In Book III, Ptolemy is going to start using actual observations to determine how things change over long periods of time. In order to do so, we will need to explore the calendar system that is used in the Almagest, namely the Egyptian calendar.
This calendar is quite simple in form. It consists of 12 months that are 30 days each. Immediately, you should notice that this is only 360 days, which means that it’s slightly short. To make up for this, 5 intercalary days (ones that aren’t part of the main calendar), or epagomenal days, are added to the end of the year.
But this still isn’t quite right as the year is actually 365 $\frac{1}{4}$ days which means this calendar would lose a day every 4 years. Ptolemy III (No relation to the astronomer Ptolemy) decreed in 238 BCE that every 4 years an extra epagomenal day should be added to make up for this, but it didn’t catch on.
The result was that the year slowly drifted completing a full cycle every 1,461 Egyptian years. Unfortunately, this makes it impossible to consistently equate a month in the Egyptian calendar with one of our own in the Julian calendar as a given month/day in the Egyptian calendar will not consistently be the same month/day in the Julian one.
To fully understand the relationship between the two, it requires knowing which epoch (or era) you are talking about. For the most part, Ptolemy uses the Nabonassar era, so named for the reign of Nabonassar, which began on February 26, 747 BCE in the Julian calendar. Thus, the first day of the first month, Thoth, began that day.
The months, in order, are:
- Thoth
- Phaopi
- Athyr
- Choiak
- Tybi
- Mechir
- Phaemenoth
- Pharmouthi
- Pachon
- Payni
- Epiphi
- Mesore
Another important note of the Egyptian calendar is that it defines the start of a day at sunrise. Thus, if it is midnight, there are still 6 hours left in the Egyptian day1. This is the convention Ptolemy uses, despite defining epochs as starting at noon on a given day.
However, this is not the only system of chronology that pops up in the Almagest. When referring to observations made by others, Ptolemy often restates the observation in whatever system they used. Indeed, the very first date we’ll encounter in Book III is from an observation made by Hipparchus who used Kallippic2 cycles which is a variation on the Metonic cycle, named after Meton of Athens. In 431 BCE, he developed a 19 year cycle consisting of 6,940 days (which comes out to 365$\frac{1}{4} + \frac{1}{76}$ days per year.
Then came Kallippos3, who revised this to an even 365$\frac{1}{4}$ days per year. To do this, he introduced an anti-leap year, dropping a day from 4 of the years in the cycle. This led to a full Kallippic cycle of 76 years being 27,759 days.
As with before, the system needed a zero point which was the summer solstice, probably June 28, 329 BCE. The second and third Kallippic cycles would then begin in the years 253 BCE and 177 BCE respectively.
So to take a quick example, Ptolemy gives a date as “the 17th year of the Third Kallippic Cycle, Mesore 30”. This would imply that we are 17 years after the beginning of the third Kallippic cycle began, which should put us right around 160 BCE. However, because the start of the year wanders, we can’t say immediately. To get that answer, we would need to do more work to determine exactly where this would fall compared to the Julian calendar which is beyond the scope of this work.
There are a few other systems that apparently crop up in the Almagest, but as the above covers everything we’ll see in Book III, I’ll leave those until a later time. In addition, the Toomer translation provides dates in the Julian calendar, so I will be presenting those alongside any other dates for convenience as my purpose is more to learn the astronomy, rather than the calendar.