The civil year consisted in general of twelve months or lunations, but occasionally a thirteenth was added in order to preserve its correspondence with the solar year.
From the same period also they have employed, in the adjustment of their solar and lunar years, a period of nineteen years, twelve of which are common, containing twelve lunations each, and the remaining seven intercalary, containing thirteen lunations.
The moons of the civil year are also distinguished by their place in the cycle of sixty; and as the intercalary moons are not reckoned, for the reason before stated, namely, that during one of these lunations the sun enters into no new sign, there are only twelve regular moons in a year, so that the cycle is renewed every five years.
METONIC CYCLE, in chronology, a period of 19 years during which there are 235 lunations, so called because discovered by Meton.
Computation from modern data shows that 235 lunations are 6939 days, 16.5 hours; and 19 solar years, 6939 days, 14.5 hours.
Twelve lunations, therefore, form a period of 354 days, which differs only by about 11 1/4 days from the solar year.
The Lunar Year, Therefore, Contained 354 Days, Falling Short Of The Exact Time Of Twelve Lunations By About 8.8 Hours.
But The True Time Of 99 Lunations Is 2923.528 Days, Which Exceeds The Above Period By 1.528 Days, Or Thirtysix Hours And A Few Minutes.
In Nineteen Solar Years There Are 235 Lunations, A Number Which, On Being Divided By Nineteen, Gives Twelve Lunations For Each Year, With Seven Of A Remainder, To Be Distributed Among The Years Of The Period.
On The Other Hand, The Exact Time Of A Synodic Revolution Of The Moon Is 29'530588 Days; 235 Lunations, Therefore, Contain 2 35 X 29 530588 = 6 939'6 8818 Days, Or 6 939 Days 16 Hours 31 Minutes, So That The Period Exceeds 235 Lunations By Only Seven And A Half Hours.
At The End For Four Cycles, Or Seventy Six Years, The Accumulation Of The Seven And A Half Hours Of Difference Between The Cycle And 235 Lunations Amounts To Thirty Hours, Or One Whole Day And Six Hours.
The lunations are supposed to consist of twenty-nine and thirty days alternately, or the lunar year of 354 days; and in order to make up nineteen solar years, six embolismic or intercalary months, of thirty days each, are introduced in the course of the cycle, and one of twenty-nine days is added at the end.
The Ancient Church Calendar Was Founded On Two Suppositions, Both Erroneous, Namely, That The Year Contains 3654 Days, And That 235 Lunations Are Exactly Equal To Nineteen Solar Years.
The Lunar Cycle Contained 6 939 Days 18 Hours, Whereas The Exact Time Of 235 Lunations, As We Have Already Seen, Is 235X29.530588= 6939 Days 16 Hours 31 Minutes.
This is a cycle of 18 years II days, or 223 lunations, discovered at an unknown epoch in Chaldaea, at the end of which the moon very nearly returns to her original position with regard as well to the sun as to her own nodes and perigee.
Further, we know that in the 8th century B.C., there were observatories in most of the large cities in the valley of the Euphrates, and that professional astronomers regularly took observations of the heavens, copies of which were sent to the king of Assyria; and from a cuneiform inscription found in the palace of Sennacherib at Nineveh, the text of which is given by George Smith,5 we learn that at that time the epochs of eclipses of both sun and moon were predicted as possible - probably by means of the cycle of 223 lunations or Chaldaean Saros - and that observations were made accordingly.
To Compute The Times Of The New Moons Which Determine The Commencement Of Successive Years, It Must Be Observed That In Passing From An Ordinary Year The New Moon Of The Following Year Is Deduced By Subtracting The Interval That Twelve Lunations Fall Short Of The Corresponding Gregorian Year Of 365 Or 366 Days; And That, In Passing From An Embolismic Year, It Is To Be Found By Adding The Excess Of Thirteen Lunations Over The Gregorian Year.
The lunations are estimated with much greater precision.