The solar cycle

"... in the 9th summer of the reign of Volodymyr, from Adam, to the baptism of Ruskago, 6496 years, indie 1, summer 6497, the key of the borders of P, circle of the Sun 28. 3, and the moon 17. ..".

So the Pskov chronicle dates the year of the baptism of Rus( 988 AD).Let us consider successively all the elements of this dating, as well as the properties of the cycles mentioned.

After 28 years. In the simple year of the Julian calendar, there are 365 days, in a leap year 366, and every fourth year is a leap year. The full week consists of seven days. What conclusions follow from the comparison of these numbers?

First of all, 365 = 52 * 7 + 1, 366 = 52 * 7 + 2. This means that a simple year ends on the same day of the week as it began( for example, on January 1 and December 31).The new year, after the previous simple, falls on the next day of the week. And if there were no leap years at all, then the distribution of the days of the week by the number of months would be completely repeated every seven years.

In turn, if in the leap year an additional 366th day was inserted at the end of December, such a repetition would take place in five or six years."Individually", for some years it is approximately the way it is. It is enough to look down on any column "second two digits of the year" to see this. So, after an arbitrary leap year, for example 64th( this may be 1964 or 1864), the same distribution of days of the week by the number of months was at intervals of 6( in 70), 11( in 81), 6( in 87 g.) and 5( in 92 g.) years. The first three years were simple( therefore the coincidence of dates with the days of the week of 64th year was only beginning on March 1), the fourth one is again a leap year( here the complete coincidence already).But the "right" to the right of this "source" is the year 65th simple, therefore the same distribution of the days of the week by the number of months is repeated here in another order - after 6, 5, 6 and 11 years. The year 66 is the second after the leap year, here this series will be as follows: 11, 6, 5, 6. For the year 67, the third after the leap year, we find a change of coincidence in this order: 5, 6, 11, 6 years.

And only after 28 years the schedule of the days of the week by the number of months - the "calendar card" habitual for us - is completely repeated( from year to year!) In the same order, as 6 + 11 + 6 + 5 = 6 + 5 +6 + 11 = 11 + 6 + 5 + 6 = 5 + 6 + 11 + 6 = 28. Therefore, the "calendar card" will be repeated at 64 + 28 = 92th year, 65+ 28 = 93th, 66+28 = 94th, and so on.

The time interval through which the distribution of the days of the week by the number of months is completely repeated is called the 28-year solar cycle. In the Julian calendar we have

28 Julian years =( 365.25 * 28 =) 10,227 days =( 10,227: 7 =) 1461 weeks.

Just because 28 years later the "day of the Sun" - dies Solis - as the most important, festive day of the week returns to its place in relation to the numbers of calendar months, this cycle was called solar.

Note that everything said above about the coincidence of the days of the week and the numbers of the months in 5, 6 and 11 years for individual years and after 28 years applies to the Gregorian calendar, however, only within this or that century. If the centenary is simple, then the regularity of the alternation between simple and leap years, and therefore the specified order of coincidence of the "calendar-calendar" is violated.

Therefore, for the Julian calendar too, the table can easily be extended to the past for any number of centuries: in the columns "the first two digits of the year" when going from bottom to top one position, hundreds of years decrease by one, and on the left - by seven( except for the casefrom -0 to -6).The dating of events in the Gregorian calendar( for him, simple centennial years move forward through one position) is carried out only from the time of reform in 1582

Circle of the Sun .The ordinal place of the year in the 28-year solar cycle is called the circle of the Sun Q.

Initially, the account was conducted from 28 September on September 1 or October( this is also the case of the Novgorod scholar XII century Kirik in his "Teaching him to know the number of all the years") 5509 BC.e. Later, both in Byzantium and in Rus, the March style of the era from the "creation of the world" spread widely. Therefore, the account of solar cycles is conducted from March 1, 5508 BC.e.

Dividing the year of the era from the "creation of the world" B by 28, in the remainder, and find the circle of the sun Q:

( direct brackets | | denote the remainder of the division).

Table. Circles of the Sun

The circle of the Sun can also be determined by taking the remainder of the division by the 28th day of the year.e. R, reduced by 8, so that

For example, in 1986 n.e.- this( 5508 + 1986 =) 7494 AD from the "creation of the world."Dividing the number 7494 by 28, we find that 267 complete 28-year cycles have passed from the era of the era and we have 18 in the remainder. Hence, for 1986 the circle of the sun is Q = 18. The same is obtained by dividing by 28 the number 1986 - 8 =1978.

The values ​​of the circle of the Sun for any year of our or Byzantine era are given in Table.5. It is worth recalling that every fourth year of the cycle is leap year( for Q = 3, 7, 11, etc.).