Leap day

This yere leapt, and the leap day was the morrow after the feast Terminalia.

The lunar cycle among the Chaldeans was called the saros and sara, from סהרא, sahara, the moon. This cycle it is said contained two hundred and twenty-three synodical months, or eighteen Julian years, ten days, when the same cycle or period contains five leap days, and eleven days when it contains four leap days, seven hours, forty-eight minutes, and one-fourth; in which time all the corresponding new and full moons and eclipses return again.

We observe then, with respect to the Julian cycle of leap-year, that, though we speak of it commonly as the cycle of the leap-year, it is in reality only the cycle of the leap-day. And this distinction is of much importance, especially to the present question. For the cycle of leap-year according to the Julian rule is one of four years, because the cycle of the leap-day in the Julian calendar is one of four also.

According to our current calendar, on what day of the week will January 1 fall in the year 3000? in the year 1,000,000? in the year 10^(1,000,000)? […] In the thousand years from the year 2000 to the year 3000, there are 365,000 days, plus 250 leap days, minus 10 century leap days omitted, plus 3 leap days restored in the years 2000, 2400, and 2800, for a total of 365,243 days, or 57,177 weeks and 4 days. Since January 1 falls on a Saturday in the year 2000, it will fall four days later on a Wednesday in the year 3000.

According to the new leap rule, leap years are years whose last two digits are divisible by 4. To correct for the slightly shorter length of the solar year, 3 leap years are omitted every 400 years, and to that end, leap days are omitted in the secular years whose unit is not divisible by 4. Accordingly, the years 1700, 1800, and 1900 were not leap years, but 2000 was one again.