Length of daylight (1)

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A particular modification of an early scheme in Babylonian astronomy has greatly influenced ancient geography - these are the arithmetical patterns for relating the variable length of daylight to the position of the sun in the ecliptic. This simple scheme exists in two variants, “System A,” strictly linear, and “System B” with double the ordinary difference in the middle of the increasing and decreasing branches. This scheme was adapted, probably in the second century BCE, to the latitude of Alexandria and subsequently to other geographical latitudes. The earliest source is Hypsicles’ Anaphorikos. There is no trace in Babylonian astronomy for the concept of geographical latitude and consequently for provisions necessary for the adaption of their procedures for localities other than Babylonia. The Hellenistic world of Alexandria had far greater extensions, and obviously the Babylonian scheme for the variation of the length of days and nights did not fit for such an area. But the mathematical device in itself was simple and easy to modify - in a typical Babylonian fashion by a linear variation of the extremal length of daylight but otherwise unchanged pattern. According to this scheme one distinguishes “climates” of equal length of daylight, arranged in the simple pattern of half-hour increment of the longest day.

The strictly Babylonian procedure was eventually eliminated when Greek spherical trigonometry replaced the cruder arithmetical patterns, probably shortly before Ptolemy. But, as a concept, the sequence of the climates of linearly increasing length of the longest day remained unchanged and dominated geographical lore from antiquity through Islam and the western Middle Ages. Simultaneously the original Babylonian scheme remained in use in the astrological literature, e.g. in the Anthology of Vettius Valens (second century CE). Even such details as the definition of the eighth degree of Aries as the solar position at the vernal equinox are occasionally preserved. With the astrological literature the Babylonian scheme spread to India, where we find the unchanged Babylonian system A in the writings of Varaha Mihira (6th century CE) applied for latitudes entirely different from Babylon. Intelligent modifications of the Babylonian arithmetical scheme for the latitude of Persia are described by al-Bīrūnī (around 1000 CE) as used by “the people of Babylon”.

Bibliography

Amar Annus

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