Definition:Calendar/Julian

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Definition

The Julian calendar is the calendar which was introduced by Julius Caesar in $45 \, \text{BCE}$.

It divides the year into:

$365$ days for every $3$ out of $4$ years

and:

$366$ days for every $1$ out of $4$ years, known as a leap year.

The years themselves are given an index number, and are known by that number.


A standard numbering system was introduced by Dionysus Exiguus.

He identified a particular year as being $525 \, \text{A.D.}$, where $\text{A.D.}$ is an abbreviation for Anno Domini, Latin for in the year of the Lord.

The year $1$ was conventionally supposed to identify the year of the birth of Jesus of Nazareth, although the accuracy of this has since been questioned.

Years before $1 \, \text{A.D.}$ are counted backwards and assigned the label $\text{B.C.}$.

However, note that the year immediately prior to $1 \, \text{A.D.}$ is $1 \, \text{B.C.}$, not the intuitive year $0$, a discrepancy that can cause confusion.


Using this system of numbering, a leap year is identified by this number being divisible by $4$.


The $365$ or $366$ days in the year are divided into $12$ approximately equal sections called months, which are assigned both names and index numbers:

\(\ds 1:\) \(\) \(\ds \) January \(\quad\) $31$ days
\(\ds 2:\) \(\) \(\ds \) February \(\quad\) $28$ days, or $29$ days in a leap year
\(\ds 3:\) \(\) \(\ds \) March \(\quad\) $31$ days
\(\ds 4:\) \(\) \(\ds \) April \(\quad\) $30$ days
\(\ds 5:\) \(\) \(\ds \) May \(\quad\) $31$ days
\(\ds 6:\) \(\) \(\ds \) June \(\quad\) $30$ days
\(\ds 7:\) \(\) \(\ds \) July \(\quad\) $31$ days
\(\ds 8:\) \(\) \(\ds \) August \(\quad\) $31$ days
\(\ds 9:\) \(\) \(\ds \) September \(\quad\) $30$ days
\(\ds 10:\) \(\) \(\ds \) October \(\quad\) $31$ days
\(\ds 11:\) \(\) \(\ds \) November \(\quad\) $30$ days
\(\ds 12:\) \(\) \(\ds \) December \(\quad\) $31$ days


Thus, for example, the day following the $31$st of January is the $1$st of February, and the $30$th of June is followed by the $1$st of July.


Julian Year

A Julian year is the length of a year as defined using the Julian calendar.

$1$ Julian year $= \begin{cases} 366 \, \text {days} & : 4 \divides y \\ 365 \, \text {days} & : 4 \nmid y \end{cases}$

where:

$y$ denotes the number of the year
$4 \divides y$ denotes that $y$ is divisible by $4$
$4 \nmid y$ denotes that $y$ is not divisible by $4$.


Also see


Sources