It is one of the tools of a medieval calendar,
which served for
determining the day in the week for a given date. In this system, 1^{st}
January is assigned A, 2^{nd} January B, etc. 7^{th}
January is assigned G. This sequence of letters is repeated all year round. The
dominical letter of given year is then the letter that pertains to the first
Sunday in January. If Sunday pertains e. g. to 2^{nd}
January, the dominical letter is B, if it is 6^{th} January, the dominical letter is F.
In 2009, the first Sunday was on 4^{th} January so
the dominical letter was D. For Monday
5^{th} January it was E, for Tuesday 6^{th}
January F, for Wednesday 7^{th} January G. Thursday 8^{th}
was assigned A again... etc.

In case of leap year, there are two applicable letters: the first one for January and February and the second one for the rest of the year. For the next year (if it is not a leap year), the cycle shifts one letter backwards; that means, the dominical letter for 2010 will be C, for 2011 B, for 2012 A and G, for 2013 F… The cycle repeats after 28 years (the Sun cycle). This manner of the determination of the dominical letter was created by Luigi Lilio in connection with the reformation of the calendar performed by Pope Gregory XIII in 1582.

Clockmakers lightened their work and they copied a chart of valid dominical letters in the astronomical book on page 50. We shall add an explanation that the dominical letters change in the cycle of 28 years (with the exception of the Gregorian calendar which repeats every 400 years, not 100 years).

If we divide a year by 28, the remainder after dividing by an integral number and increased by nine indicates a line in this chart. Because the Gregorian calendar elaborated insertion of leap years, we get different dominical letters for years from the Julian calendar and the Gregorian calendar. We shall also add that the clerk made a mistake and he inscribed the heading of the third column again: "Litera Domini: Anni Juliani" instead of "Gregoriani". It is sure the third column shows dominical letters for the Gregorian calendar.

A calculator
corresponding with the chart for 17^{th} century
(years 1601 – 1699, to
be precise).

The
astronomical clock does not display the dominical letter. It was
announced and
posted up for every year separately. It is inscribed on the calendar
desk and
it can display the day of the week and the day of the month with just
one
indicator. You can see how it works in the simulator of the calendarium.