What do leap year and leap frog have in common? I have absolutely no idea, but frogs do seem to epitomize the concept of leap year and on this coming February 29th, it will happen again. To leap or not isn’t the only question, but to fully understand the issue requires an explanation of calendars, solar years, tropical years, lunar years, many moons (usually limited to old cowboys and Indian movies) and some lunacy as well. So let me proceed with all the expertise and daring of both a non-authority and a non-scientist. Maybe we can figure this out together and maybe we can’t. But here goes.

The calendar year is 365 days long, unless the year is exactly divisible by 4, in which case an extra day is added to February to make the year 366 days long. If the year is the last year of a century, e.g. 1800, 1900, 2000, then it is only a leap year if it is exactly divisible by 400. Therefore, 1900 wasn’t a leap year but 2000 was. (If this is clear to you, you are one ahead of me. I was absent the day they did that.) In any case, the reason for these rules is to bring the average length of the calendar year into line with the length of the earth’s orbit around the Sun, insuring that the seasons always occur during the same months each year. While some rules are perhaps meant to be broken, this isn’t one of them.

A year is defined as being the interval between two successive passages of the Sun through the vernal equinox. (In actuality, the earth is orbiting around the Sun.) The vernal equinox occurs the instant the Sun is above the earth’s equator while traveling from the south to the north. (We are assuming here that it knows which way it’s going. That is more than I can say for myself most of the time.) This is considered the beginning of Spring. The two passages of the Sun through the vernal equinox comprise a tropical year, whose length determines the repetition of the seasons. The exact length of a tropical year is 365.24219 days.

The purpose of the calendar is to reckon past or future time, to show how many days until a certain event takes place, to mark a harvest or religious festival or how long since something important happened. The earliest calendars were in all probability strongly influenced by the geographical location of the people who made them. In colder climates, the concept of the year was determined by the seasons, specifically by the end of winter. In warmer countries, where the seasons are less pronounced, the Moon became the basic unit for time reckoning. An old Jewish book says that "the Moon was created for the counting of the days." (Can you imagine uncovering an old inscription that reads: "on this day in this year absolutely nothing happened?") Many of the oldest calendars were lunar calendars, based on the time interval from one new moon to the next (a lunation). But even in a warm climate there are annual events that ignore the phases of the Moon: in some areas it was a rainy season; in Egypt the annual flooding of the Nile River. The calendar had to account for these yearly events as well.

With the lunar calendars, a solar year was based upon a 19-year period (almost through puberty in human terms). Seven of these years had 13 months. The entire period contained 235 months. Still using the lunation value of 29 and a 1/2 days devised by lunatics, this made a total of 6,932 and 1/2 days, while 19 solar years added up to 6,939.7 days, a difference of just one week per period and about five weeks per century. (Still with me? I lost myself about a sentence ago.)

Even this 19-year period required some adjustment, but still it became the basis of the calendars of the ancient Chinese, Babylonians, Greeks and Jews. This same calendar was also used by the Arabs, but Mohammed later forbade shifting from 12 months to 13 months, so that the Islamic calendar, even today, has a lunar year of 354 days. As a result, the months as well as Islamic religious festivals migrate through all the seasons of the year. (Consider the ramifications for a Moslem couple who wish to marry in June. If they aren’t careful, it could be a December wedding! And all that food and inconvenience…)

The ancient Egyptians used a calendar with twelve months of thirty days each, for a total of three hundred and sixty days per year. About 4,000 BC they added five extra days at the end of every year to bring it more in line with the solar year (365 1/4 days). These five days became a festival because it was thought to be unlucky to work at that time (or to let one’s black cat leave for work at this time). Instead of having a single leap day every four years (as we do now) the Egyptians allowed the one-quarter day accumulate. After 1,460 years, or four periods of three hundred and sixty five years, they added an entire leap year of three hundred and sixty five days. As the years passed, the Egyptians fell out of sync with both the seasons and other Egyptians, and the summer months eventually fell in the winter. Only once every 1,460 years did their calendar year coincide precisely with the solar year. Surely one dilemma had to have been whether they had to wear summer clothes in the wintertime and vice versa.

When Rome emerged as a world power, the difficulties of making a calendar were more complicated because of their superstition that even numbers were unlucky. Hence, their months were 29 or 31 days long, with the exception of February, which had 28 days. The problem was, however, that four months of 31 days, seven months of 29 days, and one month of 28 days only added up to 355 days. Therefore, the Romans introduced an extra month at no additional charge called Mercedonius, which contained 22 or 23 days and was added every second year. Even with Mercedonius, the calendar became so far off that Julius Caesar, advised by the astronomer, Sosigenes, ordered a sweeping reform.