Arc of direction and direct vs. converse motion

Meaning

The arc of direction (arcus directionis, written ΔRAMC) is the fundamental angular measurement of a primary direction. Measured in degrees, minutes, and seconds along the celestial equator, it is the exact rotational angle through which the Midheaven's right ascension (RAMC) advances after birth until the promissor and significator share the same horizon-meridian coordinate.

Once the equatorial arc ΔRAMC is solved on the sphere, a primary direction time-key converts that arc into years, months, and days of life.

Direct vs. Converse Motion

Because primary directions are caused by the diurnal westward rotation of the heavens (the Primum Mobile), which carries degrees of higher right ascension (later zodiacal degrees) westward toward degrees of lower right ascension, every pair of points can meet in two ways:

1. Direct Motion (Direct): The significator's natal mundane seat (its proportional semi-arc fraction f or circle of position) remains fixed as a geometric target in the local sky, while the promissor is carried westward by the diurnal rotation of the sphere until it reaches that seat. Because later zodiacal degrees rise and culminate after earlier degrees, a direct promissor lies later in zodiacal order (in the signs following) than the significator.
2. Converse Motion (Converse): In Traditional Converse doctrine (Ptolemy, Placidus, Lilly), the significator itself is carried westward by true diurnal rotation after birth until it arrives at the promissor's fixed natal mundane seat. Both Direct and Traditional Converse directions are driven by the same forward, clockwise diurnal turning of the sky after birth; they differ only in which body holds its natal mundane seat and which body is carried by the sphere [1][3]. (By contrast, Neo-Converse or "Regressive" motion turns the celestial sphere backward in time prior to birth.)

How the Arc is Solved Across the Four Principal Schools

For a direction to the Midheaven (MC), all spherical schools agree: the arc of direction is simply the difference in right ascension (Δα = α_P − α_S). For a direction to the Ascendant (ASC), all schools likewise agree: the arc is the difference in Oblique Ascension (OA = α − AD) at the birth latitude φ.

When the significator lies between the horizon and meridian (for example, the Sun in the 10th house or Moon in the 8th house), the four classical schools define the intermediate mundane position differently: