Leap days keep the calendar aligned with astronomical observations.  The connection is doubly important when religious holidays are tied to the seasons.  Easter is a movable feast celebrated near the vernal equinox. Christmas is fixed at December 25, a date significant for its ancient relationship to the winter solstice.  The Roman calendar dated the winter solstice to December 25.  In pagan northern Europe, the date was noted as the first day after the winter solstice with measurably more daylight.

Without leap years, both holidays would drift.  It takes the earth a few hours more than 365 days to revolve from one vernal equinox to the next.  If we start a 365-day calendar by recording an equinox on March 21, we would find that after four years the vernal equinox would occur on March 22.  After a century, it would fall in mid-April.  A calendar of 365 days turns the page on a new year too soon to keep the vernal equinox to the desired date.

Easter is the first Sunday following the first full moon after the vernal equinox.  If the calendar is allowed to drift without leap days, the date of Easter would fall later and later in the year as the decades and centuries roll by and the calendar falls behind the equinox at the rate of about a quarter of a day per year.

If the calendar is allowed to drift, the date of the winter solstice would also fall later and later.  If December 21 is the date of the solstice in Year 1, it will fall about a day before the solstice in Year 4.  After a century, it will be more than three weeks earlier than the solstice.  A holiday like Christmas that is celebrated on a fixed date would gradually float backwards through the seasons over long periods of time.  It would return to the date that falls four days after the winter solstice after a tour of some 14 centuries. (365/0.25=1460.)

My personal view is that this arrangement would have lent more interest to these holidays.  There would be long periods of time when the two holidays occurred in the same month.  They might even fall on the same day in a given year.  After that, there would come a time when elders would fondly recall the days when, as children, they found Easter eggs hidden under the Christmas tree.

Long before Easter and Christmas became Christian holidays, other keepers of calendars felt the need to make adjustments to keep their holidays at the traditional and desired time of year.  Two lunar calendars – the Chinese calendar and the Jewish calendar – add a “leap month” every few years.  That allows the Chinese New Year to be calculated by counting new moons after the winter solstice, two for a common year and three for a leap year.  A leap month keeps the Jewish High Holy Days tied to the fall of the year and Passover tied to the spring.

The Islamic calendar starts a new month with the first sighting of a crescent moon after a new moon.  A year consists of twelve lunar cycles and is some 355 days long.  There is a Koranic prohibition against the use of leap months.  Consequently, the holy month of Ramadan falls some ten days earlier each year on a solar calendar.  (One wag asked “Is it my imagination or is Ramadan coming earlier each year?”)

During Ramadan, observant Muslims may not eat during daylight hours.  That rule has a consequence for physical laborers in higher latitudes during those periods when Ramadan falls in the summer months.  My gardener is a devout Muslim and was forced to cut back on his work schedule a few years ago when Ramadan was observed during high summer.  Apart from that, allowing the lunar calendar to drift relative to the solar calendar does not appear to have done Islam any harm.

The Romans imposed order on a solar calendar more than 2000 years ago.  Prior to the year 46 BC, the Roman practice was to add a variable number of days to the month of February every few years ad hoc as the need arose.  (Needless to say, the Romans did not refer to that year as 46 BC.)  Julius Caesar gathered the best astronomers of his day who advised him to reform the calendar systematically by adding one day to the calendar every four years.  The Julian calendar was born.

Unfortunately, the Julian calendar overdid the required correction.  If you add a day to the calendar every four years, you have made the average year 365.25 days long, or 365 days and six hours.  [(365 + 365 + 365 + 366)/4 = 365.25.]  A year – measured from one vernal equinox to the next – doesn’t take that long.  The earth arrives at a vernal equinox 365 days, 5 hours, 48 minutes and 45 seconds (on the average) after the previous one.

The 365-day calendar turned its pages too quickly.  The 365.25-day calendar took too long.  The built-in error of eleven minutes and 15 seconds per year accumulated inexorably.  After a century, the Julian calendar had added some 18 hours more than was necessary.  The date of the vernal equinox began to move backward. In 1582, when Pope Gregory took the matter in hand, the vernal equinox occurred on March 11.

The solution was to reduce the number of leap years in a 400-year cycle by three.  Instead of adding 100 leap days over 400 years, the Gregorian calendar adds 97.  Years divisible by 100 are not leap years unless they are also divisible by 400.  1900 was not a leap year, but 2000 was.  To get the vernal equinox back to the desired date, ten calendar days were skipped by fiat.  In places where the Pope’s word was authoritative, the day after October 4, 1582 was October 15, 1582.

Even so, the calendar will need an adjustment in the distant future.  The average year in the Gregorian calendar is 365.2425 days long.  [(365×303) + (366×97)]/400=365.2425.  However, the observed average length of the time it takes for the earth to complete the circuit from one vernal equinox to the next is 365.24219 days.  That tiny difference means that the Gregorian calendar adds about 27 unnecessary seconds per year.

It will take a bit more than 3000 years (counting from 1582) for those 27 seconds to amount to one full surplus day.  Our remote descendants may decide to skip a leap year to further improve the alignment of the calendar to the seasons.  The simplest proposal is to treat the year 4000 and future years divisible by 4000 as common years of 365 days.  Of course, the kids will do whatever they think best.  There is plenty of time to decide.