But to match this cycle with the solar year to over 160 years (calculated in Alexandria astronomer Eratosthenes of Cyrene (275 – 195 years. BC) to throw one month in 30 days. Improved lunar-solar calendars based on the fact that 19 solar years correspond to 235 lunar months: 365,24219879 x 19 = 6939.6018 days: 29.5305882 '235 = 6939.6882 days. As we see, the difference is only 0.0864 days. This 19-year astronomical cycle, called the "circle of the Moon" or "cycle of melon, was widely used in the construction of lunar and solar calendars.
For twenty years the author attempted to agree on the value of the tropical year with the lunar (synodic) months, to agree among themselves, all three kinds of calendars. After a painstaking study even found a single cycle: 29 years 100 series = 2900 years' 365.242413793 days = 1,059,203 days (for the solar calendar), 49 61 = 2989 years cycle 354,367012378 days = 1,059,203 days 35868 lunar month = 29.5305843648 days (for lunar and lunar-solar calendar), but, in the development of this series revealed that the system eliminates a visokosov days every 100 years (to reach the average length of tropical year in 2900 years), and instability or "shift" tropical year, making all attempts to reunite three kinds of calendars in the "eternal and unchanging one cycle impossible. And here we found a major error! To reunite all three types of calendars in a single cycle – day must be continuous. To this requirement can only answer – the Julian calendar.