Why Is It That 1896 Was a Leap Year But Not 1900?

The rules for determining leap years are rooted in the Gregorian calendar, which is the most widely used calendar system in the world today. Understanding these rules requires a thorough knowledge of the calendar system, as well as the concept of sidereal days and the Earth's revolution around the Sun.

What Is a Leap Year?

A leap year is defined as a year containing an additional day in the month of February, making it 366 days long instead of the usual 365. This extra day, February 29, is added to keep the calendar year in alignment with the Earth's revolutions around the Sun.

The Rules for Determining Leap Years

The main rule for identifying leap years is that a year must be divisible by 4. However, there are exceptions to this rule, particularly for years that are divisible by 100. Here’s a detailed breakdown of the leap year rules:

Basic Rule

A year is a leap year if it is divisible by 4. This means that any year ending in '00' or any multiple of 4 is a potential leap year.

Exception for Centuries

However, if a year is divisible by 100, it is not a leap year unless:

Exception to the Exception

The year must also be divisible by 400 to be a leap year. This is the key distinction that differentiates between a century year that is a leap year and one that is not.

Application to 1896 and 1900:

1896: 1896 is divisible by 4 (1896 ÷ 4 474), so it is a leap year. 1900: 1900 is divisible by 4 (1900 ÷ 4 475) and also by 100 (1900 ÷ 100 19). According to the Gregorian rules, since 1900 is a century year and not divisible by 400, it is not a leap year.

Understanding the Earth's Revolution

To properly understand why 1900 was not a leap year, we need to consider the period of the Earth's revolution around the Sun. A sidereal day lasts for 23 hours 56 minutes 4.091 seconds and is slightly shorter than the solar day, which is measured from noon to noon and lasts for 24 hours.

In the Gregorian calendar, a normal year consists of 365.242189 days. This is slightly shorter than the actual length of a sidereal year, which is 365.2425 days. To reconcile this discrepancy, leap years are introduced every four years, with the exception of century years that are not divisible by 400.

Years That Are Not Leap Years Due to the Exception:

The following years do not qualify as leap years since they are evenly divisible by 100 but not by 400:

1700 1800 1900 2100 2200 2300 2500 2600

Years That Are Leap Years:

The following years are leap years because they are evenly divisible by both 100 and 400:

1600 2000 2400

Declaring a Year as a Leap Year

To determine whether a year is a leap year, follow these guidelines:

The year must be divisible by 4. In the case of century years, the year must also be divisible by 400. Leap years have 366 days, while normal years have 365 days.

Examples:

1896 is a leap year because 1896 ÷ 4 474. 1900 is not a leap year because although 1900 ÷ 4 475 and 1900 ÷ 100 19, 1900 is not divisible by 400. 1996 is a leap year because 1996 ÷ 4 499. 2100 is not a leap year because although 2100 ÷ 100 21, it is not divisible by 400.

In conclusion, the rules for determining leap years are critical to maintaining the accuracy of the Gregorian calendar. The exceptions for century years not divisible by 400 are what set 1896 apart from 1900, making 1896 a leap year and 1900 a common year.