If The Last Lunation Of Any Year Ends, For Example, On The 2Nd Of December, The New Moon Falls On The 3Rd; And The Moon'S Age On The 31St, Or At The End Of The Year, Is Twenty Nine Days.
It must happen sometimes that in the course of a lunation the sun enters into no new sign; in this case the month is intercalary, and is called by the same name as the preceding month.
Now That Lunation Having Commenced On The 3Rd Of December, And Consisting Of Thirty Days, Will End On The 1St Of January.
The Calendar Is Constructed On The Assumptions That The Mean Lunation Is 29 Days 12 Hours 44 Min.
Hence, If In That Year The Epact Should Be 19, A New Moon Would Fall On The 2Nd Of December, And The Lunation Would Terminate On The 30Th, So That The Next New Moon Would Arrive On The 3 Ist.
The Mean Length Of The Year Is Therefore 3541) Days, Or 354 Days 8 Hours 48 Min., Which Divided By 12 Gives 293 G O Days, Or 29 Days 12 Hours 44 Min., As The Time Of A Mean Lunation, And This Differs From The Astronomical Mean Lunation By Only 2.8 Seconds.
As It Had Now Been Discovered That The Exact Length Of The Lunation Is A Little More Than Twenty Nine And A Half Days, It Became Necessary To Abandon The Alternate Succession Of Full And Deficient Months; And, In Order To Preserve A More Accurate Correspondence Between The Civil Month And The Lunation, Meton Divided The Cycle Into 125 Full Months Of Thirty Days, And 110 Deficient Months Of Twenty Nine Days Each.
But the fourteenth of this moon falls at the latest on the 18th of April, or 29 days after the 20th of March; for by reason of the double epact that occurs at the 4th and 5th of April, this lunation has only 29 days.