LAST EDITED ON Aug-20-03 AT 05:17 PM (EST)
 
The solar year equals to 365.2422 days - not an integer. Using 1 leap year of 366 days for every 3 years of 365 days gives you the average length of the calendar year

(3·365 + 366)/4 = 365.25 days

(pretty close), which appeared good enough to Julius Ceasar, who introduced this calendar in the ancient Roman empire Therefore, it is called the Julian calendar. At the time, the the spring equinox was on March 25. A few centuries later - in the year 325, the Julian calendar was adopted by the Christian Church. By this time, the spring equinox was on March 21. However, in everal centuries the Julian calendar got considerably out of step with the Sun:

(365.25 - 365.24220) = 0.0078 days/year
(365.25 - 365.24220)·100 = 0.78 days/century
(365.25 - 365.24220)·1000 = 7.8 days/millenium

By the end of the 16th century (1582), the difference was (1582 - 325)·0.00788 » 10 days. The spring equinox, which is supposed to occur on or very close to every March 21, was occuring 10 days earlier, on March 11. An accurate solar calendar is crucial for agriculture - farmers have to know when to sow. To put the calendar back in step with the Sun, Pope Gregory 23th skipped 10 days and shortened the calendar year by not making leap years the century years not divisible by 400 (including 1700, 1800, 1900, but not 2000). Therefore, it is called the Gregorian calendar. The average calendar year is now

(365.25 * 400 - 3)/400 = 365.25 - 3/400 = 365.2425 days

and the Gregorian calendar loses

(365.2425 - 365.24220)·1000 = 0.3 days/millenium

on the solar millenium. Of course, we could still improve the calendar by not making leap years the millenia years divisible by 4000. Such improved calendar would have the average calendar year

(365.2425 * 4000 - 1)/4000 = 365.2425 - 1/4000 = 365.24225 days

and it would lose only

(365.24225 - 365.24220)·1000 = 0.05 days/millenium
(365.24225 - 365.24220)·20000 = 1 day/20 millenia

on the solar millenium resp. 20 solar millenia.

By the end of the 16th century, the Christian Church had been split by the Reformation, and Protestants of those times would rather do the exact opposite of what the Pope said. Countries with predominant Protestant denominations and countries with predominant Ortodox Church accepted the Gregorian calendar at various later times, for example the United States after the Declaration of Independence. Russia was the last - she accepted the Gregorian calendar shortly after the Bolshevic revolution in 1917. By this time, the Julian calendar lost another 3 days, for a total of 13 days, which had to be skipped.

The only thing that remains to explain is the name "leap year". Since 365 = 1 mod 7, we have 52 weeks plus 1 day in a normal year. The days of week march forward by 1 day for the same dates in 2 subsequent normal years. For example, if July 4 falls on Sunday in a normal year, it will fall on Monday in the next normal year. In a leap year we have 52 weeks plus 2 days. Again, if July 4 falls on Sunday in a normal year, the day of week leaps over Monday if the next year has 366 days and July 4 will be on Tuesday.