Having established that the sphere of fixed stars has a rearwards motion, Ptolemy turns now to
making our observations and records of each of the above fixed stars, and of the others too, to give their positions, as observed in our time, in terms of longitude and latitude, not with respect to the equator, but with respect to the ecliptic, [i.e.,] as determined by the great circle drawn through the poles of the ecliptic and each individual star. In this way, in accordance with the hypothesis of their motion established above, their positions in latitude with respect to the ecliptic must necessarily remain the same, while their positions in longitude must always traverse equal arcs towards the rear in equal times.
In short, Ptolemy is going to lay out a table of stars given in ecliptic coordinates. He justifies this choice by pointing out that this is a simpler system to use over long periods of time since their positions will only change in ecliptic longitude and not latitude and at a constant rate.
He refers back to the instrument he first described for use for the moon which he called an astrolabe and we would refer to as an armillary sphere and describes how it can function for the purpose of finding the position of stars down to sixth magnitude. To help us get started, let’s bring back the picture of the instrument so we can refer to it more easily:
We arranged the first of the above-mentioned astrolabe rings [to sight] one of the bright stars whose position we had previously determined by means of the moon, setting the ring to the proper graduation on the ecliptic [ring $3$] for that star
If we refer back to the instructions on how to use this instrument from Book V, you’ll see this step mirrors the instructions there, except Ptolemy is now describing doing this for a star of known position instead of the sun for its calculated position. However, the concept is the same. What he’s describing is aligning rings $2$ and $3$, which are the ecliptic latitude and longitude respectively, so they are aligned with the celestial coordinate systems. This is done by sighting the star with ring $5$. You’ll note that this ring doesn’t have one of the small sights that rotates in the plane of the ring like we see on ring $2$. So what Ptolemy is really doing is trying to look over the edge of the ring until the star just seems to lie on the face as you look down the edge. What’s not mentioned in this section is that ring $4$ will need to be rotated properly to allow for this although that was mentioned in the instructions in Book V.
Then, while that is held in position the affixed set of equatorial rings ($3$ and $4$) are rotated until the known ecliptic longitude of the star falls at the edge that was sighted down of ring $5$. This aligns the equatorial rings.
then set the other ring [ring $2$], which was graduated along its entire length and could also be rotated in latitude towards the poles of the ecliptic, to the required star, so that at the same time as the control star was sighted [in its proper position], this star too was sighted through the hole on its own ring. For, when these conditions are met, we could readily obtain both coordinates of the required star at the same time by means of its astrolabe ring [ring $2$]: the position in longitude was defined by the intersection of that ring [ring $2$] and the ecliptic [ring, $3$], and the position in latitude by the arc of the astrolabe ring [$2$] cut off between the same intersection and the upper sighting hole.
Once the equatorial rings were aligned, ring $2$ is used to sight the target star. Readings can then be taken from rings $2$ and $3$. The ecliptic longitude by where the edge of ring $2$ falls on ring $3$, and the ecliptic latitude by the position of the rotating sight on ring $2$.
Ptolemy indicates that one of his goals, by making these observations is to “display the arrangement of stars on the solid globe”1.
Next, he indicates that the upcoming star catalog will be broken down into four columns. The first will be a description of the star’s position “as part of the constellation”.
The second is the position in ecliptic longitude for the “beginning of the reign of Antoninus”. Toomer cites this as July $20$, $137$ CE. If you look Antononius up online, it appears his reign started in $138$ CE, so I suspect Ptolemy is not using the actual date of his ascension, but rather, the first day of that year in the Egyptian calendar. Since Ptolemy is giving a specific date, my suspicion is that he is adjusting the stellar positions using the precession we derived in the previous posts, to standardize each observation for that date. However, he does not directly state this2 nor expound on how he has performed the calculation3. Also, when entering values into this column, Ptolemy states that he will, as usual, not give the total ecliptic longitude, but rather break the longitude down by zodiological signs.
In the third column, he gives the ecliptic latitude, north or south of the ecliptic.
In the final column, he lists the observed magnitude of the star.
Ptolemy then gives some definitions which should already be familiar. He defines what it means for a star to be “in advance of” or “to the rear of” as a star whose ecliptic position [i.e., longitude] is “in advance of” the other. This is rather circular, but we can remember that “in advance” tends to mean in the direction of the motion of the sky (east to west) and “rearward” means the opposite (west to east)4.
He also defines “north” and “south” as meaning closer to the respective north or south pole of the ecliptic.
Lastly, he notes that the description of the positions of the stars he gives may not match those of the astronomers that came before them because Ptolemy likely imagined the figure representing the constellation differently. For example:
those stars which Hipparchus places “on the shoulders of Virgo” we describe as “on her sides” since their distance from the stars in her head appears greater than their distance from the stars in her hands, and that situation fits [a location] “on her side”, but is totally inappropriate to [a location] “on her shoulders”.
However, he reminds us, that if we are unable to identify a star by its description, we can merely compare the positions to get an identification. Interestingly, the identity of all the stars Ptolemy lists are not entirely known to modern astronomers. That’s beyond the scope of this post, but I do hope to be able to research and discuss their identification further at some point.
And that’s essentially the end of Book VII. The remainder of it will consist of the star catalog which spills over into the beginning of Book VIII as well.
- He’ll describe this globe in $VIII.3$.
- Although the discussion above regarding the choice of coordinate system could be taken to indicate such.
- Not that such a simple calculation should need explanation.
- We do see some exceptions to this, but Ptolemy generally notes that this will be “in advance of the order of the signs”.