Astronomy etc.
Greek Estimates of the Synodic Month
by Livio Stecchini
The problem that Meton intended to solve was - which is the smallest number of solar years that can be divided exactly into a series of more or less alternating months of 30 and 29 days? He knew that solar years are about 365.25 days and that a lunar month is about 29.5 days. He counted that 19 solar years are:
19 x 365.25 = 6939.75 days
He assumed that 19 solar years are 6940 days, either because he did not take 365.25 as an exact figure or because he chose to disregard a difference of 0.25 days. By dividing he found that in 6940 days there are 235 lunar months of 29.5 days, with a remainder of 7.5 days. If there had been no remainder he would have divided the 6940 days into 117 1/2 months of 30 days and 117 1/2 months of 29 days; but since there was a remainder of 7.5 days, he increased the number of months of 30 days to 117.5 + 7.5 = 125. The number of months of 29 days had to be reduced to 117.5 - 7.5 = 110.
One hundred years later, Callippus objected to the system of Meton on the ground that the solar year should be calculated as exactly 365.25 days. Since, according to this reckoning, the 19 years of the Metonic cycle are 6939.75 days, he quadrupled the years of this cycle to 76 years, in order to obtain a round figure of 27,759 days. According to the Metonic cycle this period would contain:
4 x 125 = 500 months of 30 days
4 x 110 = 440 months of 29 days
Since Callipus had found an excess of one day in 76 years, he changed the pattern to:
499 months of 30 days
441 months of 29 days
Hipparchus (around 150 BC), since he knew that a solar year is somewhat shorter than 365.25 days, proposed that the cycle of Callippus be quadrupled to 304 years, but deducting one day. He assumed that 304 solar years are (304 x 365.25)-1 = 111,035 days, which makes a solar year equal to 365.24671 days. Calculating correctly, 304 years are 111,033.6 days. As to the lunar months Hipparchus limited himself to quadrupling the figure of the cycle of Callippus:
4 x 499 months of 30 days
4 x 441 months of 29 days
If we average the length of the months according to the three cycles, we have:
Meton 29.531915 solar days
Callippus 29.530851
Hipparchus 29.530581
(correct figure - 29.530588)
Meton was correct to the second decimal figure, Callippus to the third, and Hipparchus to the fifth. The datum of Hipparchus is breathtaking since it differs by a second from the correct one, whereas he was off by about 7 minutes in calculating the length of the solar year.
The precision achieved in calculating duration of the synodic month is not difficult to explain. The basic problem was simple: it was a matter of counting how many new moons occur in a period of solar years.
The observations could have been made simply by recording at each summer solstice how much sooner was the preceding new moon and how much later was the following new moon. In a few years one could arrive at a good datum for the length of the lunar month. It is true that in marking the date of new moons there was a constant danger of erring by a day, but in the long run these errors would even out and the very development of luni-solar calendars would call the errors to attention.
Several cultures adopted independently the Metonic calendar because calendars were used not only to regulate political and economic activities, but also to record the occurrence of eclipses. The date of eclipses was not a matter of mere scientific interest and the ability to predict them had great social value. They were the foundation of the power of shamans and medicine men to show their people the great influence they had even over the heavenly bodies enabling them to put on great displays of these powers and even demanding human sacrifices to `appease' the gods. The ability to predict eclipses was the secret to their success and fear among their own.With the Metonic calendar, the good recording of eclipses and their prediction became an elementary operation. Eclipses repeat themselves according to the same pattern after 223 lunar months, that is, about 18 solar years and 11 days. They occur in approximately the same part of the sky in three cycles of 223 months. If the lunar month were to be calculated with an accuracy of less than 29.53 days, in less than 6 years one would notice that eclipses occur not only at the wrong time, but also on the wrong solar day. Because the Metonic cycle was used to calculate the date of eclipses, the Greeks were driven to introduce refinements into it. Hipparchus proposed that for the sake of predicting eclipses there be adopted a cycle of:
19 x 223 lunar months
According to him, this was the shortest period in which a series of lunar months equals a whole number of solar days. He assumed that:
19 x 223 lunar months = 125,121 solar days or
342 solar years and 208.17 days
Textbooks repeat that the Greek mathematician Hipparchus (150 BC) reckoned the solar years as:
365.24 days [the correct value is=365.242199]
That is how far one summer solstice is apart from the next one. All this proves that the calculation of the ratio between lunar month and solar year did not involve elaborate observational procedures, so that it could result in gathering of extremely accurate data.
Eclipses in Egypt
Q: Is it not true that certain kings and events have been dated with lunar and/or solar eclipses giving them dates which fit the conventional model of history?
A: I have read a lot of those assumptions of celestial dating methods fitting certain kings and/or events. All in all there were supposed to have been 28 total solar eclipses whose path crossed the Nile in the conventional years from 2837 to 493 BC and 10 lunar eclipses in close succession. But when we assume certain statements in ancient texts refer to celestial events and then sit down, if for example, an eclipse occurred in 1311 or in 1338, to use an arbitrary number linking a certain king or event to that year, we must also ask if there was such an eclipse in, lets say, 831 BC. These celestial events take place every year somewhere in the world and unless we also ask ourselves if such an event occurred during the time when the revised model places these kings we are non the wiser.
But as far as the well known 1338 BC eclipse over Shtub is concerned, there was one in 831 BC from the Mediterranean region to Memphis, Egypt. Neither one of these eclipses were visible from the capital of Pharaoh Amenophis IV and any reports of them would have been by word of mouth. In revised view Akhnaton is dated from about 843 -826 BC, well within the eclipse of 831 BC. In our view the 1338 BC eclipse occurred during the Hyksos/Amalekite occupation of Egypt and we must look in their literature to find the account of it.
Q: Ok, thank you for your comment.
Lunations
According to dated information 223 lunations take place in 18 years and 10 days, or 36 times in 223 (36x223) in 649 years and 1 month. According to Josephus (Ant. I, 39) that early men before the flood knew the accurate length of the tropical year is proven by their use of the `Great Year' of 600 years. In 600 tropical years and one day (600 yrs + 1day) there are 7421 lunations. In that period the New Moon and the Spring Equinox correspond within an hour. [Rev. F.A. Jones, `The Ancient Year and the Sothic Cycle' in PSBA, Vol. XXX, 1908, p. 95-106. The article also features charts.]
for waning, German `abnehmend', shows which way the moon curves when it is in that phase. The curve of the older style for the letter `Z' 
for waxing, German `zunehmend', shows the way the moon curves when it is in that phase.
Sonnenfinsternis auch im Jahre 831 v.Chr. stattfand, gerade in der Mitte unserer Datierung des gleichen Königs und unsere Daten beruhen nicht auf dieses himmlische Ereignis. Diese Finsternisse finden jedes Jahr irgendwo in der Welt statt und wenn wir uns nicht die Frage stellen, ob so etwas nicht in beide Chronologien passt werden wir nicht viel davon gelernt haben.
Bible Topics