator. Because each school uses a different reference circle, the same pair of planets yields a different arc of direction depending on which method you choose.

Historical Origin

Semi-arc geometry is implied in Ptolemy's Tetrabiblos and in Almagest II.7-9, where rising times are calculated. The term itself, and its use in primary directions, was systematized in Regiomontanus' Tabulae Directionum (1467), Placidus' Tabulae Primi Mobilis (1657), and Morinus' Astrologia Gallica (1661). For a modern treatment, see Gansten's Primary Directions (2009).

Further Reading

  • Bernhard Gansten, Primary Directions: Astrology's Old Master Technique
  • Marion March & Joan McEvers, The Only Way to Learn Astrology Volume V & VI
  • Claudius Ptolemy, Almagest