Almagest

The library · The glossary

Out of bounds

every reader

What the tradition reads

Declination measures how far north or south of the celestial equator a body stands, the sky's own counterpart to latitude on Earth: points north of the celestial equator carry a positive declination and points south a negative one, and no declination can exceed ninety degrees, since the celestial poles are the northernmost and southernmost points the sky allows. The Sun's declination changes with the seasons, reaching its two extremes at the solstices, the same swing responsible for the midnight sun at high latitudes near the summer solstice and the polar night near the winter one; how far that seasonal swing can reach is set by the Earth's axial tilt, presently about twenty three and a half degrees and slowly decreasing. Astrologers who use the phrase out of bounds apply it to a planet whose declination exceeds this greatest reach the Sun's own path allows, treating that limit as an outer edge no ordinary planet crosses; a planet whose declination goes further than the Sun ever travels is, in the plainest sense, moving somewhere the Sun's own path never takes it. Neither of this entry's two sources, both articles about the astronomical coordinates themselves, discusses astrology or this specific phrase at all, so this entry limits itself to the geometry those pages actually state rather than to any particular reading a source has not been found to give it.

The story

The boundary itself is a plain consequence of the tilt of the Earth's own axis against the plane of its orbit, what astronomers call the obliquity of the ecliptic, presently measured at about 23.44 degrees. Wikipedia's axial tilt article gives the Greek letter used for this angle, epsilon, and states that the figure is not perfectly fixed: at present it is decreasing at a rate of about 46.8 arcseconds per century, so the precise boundary a chart uses shifts by a small fraction of a degree across a lifetime, though far too little to matter for any individual reading. Ancient measurements of the same angle survive from as early as about 350 BCE, when Pytheas of Marseilles measured a gnomon's shadow at the summer solstice, and later from the ninth century Baghdad court of Caliph al-Mamun and from Ulugh Beg's fifteenth century value of 23 degrees, 30 minutes, 17 seconds, so the underlying quantity has been tracked by astronomers of several different traditions long before any astrologer attached the phrase out of bounds to it. Because neither source consulted for this entry is itself an astrological text, this corpus does not claim to know when or by whom that specific astrological use began, and states that plainly rather than inventing a history for it.

Written from

Corpus key glossary:out-of-bounds.