I’ve known this chapter was coming for awhile, and have struggled to decide how to deal with it. The reason is that, Ptolemy goes through various climate zones as defined by Hipparchus. In particular, they are defined by their latitudes, beginning with the equator, all the way up to the north pole. For that 90º, it is broken into 39 zones.
As such, this chapter has much in common with the tables we’ve seen previously. But those were straightforward to reproduce. But since the information in this chapter is not particularly tabular, it would be a hefty post to cover each one. But on the other hand, the footnotes in the translation make specific note that the information in this chapter is not referenced again.
Thus, I’ve debated about how much to say about it, and after deliberation, I’ve decided to only give a few highlights.
The Equator
[The equator] is the only parallel which has every day equal to every night.
When I taught astronomy labs back at KU, students were given a long term project in which they had to observe the sunset over the course of the semester to see how it changed. The result was that the points it rose and set was more northwards in the summer, and southwards in the winter. This resulted in a longer arc in the summer and a shorter one in the winter which is the reason for the difference in length of day.
But this change in position is an effect of the latitude. At the equator, the sun rises and sets east and west every day. While the sun still only passes the zenith on the equinoxes, since it rises and sets due east and west, this creates equal arcs across the sky: 180º no matter how you slice it since it’s always a great circle. Thus, the length of day and night are equal1.
While the sun hits the zenith on these dates, on the other dates the sun peaks more north or south from the zenith, which means that the direction a gnomon can point either direction. This is true for all latitudes between the tropics.
Interestingly, if you look at the map I’ve posted above, you’ll notice it doesn’t extend all the way down to the equator2. Ptolemy merely discusses this region as a thought experiment. As it was a region unknown to Ptolemy he engages in a bit of speculation:
It is said that the regions beneath3 the equator could be inhabited, since the climate must be quite temperate.
Arctic Circle
The parallel where the longest day is 24 equinoctal hours is 66;8,40º from the equator.
Here, Ptolemy defines the arctic circle although he does not call it such. There, on the summer solstice, the sun skirts the horizon, but never quite sets. The result of this:
[T]he shadow of the gnomon points towards every part of the horizon.
From here, Ptolemy again declares that we’re in uncharted territory and continuation is merely a thought exercise.
North Pole
[At the north pole] every year contains only one day and one night, each about six months long, and the gnomons always throw shadows in all directions. Further special characteristics of this latitude are that the north [celestial] pole is in the zenith, and the equator coincides…with the horizon.
The north pole ends up being in my mind a very easy place to visualize. In most cases, I try to visualize the way the sky works by imagining a hemisphere of the celestial sphere with its apex being the point directly above the point on the globe at the center. In other words, your location’s zenith projected onto the celestial sphere. That hemisphere is the sky for that location.
The trouble with visualizing things is that the Earth is spinning, so that hemisphere is always sweeping around the celestial sphere. It makes it messy. But at the north pole, the point of the zenith coincides with the north celestial pole, which means that the hemisphere of the sky is always the northern hemisphere of the celestial sphere. It simply rotates under it. This makes things a lot easier to visualize.
Or as Ptolemy puts it:
[T]he whole hemisphere north of the [celestial] equator is always above the earth, and the whole hemisphere south of the [celestial] equator is always below the earth.
- If we want to flesh this out a bit more, this is not strictly true as this treats the sun as a single point of its center. Because the sun has an angular width, the edge will rise before the center, and the center will set before the trailing edge which extends the daylight by a few minutes. In addition, the atmospheric refraction also extends the length of the daylight.
- In case you can’t remember exactly where the equator falls in Africa, it pretty much cuts it in half vertically, below the portion that sticks out into the Atlantic in the west, well below where the map cuts off.
- When Ptolemy says “beneath”, in this context he is meaning “on”, not “south of”. I suspect the usage of beneath stems from his concentration on the celestial sphere, and thus, objects “on” the equator, fall “beneath” it in the larger projection.