An Excerpt from The Calendar God Gave to Moses by Herb Solinsky  and Rob Anderson (version 9/23/82 )
 

Ancient Determination of the Equinoxes and Solstices.
 

A person who views sunsets daily from a place at which there is a clear view of the horizon might notice that the sun does not set at the same part of the horizon each day. He might think of performing the following experiment to determine the daily change in the position of the sun at sunset.
 

Permanently place a straight board and an object with a sighting point so that the middle of the board is about the length of a person west of the sighting point and when looking approximately west with one's eye at the sighting point, the long top edge of the board is even with the horizon. Each day near sunset make a mark on the board where the board crosses the line of sight from the sighting point to the middle of the sun. For accuracy this should be done when the center of the sun is at the horizon.
 

If this is done from Jerusalem (latitude 31.8 degrees north) during the coldest part of the year, the daily marks on the board keep going north. During the hottest part of the year the daily marks on the board keep going south. For several days while the temperature is getting quite hot, the marks will be at about the spot that is the furthest north of the marks; the middle day of this group is the day of the summer solstice. For several days while the temperature is getting quite cold, the marks will be at about the spot that is the furthest south of the marks; the middle day of this group is the day of the winter solstice. The word "solstice" means "stopping of the sun" which describes the state of the marks at the solstices. At all other times of the year the marks are separated from one another while heading north, or separated from one another while heading south.
 

The marks on the board are furthest from one another at the midpoint between the solstice marks because the north-south motion of the sun is fastest at these points (pages 62-64, AVENI8O; page XII of Sternberg's introduction in GANDZ; pages 64, 80-81, LOCKYER; page ?44, NAKAYAMA; page 36, NEW-CR). The mark closest to the midpoint while the marks are heading north is the mark at the vernal equinox. The mark closest to the midpoint while the marks are heading south is the mark at the autumnal equinox. On the day of an equinox, the shadow cast by a vertical object at sunrise and at sunset will be the exact east-west direction as a line of latitude; the further from an equinox, the greater this direction from the exact east-west (page 62, AVENI8O). For a latitude of 20 degrees north, at about the day of the vernal equinox the horizon points of the sun move about five-sixths of a visible solar diameter at sunset (pages 63-64, AVENI8O). In the previously described experiment, if the sighting point and board were 100 meters apart, one day after the vernal equinox the observer would have to move 80 centimeters north of the sighting point to see the sun at the previous day's mark; this would only be about 0.8 centimeters for a solstice (page 64, AVENI8O). Although this method determines the equinoxes quite precisely by first knowing the solstices, it is not necessary to know the day of the solstices precisely because the marks barely change for several days about a solstice.

The Inca in Cuzco, Peru erected monuments that could show the equinoxes by sighting (pages 66-67, AVENI79). Many ancient picture documents from the Americas show people peering into the distant horizon through the upper notch of crossed sticks affixed to the top of a pole, which indicates an examination of the sun's daily motion (page 65, AVENI79).

The following is quoted from pages 63-64 of LOCKYER.
 

Next suppose an ancient Egyptian wished to determine the time of an equinox. We know from the Egyptian tombs that their stock-in-trade, so far as building went, was very considerable; they had squares, they had plumb-lines, they had scales, and all that sort of thing, just as we have. He would first of all make a platform quite flat; he could do that by means of the square or plumb-line; then he would get a ruler with pretty sharp edges (and such rulers are found in their tombs), and in the morning of any day he would direct this. ruler to the position of the sun when it was rising, and he would from a given point draw a line towards the sun; he would do the same thing in the evening when the sun set; he would bisect the angle made by these two, lines, and it would give him naturally a north and south line,, and a right angle to this would give him east and west. So that from observations of the sun on any one day in the year he would practically be in a position to determine the points at which the sun would rise and set at the equinox - that is, the true east and west points.
 

Suppose that the sun is rising, let a rod throw a shadow; mark the position of the shadow; at sunset we again note where the shadow falls. If the sun rises exactly in the east and sets exactly in the west those two shadows will be continuous, and we shall have made an observation at the absolute equinox...
 

It is true that there may be a slight error unless we are very careful about the time of the year at which we make the observations because when the sun is exactly east or west at the time of rising or setting it changes its declination [change in north-south angle measured from the center of the earth] most quickly. So it is better to make the above observations of the sun nearer the solstices than the equinoxes, for the reason stated.
 

Most of the Egyptian pyramids are oriented east-west (page 333, LOCKYER). The two largest pyramids at Gizeh built by Cheops and Chephren are oriented east-west. Certainly the Egyptians realized that on two days of the year the sun's shadow followed the straight lines along each east-west wall of these pyramids. This indicates that the Egyptians had a knowledge of the equinoxes (pages 336-337, LOCKYER).
 

Ancient peoples were capable of using noontime shadows to determine the day of the equinoxes. A gnomon is an upright stick which casts a shadow on a plane surface ~page 23, GANDZ-GN). The upright pole of a sundial may be called a gnomon. The gnomon was used in Egypt, Babylon, Greece, and other ancient nations. Although the word "gnomon was not used in the definition of noontime, its meaning was employed; thus, a gnomon was commonly used to determine noontime. At noontime the angle from the top of the gnomon to the end of its shadow to the base of the gnomon defines the elevation angle of the sun (page 38, NEW-CR).
 

The gnomon may be used to determine the equinoxes and solstice.. The minimum length for a year of all noontime shadows of the gnomon determines the summer solstice (assuming the gnomon is in the Northern Hemisphere). The maximum length for a year of all noontime shadows of the gnomon determines the winter solstice. If the elevation angles of the sun at the two solstices are bisected and the shadow length for that bisected angle is noted, the noontime shadow length closest to the noted shadow length determines the day of an equinox (page 82, NEW-CR). For a few days near the solstices the noontime shadow lengths hardly change, so the days of the solstices need not be determined precisely in order to determine the equinoxes. The vernal equinox is determined as the noontime shadow lengths are decreasing, and the autumnal equinox is determined as the noontime shadow lengths are increasing. Atmospheric refraction is the bending of light rays as they pass through the atmosphere. When the sun's rays are perpendicular to the surface of the earth there is no refraction. The further away from perpendicular the rays, the more the refraction. The noontime error for the determination of an equinox due to refraction is. at most three hours about the latitude of northern Egypt and Palestine (page 256, NAKAYAMA).
 

An instrument called an equatorial ring was used by Ptolemy and Hipparchus to determine the equinoxes and solstices (pages 24-26, ALMAGEST; pages 79, 88, NEW-CR). If the gnomon height is two meters, at a latitude of 34.6 degrees north, a one centimeter error in the measurement of the gnomon 's shadow produces a four to five day error in the determination of the winter solstice and an eight day error for the summer solstice, but a similar height and measurement error for an equatorial ring only produces a 17 to 18 hour error for determining the winter solstice (pages 242-244, NAKAYAMA). In actual practice the error of measurement should not exceed three millimeters (page 244, NAKAYAMA).
 

Page 30 of BICK states "Yet he [the Greek astronomer Hipparchus. c. 125 B.C.E.] acknowledges the possibility of error in the observations, which according to him could amount up to 3/4 day for the time of a solstice and up to 6 hours for the time of an equinox" (pages 77-83, 139-142, ALMAGEST).
 

Page. 142 of HARTNER72 states, "The same method [of calculation], though to my knowledge not mentioned expressis verbis, has to be postulated in Western Antiquity because actually there is no other way yielding the solstice to the day or even to the hour." (Idiomatic English would switch the words "day" and "hour".)
 

Page 29 of DICKS states, "In fact, such observations [of the shadow of a gnomon] can be expected to give only the times of noon (shortest daily shadow) and of the solstices (longest and shortest noon shadows in the course of a year), the latter probably to an accuracy of at best some five or six days."
 

Because of the refraction by the earth's atmosphere, at United States' latitudes the daytime exceeds the nighttime by about ten minutes on the days of the equinoxes (see appendix 1). The days of equal daytime and nighttime precede the vernal equinox and follow the autumnal equinox by a few days. The latitude of Jerusalem is 31.8 degrees north, so appendix 1 indicates that the days of equal daytime and nighttime in Jerusalem do not coincide with the equinoxes. About 3000 years ago there were no clocks capable of measuring 12 hours accurately to within a few minutes, so precise equality between day and night was not the ancient method for determining the equinoxes (pages 366-367, 1069, NEUGHAMA). Based on the precision of most of the times given by Ptolemy, Robert Newton concludes that ancient time measurements had an accuracy of at most about 15 minutes (pages 123-124, NEWCR). Page 32 of DICKS states, "Direct measurement of the length of day and night can be entirely discounted; a glance at tables of sunrise and sunset for Greece will show that over the ten days spanning the equinox there is a total change of some eighteen minutes in the length of the day, i.e. less than two minutes a day, and this standard of accuracy is out of the question for the water-clocks and other devices of ancient time-measurement even in late antiquity." Despite this, the word "equinox means equal night" in Latin so the choice of word is not accurate.
 

The vernal equinox almost always occurs on March 20 or 21 , but it is possible for it to occur on March 19 (volume 4, page 618, BRIT73). When Pope Gregory XIII established the Gregorian calendar in 1582, he adjusted the date so that the vernal equinox fell on March 21 as it had been in 325 C.E., the year of the Council of Nicaea (page 64, FRED). The astronomical deviation of the Gregorian calendar year (which is in current use) from the tropical year is only one day in 3323 years (page 157, SILVER). It is commonly assumed that an extraordinary one day adjustment in the Gregorian calendar will be made as needed so as to keep the vernal equinox in harmony with March 21 as its latest date from the time perspective of Greenwich, England. If no extraordinary one day adjustment is made to the extrapolated Gregorian calendar of roughly 3000 years ago, the vernal equinox in some of those years will fall on March 22.

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