Day. In historical terms, the fundamental measure of time, caused by the rotation of the Earth on its axis. It is defined by the time taken for the Sun to occupy exactly the same position in the sky on successive occasions such as sunrise to sunrise, sunset to sunset, midday to midday or midnight to midnight. More formally, the solar day is usually taken as the period between two successive solar culminations.
In modern terms the civil day starts at midnight (lower culmination of the Sun) and is defined as 86400 (= 24 × 60 × 60) seconds. However, since the second was redefined atomically in 1967, the day averages about 86400.002 seconds owing to the fact that the rotation of the Earth is not completely uniform but varies by up to 8 seconds per day and is in fact gradually slowing down by 1.7 milliseconds per century owing to the tidal effect of the Moon. Every few years a leap second is added to correct the ensuing anomaly. By contrast, the stellar day is the time taken for a given distant star to reappear in the same position in the sky. This is shorter than the solar day by 3 minutes and 56 seconds.
The length of the day is governed by the latitude of the observer and the time of year. In ancient Greece the variation in the length of the day by latitude was probably first discovered by the early colonists and traders in the seventh and eighth centuries BCE who travelled north to the Black Sea and south to Egypt and noticed that the longest day in the former region was longer than the longest day in the latter. Later, in Hellenistic times, the variation was quantified by astronomers such as Eratosthenes and Hipparchos. Determining the longest day and correlating it with latitude played an important part in the development of mathematical geography.
In modern terms the longest day can be found from the formula below (valid from the equator to the arctic or anarctic circles, latitudes 0° to ±66.561°):
cos ω = [ sin r – sin φ sin δ ] / [ cos φ cos δ ]where ω is the solar hour angle measured as positive or negative from the meridian, φ is the observer's latitude and δ is the solar declination. The quantity r is the atmospheric refraction plus the Sun's angular radius. This can be set to 0° if a purely geometric result is required or to a known, or commonly accepted value, such –0.833°, for a more realistic answer. The solar declination is given by sin δ = sin λ sin ε, where λ is the solar ecliptic longitude (90° for the longest day, 270° for the shortest) and ε is the obliquity of the ecliptic.
Once cos ω is known then the length of the longest day in hours is simply 2ω/15 (for the shortest day, multiply cos ω by –1). The table below shows the shortest and longest days around 150 BCE for the latitudes familiar to the ancient Greeks together with indicative cities.
| Latitude° | Longest Day (hh:mm) | Shortest Day (hh:mm) |
|---|---|---|
| 30 (Memphis) | 13:58 | 10:02 |
| 31 (Alexandria) | 14:02 | 09:58 |
| 32 (Jaffa) | 14:07 | 09:53 |
| 33 (Kyrene) | 14:13 | 09:47 |
| 34 (Beirut) | 14:18 | 09:42 |
| 35 (Kition) | 14:23 | 09:37 |
| 36 (Lindos) | 14:29 | 09:31 |
| 37 (Syracuse) | 14:35 | 09:25 |
| 38 (Athens) | 14:41 | 09:19 |
| 39 (Mytilene) | 14:47 | 09:13 |
| 40 (Troy) | 14:53 | 09:07 |
| 41 (Naples) | 14:59 | 09:01 |
| 42 (Rome) | 15:07 | 08:53 |
| 43 (Marseille) | 15:13 | 08:47 |
| 44 (Constanta) | 15:21 | 08:39 |
| 45 (Chersonesos) | 15:28 | 08:32 |
These are actual times taking into account typical atmospheric refraction. It can be seen that over the latitudes that the ancient Greeks were most familiar with, the length of the longest and shortest daya varied by about an hour and half.
Declination (δ). The orthogonal angular distance, measured in degrees, of a celestial object above or below the celestial equator. Along with right ascension it is one of the two coordinates of the equatorial coordinate system. It is the astronomical equivalent of terrestial latitude and ranges from –90° to +90°.
Doxography. The writings that constitute the ancient Greek tradition of making anthologies, compilations and summaries of earlier books. This went on for several centuries from the C3rd BCE up to the C6th CE. A doxographical source might well be an abridgement of an anthology of several older books each of which might in turn be a summary of an earlier book. Sometimes in such writings it is hard to distinguish genuine quotation from paraphrase. Generally, the doxography derives ultimately from the work of Aristotle's students in the C4th BCE who wrote about earlier philosophers or histories of specific topics such as astronomy, mathematics and philosophy. Amongst them are: Aristoxenos of Tarentum (c. 375 – c. 310), Eudemos of Rhodes (c. 370 – c. 300), and (mostly) Theophrastos of Eresos (371 – 287).
Draconic Month.
