Article of the month August

Time system conversion

Earlier articles described the Babylonian, Italian and Antique hours in brief.

See Article of the month, Archives, 2004, month 12
See Article of the month, Archives, 2005, month 01
See Article of the month, Archives, 2005, month 07


We will now discuss the relation between these time systems, and how to convert between them with a graph.
First, here are the definitions of the four time systems again:

Apparent time	the natural day is divided in 24 hours; the reference is twelve noon, in the middle of the daylight period
Babylonian time	the natural day is divided in 24 hours, starting at sunrise
Italian time	the natural day is divided in 24 hours, starting at sunset
Antique time	any daylight period, from sunrise to sunset, is divided in 12 hours

We see conversion graphs as early as those on 16th century card dials, but here is a modern version.
The lozenge pattern with straight lines in the first figure converts between apparent, Babylonian, and Italian time.

To the upper right is a combination date and latitude scale.
The date uses a zodiac calendar, and for the latitude, a range from 36 to 56 degrees was chosen.
Bottom right outlines the use of the graph.

Choose the correct combination of latitude and date and draw AB at right angles to the graph.
Draw BDC. This is the basis for this date-latitude pair.
The scale to the right reads directly the lengths of the day and night periods.
Horizontal lines from B and C to the left show the times of sunrise and sunset.

Now, how do we convert between time systems?
With BDC still in the same place, choose an apparent time on the left scale, and draw a line to the right to BDC.
Then draw a line parallel to the blue lines to read Babylonian time to the left, or follow the red lines to read Italian time.
To convert Babylonian or Italian time into apparent time, do the reverse.
This way, one given allows you to determine the other two.

And how can we convert to or from Antique time? That is the subject of the second figure, added below.
From the basis BDC, follow the magenta lines to read in which Antique hour we are.
This second figure is our final conversion graph.

A third figure, below, is a worked example.

Latitude: 52N
Date: between Aries and Taurus
Daylight period: 14 hours
Night time period: 10 hours

Sunrise: 5 hours apparent
Sunset: 19 hours apparent

Conversion :
Apparent time: 9 hours
Babylonian time: 4 hours
Italian time: 14 hours
Antique time: almost halfway through the fourth hour

Of course, equations will do as well.
Calculate the half daylight arc T in degrees: cos T = -tan phi . tan delta,
where phi is latitude and delta is the solar declination for the date.
In hours, the half daylight arc HD = T / 15 hours.
In our example, phi = 52 degrees, delta = 11.5 degrees, T = 105 degrees, HD = 7 hours.
Daylight period = 2.HD = 14 hours. Night time period = 24 – 2.HD = 10 hours.
Sunrise = 12 - HD = 5 hours, sunset = 12 + HD = 19 hours.

Conversion example:
Apparent time ZT = 9 hours
Babylonian time = ZT - ( 12 - HD ) = 4 hours
Italian time = 24 - ( 12 + HD - ZT ) = ZT + (12 - HD ) = 14 hours.
Antique time = Babylonian time . 6 / HD = 3.4 hours. This is in the fourth hour.