An alternative —and older notion— is to consider that solstices occur when the Sun makes its most northerly or southerly rising on the eastern horizon (or equivalently, when it makes its most northerly or southerly setting on the western horizon). In the northern hemisphere, the summer solstice occurs when the Sun rises in the most northerly position, and the winter solstice when it rises in the most southerly position. For the southern hemisphere these positions are again reversed.
This latter method may be termed the horizontal definition of the solstice, and was typically used in prehistory and in Greece up to the C4th BCE, whereas the former method may be termed the vertical definition of the solstice and was typically used by astronomers like Hipparchos (C2nd BCE) and Ptolemy (C2nd CE).
The name 'solstice' comes from the Latin word solstitium which means 'stationary Sun' from sol 'Sun' and sistere 'to stand still', or as the C1st BCE Roman writer Varro explains it (On the Latin Language 6.2):1
Dicta . . . solstitium, quod sol eo die sistere videbaturThis is a good description since, as the Sun approaches, day by day, its highest or lowest midday point in the sky, or its most northerly or southerly rising, it appears to slow down and, for a few days on either side of the solstice, its position relative to the previous or following day hardly changes.
Called . . . 'solstice' because on that day the Sun seemed to stand still
The Greeks, however, took a slightly more dynamic viewpoint and referred to the solstice as a τροπή 'turning', often in the full form ἠελίοιο τροπή 'turning of the Sun' which occurs as early as Hesiod (fl. c. 700 BCE)2, or more specifically as τροπή θερινή for 'summer solstice' and τροπή χειμερινή for 'winter solstice', which is to be found in C5th BCE writers such as Herodotos and Thucydides. This probably reflects more of a horizontal than a vertical viewpoint amongst the early Greeks. (A term meaning 'stationary Sun', ἠλιοστασία, is indeed found but only as a translation of the Latin word and does not seem to have had general currency).
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The Sun appears to move along the ecliptic and thus changes its position relative to Earth.
Image: Wikimedia Commons.
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More formally, a solstice occurs when the Sun appears from Earth to be at its maximum angular distance from the celestial equator. This happens twice per year at a specific date and time owing to the inclination of the Earth's rotational axis to the plane of its orbit around the Sun. In theory, a solstice could be specified to the nearest second but in practice, even with modern techniques, it is seldom determined more accurately than to within a minute.3 The limit of the Sun's angular distance from the celestial equator is set by the obliquity of the ecliptic (the apparent path of the Sun in the sky) which is currently 23.439°. Therefore, when the Sun reaches its maximum excursion from the celestial equator (which from the point of view of an observer on Earth can happen during the day or the night), its declination is either +23.439° or –23.439°. On these occasions the Sun is vertically above an imaginary line of latitude on Earth, called a 'tropic' since at this point the Sun will be seen to turn either north or south depending on the solstice.
At the summer solstice in the northern hemisphere the Sun is aligned with the zodiacal constellation of Gemini and with the zodiacal constellation of Sagittarius at the winter solstice (vice versa for the southern hemisphere). That is to say, if you could see the stars in the same part of the sky as the Sun is currently situated (but you can't because of the brightness of the Sun), those stars would be the ones in the constellations of Gemini and Sagittarius. So we could call these lines of latitude the Tropic of Gemini and the Tropic of Sagittarius respectively. But we don't, we call them the Tropic of Cancer and the Tropic of Capricorn instead. Why? The answer is that when these reference points were established over 2000 years ago (probably by Hipparchos around 140 BCE) the Sun was aligned with the signs of Cancer and Capricorn at the solstices. Since that time, the solstices have moved by a little over 30° in ecliptic longitude —one whole zodiacal sign— owing to precession. However, because of the innate conservatism of astrology (one of the main drivers for astronomical research from the C2nd BCE until the C17th CE), we still keep the original names.
How did ancient people work out the dates of the solstices and why did they try to do it? The second part is relatively easy to answer. The solstices (and the equinoxes) determine the course and the seasons of the year. The summer solstice is effectively midsummer and the winter solstice is effectively midwinter. For the agricultural communities of the past, it was important to know these reference points of the year. Indeed, many neolithic structures in Europe and beyond, such as Stonehenge in Britain, Newgrange in Ireland and Goseck in Germany, have been shown to be aligned with sunrise and sunset at the times of the solstices. In ancient Greece, too, these considerations applied, but we also find that, beginning in the late C6th BCE, there were attempts to determine how long the year was overall. As societies grew more complex and moved beyond subsistence farming to incorporate larger political and religious structures, people wanted to know with increasing exactitude when one year ended and another started. Frequently, the main motivation was to celebrate important festivals at the right time. Determining the dates of the solstices (and equinoxes) played an important part in this.
So, how did the Greeks determine the dates of the solstices? The truth is we don't know in detail since there is no step by step instuction guide that has come down to us from antiquity (at least for the earliest times) and it is likely that local solutions differed in details. However, we do have a general idea of their approach to the problem.
And it is a problem. Finding the day of the solstice, let alone the time, is actually quite hard, as the most celebrated astronomer of ancient times, Ptolemy, noted (Almagest 3.1; H1.203). In the 24 hours on either side of the solstice, for example, the declination of the Sun varies by only around 30 seconds of arc, which is just one sixtieth of the Sun's diameter. Even Ptolemy, who was able to call upon centuries of collective astronomical experience, couldn't get it right to within a day. This is because the Sun at its solstice (almost by definition) moves so slowly. Equinoxes, by comparison, are somewhat easier to determine because the Sun appears to move more quickly.
As stated above, the older horizontal method involves noting where the sun rises on the eastern horizon over successive days in order to determine the day on which the sun rises at its most northerly point for the summer solstice or the most southerly point for the winter solstice.4 Clearly, for this to work a cloudless horizon is required, as is a horizon with sufficient distinctive features by which to compare the position of the Sun. Around the summer solstice, the azimuthal (horizontal) movement of the Sun at the latitude of Athens, for example, is given by the table below:
| Days around solstice | Azimuth | Relative Azimuth |
|---|---|---|
| –15 | 60° 19' 22'' | 1° 02' 24'' |
| –10 | 59° 45' 12'' | 0° 28' 14'' |
| –05 | 59° 23' 51'' | 0° 06' 53'' |
| –02 | 59° 18' 06'' | 0° 01' 08'' |
| –01 | 59° 17' 14'' | 0° 00' 16'' |
| 0 (solstice) | 59° 16' 58'' | 0° 00' 00'' |
| +01 | 59° 17' 28'' | 0° 00' 30'' |
| +02 | 59° 18' 16'' | 0° 01' 18'' |
| +05 | 59° 24' 22'' | 0° 07' 24'' |
| +10 | 59° 46' 02'' | 0° 29' 04'' |
| +15 | 60° 21' 25'' | 1° 04' 27'' |
It can be seen from this that even ten days before or after the solstice the Sun has only moved along the horizon about 27 minutes of arc which is less than its own diameter (32'). Only over a period of about a month could the Sun be perceived to have moved twice its diameter. The difficulties of observing are further compounded by the phenomenon of refraction which distorts the circular disk of the Sun on the horizon, not to mention the weather, of course. All of which demonstrates that trying to observe the solstice by means of the sunrise on the horizon does require: a) a suitable horizon with some kind of marker; b) systematic observation and recording over at least a month; c) interpolation of the results.
The vertical method of determining the solstice involves using or measuring shadows in some way. Unlike at sunrise, one cannot look at the Sun when it is high in the sky. The simplest and earliest method was to measure the length of the midday shadow of an upright pole called a gnomon. This actually entails two sets of measurements: the first to determine when midday occurs on a specific day and the second to repeat these measurements every day on either side of the solstice until one has enough measurements to do a reasonable interpolation in order to find when the shadow was at its shortest. Later techniques involved using a meridian ring or a quadrant to cast a shadow at a particular point, or in a particular way, which could then be read off on a graduated scale. It must be remembered that the Greeks had no way to measure the time of day accurately. The only mechanical device was a water clock, the klepsydra, whose accuracy was perhaps to within a quarter of an hour, and certainly not to within a minute.
When these considerations are taken into account, measuring the length of the gnomon's shadow at its shortest is not easy. The shadow must fall upon a smooth flat surface and preferably one that is perfectly level. Moreover, the phenomenon of edge diffraction and, principally, the fact that the Sun is not an ideal point source of light, causes the shadow itself to be somewhat fuzzy in outline and this gets worse if the gnomon is made taller. Even the act of measuring was not straightforward since the Greeks did not have accurately graduated rulers with millimetre divisions, although this sort of mechanical technology did gradually improve over the centuries. Above all, there is the same difficulty that besets the horizontal method, namely that the Sun, day by day, just does not move very much when near to the solstice and neither, therefore, does the shadow. The table below shows the solar altitude and theoretical shadow lengths at midday of a hypothetical 2 metre gnomon at the latitude of Athens for various dates around the solstice of 28th June 400 BCE (which actually happened around sunrise).
| Date | Time | Max Altitude (a) | Shadow (2000 mm × cot a) |
|---|---|---|---|
| 13th June | 11:54 | 75°01'35'' | 534.9 mm |
| 18th June | 11:55 | 75°26'49'' | 519.2 mm |
| 23rd June | 11:56 | 75°41'50'' | 509.9 mm |
| 26th June | 11:56 | 75°45'51'' | 507.4 mm |
| 27th June | 11:57 | 75°46'20'' | 507.1 mm |
| 28th June | 11:57 | 75°46'26'' | 507.0 mm (solstice) |
| 29th June | 11:57 | 75°46'05'' | 507.3 mm |
| 30th June | 11:56 | 75°45'19'' | 507.7 mm |
| 3rd July | 11:58 | 75°40'30'' | 510.7 mm |
| 8th July | 11:59 | 75°24'04'' | 520.9 mm |
| 13th July | 12:00 | 74°57'16'' | 537.6 mm |
As can be seen from the table, taking a series of measurements from at least ten days and probably fifteen days on either side of the solstice would be necessary in order to pin down the correct day when the shadow was at its shortest. Furthermore, the altitudes of the Sun do not increase and decrease symmetrically, meaning that a simple interpolation for maximum altitude is not going to be completely accurate, although it will be close. The deviation of the times from 12:00 for midday is due to an anomaly in the Sun's apparent motion called the equation of time.
What do we know of how solstices were actually observed in ancient Greece and who carried them out? For the early period, the C4th BCE philosopher and student of Aristotle, Theophrastos, tells us this (On Weather Signs, ed. Hort 1916, II.4):5
And so in some regions are found good astronomers who observed the solstices such as Matriketas in Methymne by means of Lepetymnos, Kleostratos in Tenedos by means of Ida, and Phaeinos in Athens by means of Lykabettos, from whom Meton, who made the 19 year cycle, learned his craft (Phaeinos was a resident foreigner in Athens, Meton an Athenian). Other astronomers have made similar observations of the solstice.Of Matriketas nothing else is known, and very little else of Phaeinos. But we do have other information about Kleostratos and Meton. Before we look at them, however, it should be noted that it is clear from the descriptions that these are all horizontal observations using distant mountains as a horizon marker. Mount Lepetymnos is about eight kilometres east–southeast from the town of Methymne on the island of Lesbos, and Mount Ida is seventy kilometres east–southeast of Tenedos. Therefore, these observations are of the winter solstice (sunrise is south of due east). By contrast, Mount Lykabettos is two and a half kilometres east–northeast of the presumed observing point near the Pnyx in Athens and is, therefore, connected with the summer solstice (sunrise is north of due east).
Discounting Matriketas, the earliest of these astronomers is Kleostratos of Tenedos, whom we know from other sources to have flourished around 520 BCE. His observation is certainly possible since, although Mount Ida lies about 70 kilometres on the mainland east–southeast of the island of Tenedos, it is 1770 metres high and is visible from a suitable vantage point on Tenedos on a clear day. Tenedos is a relatively flat island but there is a prominent hill 185 metres in height in the northeast and this provides uninterrupted views of the mainland. Because the bearing of Mount Ida is 103° from this spot on Tenedos we know that when Kleostratos observed a solstice from here it must have been the winter solstice.
For all the reasons stated above, the observation was not likely to have been very accurate, but using interpolation and Mount Ida as a reference point an obvious strategy would have presented itself. The winter solstice in 520 BCE took place on 29th December around 17:00. On that day the Sun's azimuth at sunrise was 120° 45', well to the south of Mount Ida as viewed from Tenedos. Two months earlier, sunrise had been aligned with the mountain (azimuth 103°) on 26th October and would be so again on 27th February, a total span of 124 days. Dividing this by two and adding it to our date for the first alignment gives us the interpolated date for the most southerly excursion of the Sun, namely 27th December. This is two days too early because the apparent movement of the Sun is not completely symmetrical around the solstice, but it is not at all bad for such a simple method.
In Athens, Theophrastos refers to the observation of Phaeinos, but we'll look at his student Meton since we know from Ptolemy (Almagest 3.1; H1.205–6) that he, following in the footsteps of his teacher, also made solstice observations with his student Euktemon in Athens. Not only that, but Ptolemy (who possessed much historical material that is lost to us) tells us that observations were made of the summer solstice in 432 BCE and that Meton determined it to have occurred on 27th June at dawn (meaning possibly that he just made the observations at sunrise rather then sunset). Modern calculation shows the solstice to have occurred on 28th June at 10:26 by right ascension and at 11:40 by declination, about 36 to 37 hours later.
Determining the summer solstice was of some importance in Athens since the first month of the year, Hekatombaion (July/August), started after that, with the occurrence of the new moon. It is possible, therefore, that Meton made his determination in some sort of official capacity.
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| Lykabettos from the Pnyx. Photo by the author April 2011. |
Philochoros says that he [sc. Meton] set up nothing on Kolonos, but that in the archonship of Apseudes [433/2 BCE], who preceded Pythodoros, he placed a sundial in the present place of assembly close to the wall on the Pnyx.
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The putative location of Meton's sundial on the Pnyx is circled in
black. The square structure 25 metres away in the top centre was the assembly speaker's rostrum. Image: © Google Earth. |
Moreover, there is some possible archaeological evidence too. Excavations carried out on the Pnyx in the early C20th revealed a substantial stone base, 5.10 × 5.85 metres in area, that the excavators believed to be a candidate for a platform, on top of which would have been mounted Meton's sundial (having rejected for various reasons other possible structures, such as an altar).7 Interestingly, the location is about 15 metres away from the foundations of the wall mentioned by Philochoros. This is supposition, of course. There is no firm evidence connecting this exact location to the sundial but it does fit the facts nicely.
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The top circle marks the position of the Sun emerging from behind the southern flank of Lykabettos on the day of the solstice; the lower circle, 2° away, is the position of the Sun 15 days later (and earlier). The true horizon as seen from the Pnyx is roughly in line with the topmost row of apartment blocks.
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Although the horizontal methods of the early Greek astronomers were relatively straightforward to apply and only needed one set of measurements, they suffered from two disadvantages: i) a useful horizon was required and ii) the solstice was conceived of in terms of happening only on a specific day, not a day and a time. In the 6th and 5th centuries BCE, however, this would not have been recognised as a problem. This is because the 'turning' of the Sun was interpreted to mean the turning of the Sun on the day that it changed the direction of its daily progress along the horizon as it rose or set. The vertical interpretation on the other hand, which means the change in direction of the Sun as it approaches its maximum excursion from the celestial equator (which could happen at any time during the day or night), really requires the concept of a spherical Earth.
Before about 450 BCE, most people assumed that the Earth was (broadly speaking) flat, and usually some kind of disk or shallow cylinder. However, during the latter half of the C5th BCE leading thinkers came to believe that the Earth was (roughly) spherical. We don't know exactly how or why people changed their minds, but it is certainly the case that by the early C4th BCE, the prevailing opinion in Greece was that the Earth, and indeed the whole cosmos, was spherical. Once this concept is grasped, the idea of the solstice as an event that relates to the celestial equator, and must therefore happen at a specific time as well as on a specific day, makes sense.
Consequently, the old horizontal method of determining the solstice was eventually dropped in favour of vertical methods. But, except at sunrise and sunset one cannot look at the Sun directly, as one could a star, and measure its altitude. Instead, the method of shadows has to be adopted. We have seen, however, that the simple gnomon method is not only no more accurate than the horizontal method but is actually more difficult and laborious to carry out because it requires two sets of measurements. It is likely that it was tried for a while, but gradually astronomers worked out better methods. We can't trace the history of this in detail, because so much material in the following centuries has been lost, but we know where it ended up.
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A simple quadrant aligned N–S. A plumb bob keeps the scale
correctly positioned. When the shadow of the pin on the ground
is the same length as the pin and about to disappear from the dial,
the altitude of the Sun can be read on the scale. Image from G. J. Toomer: Ptolemy's Almagest. |
The convenience of such devices and the fact that they promised, through a more thorough interpolation procedure, to give access to the time of the solstice as well as the day was greatly in their favour. But were they actually any more accurate than using a gnomon or a horizon? If Ptolemy's account of his own solstice observation is anything to go by, the answer is probably not. For example, he states that he determined 'securely' (ἀσφαλῶς) that the summer solstice of 140 CE occurred on 25th June 'about two hours after midnight'. However, modern calculation shows that it happened at 13:51 on 23rd June by ecliptic longitude or around 12:17 by declination, some 36 to 38 hours earlier, depending on the modern or ancient definition. This is actually no improvement on Meton's result obtained nearly six hundred years earlier!8
The reason for this is threefold. First, however they are displayed, shadows are still tricky things to measure and whatever instruments were used they all depended on some sort of shadow–alignment. Second, the instruments were supposedly aligned North–South, but this is difficult to establish correctly, and if it wasn't right the shadow would not be at its longest. Third, the non-linear nature of the Sun's apparent movement around the date of the solstice meant that linear interpolation would never give the exactly the right answer.
As indicated earlier, all these efforts to determine the date and time of the solstices (and also the equinoxes) were in the main directed towards establishing a reliable and accurate calendar. And indeed, ancient Greek calendars were generally a mess. They were lunisolar, that is they used the lunar cycle to determine the months and attempted (usually badly) to reconcile these with the year. Typically, they envisaged the year as consisting of 12 alternating months of 29 and 30 days each, giving a total of 354 days. Every so often —and fairly randomly— an extra (intercalary) month was thrown in by official decree.
It is possible that Meton wanted to establish a fixed timetable for when an intercalary month should be inserted into the Athenian calendar based upon a better determination of the length of the year. This would mean that everyone would know when this would occur, rather than it just being decided by the Archon (chief magistrate) when it was politically expedient. Such a change would entail senior politicians giving up their power to control the calendar, of course. Not suprisingly, he got nowhere, and it appears that the calendar was not properly regulated for a couple of centuries.
NOTES
1. The full passage explains both the solstice and the equinox:
Alter motus solis est, aliter ac caeli, quod movetur a bruma ad solstitium. Dicta bruma, quod brevissimus tunc dies est; solstitium, quod sol eo die sistere videbatur, quo ad nos versum proximus est. Sol cum venit in medium spatium inter brumam et solstitium, quod dies aequus fit ac nox, aequinoctium dictum. Tempus a bruma ad brumam dum sol redit, vocatur annus, quod ut parvi circuli anuli, sic magni dicebantur circites ani, unde annus.As for that last etymology, the less said the better.
Another motion of the Sun is different to that of the sky, because it is moved from the winter to the summer solstice. It was called 'winter' because then is the shortest day, 'solstice' because on that day the Sun seemed to stand still, at which time it is turned nearest to us. When the Sun arrives at the middle space between the winter [solstice] and [summer] solstice, because the day and night become equal, it is called the equinox. When the Sun returns from one winter [solstice] to another, the time is called a year, because as the little circles are called 'anuli', so big circles are called 'ani', whence 'annus' [for a year].
2. The phrase occurs even earlier in Homer (Odyssey 15.404), but appears to mean the place where the Sun turns from its daily course across the sky to travel back around the Earth in preparation for the dawn, i.e. sunset at the western horizon.
3. In fact, modern determinations of the solstices are done by modelling either the ecliptic longitude of the Sun (90° and 270°) or its right ascension (6:00 and 18:00), rather than by its distance from the celestial equator (declination) which can vary slightly owing to irregularities in the Earth's motion. As a result, the official time of the solstice rarely agrees precisely with the traditional idea of the absolute maximum excursion of the Sun from the celestial equator.
4. I am concentrating on the northern hemisphere because that is the location of Greece, but we do know that people in the southern hemisphere used horizontal methods to determine the solstice too. An example is the society that lived in Chankillo, Peru in the C4th BCE who constructed a remarkable series of towers to form an artifical horizon spanning the range of the Sun's risings through the year. See Ghezzi, Ivan & Ruggles, Clive (2007) 'Chankillo: A 2300-Year-Old Solar Observatory in Coastal Peru.' Science 315, 1239–43.
5. From Theophrastus. Enquiry into Plants, and Minor Works on Odours and Weather Signs (ed. Hort, Sir Arthur, 1916 for Loeb), volume II.
6. Scholion on Aristophanes Birds 997: ὁ δὲ Φιλόχορος ἐν Κολωνῷ μὲν αὐτὸν οὐδὲν θεῖναι λέγει, ἐπὶ Ἀψεύδους δὲ τοῦ πρὸ Πυθοδώρου ἡλιοτρόπιον ἐν τῇ νῦν οὖσῃ ἐκκλησίᾳ, πρὸς τῷ τείχει τῷ ἐν τῇ Πνυκί.
7. Kourouniotes, K & Thompson, Homer A (1932). 'The Pnyx in Athens.' Hesperia: The Journal of the American School of Classical Studies at Athens, Volume 1, 90–217. The relevant pages for the sundial are 207–11.
8. Attempts have been made to argue that in ancient solstice observations in the Hellenistic era were more accurate than this, cf. Rawlins http://www.dioi.org/ passim, but this seems to be based on a number of suppositions and mathematical reconstructions.
Last updated 18/06/20
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