Introduction.
In Almagest VIII 2 Ptolemy gives a description of the Milky Way, as seen from his Alexandrian observing location. In it, he mainly focuses on three aspects of his theme: first, the location of the limits of the bands which constitute the Milky Way. He points these limits by selecting certain stars which are at or close to, the point in which the milk ceases to be perceptible. Second, he gives us some vague indications about the density of the milk along its path. These variations are conveyed through ambiguous phrases such as the indication that the milk is “somewhat denser” (ἠρέμα πυκνότερα) in some place, or with a “smoky” (καπνώδης) appearance in other. While we cannot get a very precise image from these sentences, they nevertheless allow us to have a general picture of what he was looking at, and sometimes even relate his description to modern labels given to some regions of the galactic belt.1 Third, in his description Ptolemy also gives us a general description of the structure of the Milky Way, distinguishing between two main sections. One continuous to the south, and one which is located between the regions of Ara and Cygnus. This second, northern belt is itself cut in two parts by a dark region, which today we call “the Great Rift”, and Ptolemy described as “[…] considerable gap of open space […]”2.
The description of the Milky Way is given after Ptolemy’s stellar catalogue in VIII 1, and before his instructions to build a solid globe in VIII 3. The order makes sense: he needs to have the stellar labels and coordinates in order to use the stars themselves to describe and locate the milk in a meaningful way. Because the milk itself moved together with the rest of the fixed stars, it was natural to depict it together with them in the physical representations of the celestial sphere, such as the solid globes which were crafted in those days.
Although much work has been devoted to the stellar catalogue of the Almagest, and also to the extant evidence of ancient celestial spheres, there is no substantial scholarly work devoted to Ptolemy’s description of the Milky Way. We can just barely, for example, find a couple of mentions in (Pedersen, 2010: 259 and Neugebauer, 1975: 890). I expect that this work will serve as a monograph that makes an initial survey of the topic, and provides the necessary groundwork to foster future studies.
The first section of the paper deals with the location of the Milky Way in Ptolemy’s times for an Alexandrian observer. One of the more striking features of the text is that Ptolemy describes the entire Milky Way, beginning in Centaurus, moving towards the galactic center in Sagittarius, and going all the way round up to Argo. This would not be possible for an observer today. I will show, via a brief argument, how the effect of precession account for the difference, and how the milk was positioned in ancient times with respect to an observer in those parts of the world.
The second section, which is the longest, is focused on Ptolemy’s description properly. First, I will give a general account of the structure Ptolemy gives: the aforementioned two main belts, and how they are divided. Then, following the order of the Almagest, I will begin by the southern belt in Centaurus, and continue towards Sagittarius, all the way around. After that, I will focus on the two main parts of the northern belt, one on each side of the Great Rift. Finally, I will give some concluding remarks.
The paper follows Ptolemy’s order, describing the appearance of the milk in successive constellations, starting in Centaurus. My analysis is made according to the following pattern: first, I reproduce Ptolemy’s description in a given region. Ptolemy indicates the stars (mostly) following the labels he assigned to them in his catalogue. Therefore, I in turn indicate the corresponding star number for the catalogue.3 In most cases this is a straightforward procedure. Then, I also give modern identifications for the stars in Ptolemy’s catalogue. For this, I mostly use the identification given in Toomer’s edition. After this, I identify the location of each of the stars in a high-resolution image of the Milky Way. To avoid excessively big labels which would hinder a clear visualization, I number them in the image following the order of appearance in Ptolemy’s text. The caption of these images correlates these numbers with the modern names of the stars. Then, I do the same thing in Pannekoek’s diagrams of the Milky Way (more on this below). Finally, I compare Ptolemy’s description with the depictions in the high-resolution photograph and Pannekoek’s diagrams and analyze how they relate to each other.
The use of images deserves some additional clarifications. The high-resolution photograph was produced by the European Southern Observatory as part of their GigaGalaxy Zoom Project, in association with astrophotographer Serge Brunier. Regarding Pannekoek’s diagrams, they are taken from Die Nördliche Milchstrasse (1920) and from Die Südliche Milchstrasse (1928). They are isophotic charts4 that depict the constellations around the galactic equator, together with a numeric representation of the brightness of each region. The method he uses to measure the brightness of the milk is an adaptation of Argelander’s method for measuring the brightness of stars (Pannekoek, 1920: 2; 1928: 11). It is based on a fairly sophisticated procedure that takes many normalpunkte or normalstelle, and produces a common measurement system, which is later combined with visual descriptions to produce accurate diagrams. A full explanation of the reasoning behind the values given to each region is beyond the scope of this paper. It can be found in (Pannekoek, 1920: 2-5). The inclusion of Pannekoek’s diagrams in this paper serves as an additional support to the presence of modern photographs, and as an objective instrument to evaluate the consistency of Ptolemy’s indications of brightness, particularly regarding the determination of the limits of the milk.
Finally, I will assume a division of the celestial sphere by the galactic equator, where the north will be the hemisphere in which the north galactic and celestial poles are located, and south will be the other hemisphere. This is not always the convention used by Ptolemy, who is not consistent in this regard. Thus, while he sometimes talks about north and south, in other instances he refers to my northern and southern limits of the milk as the eastern and western limits, or the equivalent more advanced or rearmost limits.
Position of the Milky Way as seen from Alexandria in Ptolemy’s times.
The equatorial position of the galactic north for B1950.0 is 192;15° for RA, and 27;24° north for declination (Meeus, 1998: 94). This means that the northernmost latitude from which the entire Milky Way’s equator is visible today is about 27;30°. Because Alexandria’s latitude is 31;12° north, this shows that today it is not the case that the entire galactic plane is visible from Alexandrian latitudes: the declination of the galactic north pole would have to be at least around 31°.
While the effect of the variation of the obliquity of the ecliptic is negligible when it comes to the inclination of the galactic equator to the celestial equator, this is not the case with the effect of precession. The B1950.0 ecliptic position of the galactic north is 179;19,29° for longitude, and 29;48,43° north for latitude. If we assume a value of 50’’ per year for precession, we get a longitude for 140 of 154;11,9°. This means a declination of the galactic north for 140 of 37;23,50°.
So, in Ptolemy’s times, an observer at Alexandria would have been able to observe the entire equator of the Milky Way (“[…] the great circle drawn approximately along the middle of it […]” Toomer, 1984: 400) throughout one year. Nevertheless, because the varying width of the Milky Way spans several degrees on both sides of the galactic equator, the visibility of the entire galactic equator does not assure that the Milky Way itself will be wholly observable in all its details, particularly some sections near its rims. As we saw, Ptolemy would have been able to see up to about 37.5° - 31° = 6° to the south of the southernmost point of the galactic equator. This is a region some 4° southeast of the intersection of the two lines in Crux, almost in the center of the Coalsack (point SP in Figure 1). The relation between maximum altitude and distance to this southernmost point in the galactic equator follows a sinusoidal curve, with a maximum altitude of about 37.5° + 31° = 68.5° at the northernmost point of the galactic equator, which is about 1.5° to the northwest of the middle star in the “W” of Cassiopeia (point NP in Figure 1). However, the altitude reached by each point of the galactic equator is not the only variable relevant to study the visibility of the belt of the Milky Way. The angle between the galactic equator and the horizon varies throughout the day. For an observer at Alexandria in 140 the maximum would have been, of course, 68.5°. This means that while some points of the galactic equator might never rise more than 8° or 12° above the horizon, the band of the Milky Way which is about 15° in width on each side might still be mostly or entirely visible, due to the fact that at that moment the angle between the galactic equator and the horizon is large enough. In Figure 1 points I (in the constellation of Vela) and II (in the constellation of Ara) indicate the limits of the southern region where the visibility of the band is always less than 15° to the south of the galactic equator.
One last variable to remember is extinction, which is the absorbing and scattering effect that the atmosphere has on the light coming from the sky. As it is natural, the closer the object is to the horizon, the more relevant this effect becomes.
Ptolemy’s description.
Ptolemy begins his description by indicating the general structure of the Milky Way. He says that “[…] the Milky Way is not strictly speaking a circle, but rather a belt of a sort of milky colour overall (whence it got its name); moreover this belt is neither uniform nor regular, but varies in width, colour, density and situation, and in one section is bifurcated […] The bifurcated part of the belt has one of its ‘forks’, so to speak, near Ara, and the other in Cygnus. But, whereas the advance [part of the] belt is in no way attached to the other part, since it forms gaps both at the fork by Ara and at the fork by Cygnus, the rearmost part is joined to the remainder of the Milky Way and forms [with it] a single belt […] It is this belt which we shall describe first, beginning with its southernmost section.”6
The description is simple. Throughout most of the Milky Way, there is a single belt. But when we approach the center in Sagittarius from each side, we find that it bifurcates, with one belt being continuous with the rest, and another going towards the north. As Ptolemy will comment later on, this second belt is itself divided into two sections. Refer to Figure 2.
As Ptolemy says, he begins with the southern belt, and he does so by studying the milk in what was for him the southernmost constellation of the Milky Way: Centaurus.
Centaurus.
Ptolemy begins his description of the Milky Way in Centaurus by locating it as passing “[…] through the legs of Centaurus”7, and then says that in this region it is dimmer than in other parts. He then indicates that “[…] the star on the knee-bend of the right hind leg is a little further south than the line [bounding] the milk to the north […]”8. The description is identical to the star XLIV 31 in his catalogue, and the identification as γ Cru is certain. He then says that the same is true of two more stars, “[…] the star on the left front knee and the star under the right hind hock.”9 In these cases the descriptions match to XLIV 36 (β Cru) and 32 (β Cen), respectively. Next, he defines the center of the band: “[…] the star in the left hind lower leg lies in the middle of the milk […]”10 Toomer identifies it as XLIV 33 (“The star under the knee-bend of the left [hind] leg”11, or δ Cru, which is a reasonable identification. With respect to the southern rim, Ptolemy indicates that “[…] the stars on the hock of the same leg and on the right front hock are to the north of the southern rim by about 2° […]”12 These stars can be identified with certainty as α Cru and α Cen, respectively. Finally, he indicates that the milk is somewhat denser in the region near the hind legs.
Refer to Figure 3. The galactic equator passes just below 2 and above 3 (refer to Figure 4 for an accurate indication of its location). Ptolemy’s description indicates that 1, 2 and 3 are just below the northern rim of the milk, which is a strange description since their galactic latitudes are very different. If we compare this description to the photograph in Figure 3, and to Pannekoek’s corresponding chart (see Figure 4) we can see that while 1 is certainly “a little further south” of the northern rim of the band13, 2 and 3 are much more separated. The positioning of 4 “in the middle of the milk” is stranger still. This is not because it is not on the galactic equator. The determination of this great circle is somewhat arbitrary, and Ptolemy might have in mind a circle a little bit to the north of our current determination of its position. The difficulty lies in the fact that 4 is to the north of 2, which was previously used to determine the northern rim. All this confusion is nevertheless understandable: this part is, as we saw, the one with the worst visibility. Ptolemy would have not been able to see much under the Cross, and even the observations of those stars which were visible would have been much disturbed by their low altitude.
This also explains why he does not mention one of the most salient features of this region, the Coalsack (at the center of Figure 4, and whose lack of luminosity is marked by Pannekoek with a definite “00”).14 Ptolemy does, nevertheless, notice the increased brightness in the rear legs of the Centaur. He is likely referring to the bright clouds in Crux and Carina, clearly visible to the right of the Cross.
Lupus and Ara.
The next section he considers is within Lupus and Ara. He says that “[…] the northern rim of the milk is about 1.5° from the star on the rump of Lupus, and the southern rim encloses the star on the burning-apparatus of Ara, but just grazes the northernmost of the two stars close together on the brazier and the southernmost of the two stars in the base, while the star in the northern part of the brazier and the one in the middle of the brazier lie right in the milk.”15 There are six stars in this description, and they can be identified with certainty. The one determining the northern rim is XLV 10 (ζ Lup). The one enclosed by the southern rim is XLVI 7 (ζ Ara). The two which are “just grazed” by the southern rim are XLVI 6 (β Ara) and XLVI 2 (θ Ara). The last two, those which “lie in the middle of the milk”, are XLVI 4 (ε Ara) and XLVI 3 (α Ara). Ptolemy ends this part of the description indicating that “[t]hese sections are rather less dense.”16
Refer to Figure 5. From Lupus we can see ζ Lup, while we have several stars from Ara: ζ Ara, β Ara, θ Ara, ε Ara and α Ara. Ptolemy’s description is fairly consistent with the photograph in Figure 5, and with Pannekoek’s evaluation in Figure 6. While it seems that the 1½° from 1 to the northern rim was a conservative estimate, in the case of the southern rim the limit indicated by 3 and 4 seems more accurate. As in the previous case, the low altitude explains the general lack of consistency: the maximum altitude this region reached in Alexandria was about 11°. With such values, atmospheric extinction plays a major role, and indeed this region would have seemed “less dense” than others. Had Ptolemy been able to have clearer views, he might have noticed the very bright Norma Star Cloud in-between 1 and 5, whose brightness Pannekoek marks with a “73”.
Scorpius and Sagittarius.
The following section is focused on Scorpius and Sagittarius. This is the part of the Milky Way which is in the direction of the galactic center, where the stellar population is the densest, and therefore the appearance of the milk is the brightest. He references many stars: “[…] the northern part of the milk encloses the three joints before the sting of Scorpius and the nebulous mass to the rear of the sting, while the southern rim touches the star in the right front hock of Sagittarius, and encloses the star on his left hand.”17 The three stars near the sting are XXIX 17, 18 and 19 (θ, ι and κ Sco, respectively). The “nebulous mass to the rear of the sting” is M7, an open cluster which is about 0;40° across. In Ptolemy’s catalogue it is XXIX 22.18 The two stars in Sagittarius described here are XXX 25 (η Sgr) and 2 (δ Sgr), respectively. He continues explaining that “[t]he star on the southern portion of the bow is outside the milk, but the star on the point of the arrow lies in the middle of it, while the stars in the northern part of the bow also lie in it, each of them being a little more than 1° removed from one of the rims, the southern star from the southern rim, the northern star form the opposite rim.”19 These four stars are XXX 3 (ε Sgr), 1 (γ Sgr), 4 (λ Sgr) and 5 (μ Sgr), respectively. He ends the section by pointing out that “[t]he area near the three joints is somewhat denser, while the area around the point [of the arrow] is very dense indeed and appears smoky.”20
Refer to Figure 7 and Figure 8. This description shows a remarkable match to the lines in Pannekoek that indicate, in his scale, a density of 30-40. Almost all of the stars that Ptolemy references, and which are in or close to, the sting, are within such areas. If we look at the location of 5, it is remarkably close to the line, while 6 is a couple of degrees inside that limit, just as Ptolemy says. Moreover, 7 is just outside the line, and 8 is indeed “in the middle of it”, lying almost at the very center of the Large Sagittarius Star Cloud. This explains Ptolemy’s note that the area is so dense as to appear “smoky”. Finally, the indication of 9 and 10 as being “a little more than 1°” removed from the northern and southern rims also fits the 30-40 limit Ptolemy seems to be following.
Ophiuchus, Aquila and Sagitta.
Next, Ptolemy describes the parts of the Milky Way in Ophiuchus, Aquila and Sagitta, and it is a somewhat longer description than the previous ones: “The following section is a little less dense […] maintaining about the same width throughout. The star on the tip of the tail of the snake held by Ophiuchus lies in the open, a little more than one degree away from the advance rim of the milk, while the two most advanced of the bright stars below it lie right in the milk: the southern one is 1° from the rear rim, and the northern one, 2° [from it].”21 The three stars he is referring to here are XIV 18 (θ Ser), 15 (λ Aql) and 12 (δ Aql). He continues: “The rearmost of the stars in the right shoulder of Aquila touches the same rim, while the more advanced one is cut off inside it, as is also the more advanced, bright star of those in the left wing.”22 This triplet refers to XVI 8 (σ Aql), 7 (μ Aql) and 5 (γ Aql) in Ptolemy’s catalogue. “Furthermore, the bright star on the place between the shoulders and the two stars which lie on a straight line with it fall a little short of touching the same rim. Next, Sagitta is enclosed entirely within the milk. The star on the arrowhead lies one degree from the eastern rim, while the star on the notch lies two degrees from the western rim. The section around Aquila is slightly denser, and the remainder slightly less dense.”23 The three aligned stars which he indicates are XVI 3 (α Aql), 6 (φ Aql) and one which is not in the catalogue, υ Aql, respectively.24 The two stars in Sagitta are XV 1 (γ Sge) and 5 (β Sge).
Refer to Figure 9 and Figure 10. 1 is right in the middle of one of the darkest parts of the Great Rift, which explains Ptolemy’s description of it as lying “in the open”, i.e., outside the milk. Both 2 and 3 are approximately at the same distance from the southern rim. Ptolemy’s assertion that 2 is closer to the rim than 3 may be grounded on the fact that 2 is within a somewhat darker area than 3, and thus it may be that the milk there is a little bit thinner. Ptolemy’s description says that stars 4, 7, 8 and 9 either “touch” or “fall a little short of touching” the southern rim. In this case, then, it would seem that Ptolemy’s brightness-criterion for determining the rim of the milk is close to Pannekoek’s “20”. The limits indicated with the stars in Sagitta vaguely follow the limits imposed from the north by the Great Rift, and from the south by the gradual darkening of the sky. The region’s brightness tends to gradually fade in the direction of Sagitta, and to be harshly interrupted to the north. This explains Ptolemy’s indication that Aquila’s region is the brightest in the section of the Milky Way described here.
Cygnus and Cepheus.
The regions in Cygnus and Cepheus are next: “Its north-western rim is defined in a reentrant angle by the star in the southern shoulder of Cygnus, the star under it in the same [southern] wing, and the two stars on the southern leg.” 25 Even if their descriptions are not the same, we can match these four stars as IX 11, 10, 13 and 14 in Ptolemy’s catalogue. They correspond to λ, ε, ν and ξ Cyg, respectively. “Its south-eastern rim is defined by the star in the tip of the southern wing-feathers, and encloses the two stars under the same wing outside the constellation, which are about 2° from it [the rim]. The section around the wing is slightly denser.” These stars are IX 12, 18 and 19 (ζ, τ and σ Cyg, respectively). He ends the section with a somewhat detailed description: “The next section is continuous with that belt, but is much denser and seems to have a different starting-point. For it points towards the end parts of the other belt, but leaves a gap between it [and itself]: on it southern side it joins the belt which we are currently describing, which is very rarefied at the junction; but after the point where it forms a gap with the other belt it gets denser, beginning from the bright star in the rump of Cygnus and the nebulous mass in the northern knee. Then it makes a slight bend as far as the star on the southern knee, and continues gradually diminishing in density, up to the tiara of Cepheus. The northern side is delimited by the southernmost of the three stars in the tiara and the star to the rear of those three, at which it also forms two outrunners, one verging to the north and east, the other to the south and east.” The “star in the rump of Cygnus” is IX 5 (α Cyg), while the “nebulous mass in the northern knee” is IX 17 (ω Cyg). The “star on the southern knee” is IX 14 (ξ Cyg), and “the southernmost of the three stars in the tiara [of Cephus]” corresponds to IV 9 (ε Cep). Finally, the star “to the rear [of the three in the tiara]” is IV 13 (δ Cep).
Refer to Figure 11 and Figure 12. As Ptolemy says at the beginning of his description of the Milky Way, its two belts are joined in Cygnus. Since he is now describing the southern belt, here he begins by indicating the general direction of the “reentrant angle” it shows in this region. This is indicated by line 2-1-3-4, which is clearly tilted with respect to the galactic equator, and ends up right in the middle of the part where the belt is forked. The southern rim of this belt is indicated by 5, showing a near perfect coincidence with Pannekoek’s determination. The 2° distance indicated by Ptolemy is about half of the distance implied by the limit he himself determined. Ptolemy’s comment about the slight increase in density around the wing might be due to the contrast the section shows with respect to the far darker regions to the north (the so called “Northern Coalsack”) and the east.
Ptolemy then says that if one follows at the belt in the west-east direction, one will find that it bends to the north, in the direction of the northern belt, only that it is separated from it in the region indicated by the 8-9 line. Pannekoek gives a similar description in his plates, only that he puts the obscuration a little bit to the north-east than where Ptolemy does. There is, however, a clear dark cloud that comes from the north, the Funnel Cloud, which frames this northerly inclined section Ptolemy talks about.
Ptolemy says that this inclined section of the belt goes as far south as 4, much less than the distanced Pannekoek indicates. His indication that the density diminishes to the west is, however, correct. Stars 10 and 11 indeed follow the northern rim of the belt, although Pannekoek indicates a slightly denser spot just above 10.
Cassiopeia.
After Cepheus, Ptolemy briefly describes the Milky Way at Cassiopeia: “Next the milk encloses the whole of Cassiopeia except for the star in the end of the leg. The southern rim is defined by the star in the head of Cassiopeia, and the northern rim by the star in the foot of the throne and the star in the lower leg of Cassiopeia. The other stars and all those round about this [constellation] lie in the milk. The areas near the rims are of thinner consistency, but those at the middle of Cassiopeia display a dense patch running the length [of the Milky Way].”26 The star at the “end of the leg” which is left outside the milk is X 7 (ι Cas). The star that defines the southern rim is X 1 (ζ Cas), and the two stars that define the northern rim are X 11 (κ Cas) and 6 (ε Cas), respectively.
Refer to Figure 13 and Figure 14. 1 is clearly outside the milk, right in the middle of a darker patch. According to Pannekoek’s rendition, line 3-4 indeed follows the northern rim, and 2 almost grazes the southern one. Pannekoek also supports Ptolemy’s indication that there is a strong difference between the much more luminous inner region of the belt at the constellation and the “thinner consistency” of the milk near the rims.27
Perseus.
Perseus is the next constellation: “[…] the righthand parts of Perseus are enclosed in the milk. Furthermore, its northern edge, which is very rarified, is defined by the lone star outside the right knee of Perseus, and its southern edge, which is very dense, by the bright star on his right side and by the two rearmost stars of the three to the south of that.” These four stars are XI 28 (HIP 19949), 7 (α Per), 9 (ψ Per) and 10 (δ Per), respectively. Then, he continues: “Enclosed in it also are the nebulous mass on the hilt, the star in the head, the star in the right shoulder and the star on the right elbow. The quadrilateral in the right knee and also the star on the same calf lie in the midst of the milk, while the star in the right heel is also inside it, a little distance from the southern border.” The nebulous mass refers to XI 1, which is a double cluster: NGC 884 and NGC 869. The star in the head is XI 5 (τ Per), the star in the right shoulder is XI 3 (γ Per), and the star on the right elbow XI 2 (η Per). Afterwards, the “quadrilateral in the right knee” is a reference to XI 16, 17, 18, 19 (b, λ, c and μ Per, respectively). Finally, the stars in the right calf and heel are XI 20 (d Per) and 21 (58 Per), respectively.
Refer to Figure 15 and Figure 16. Ptolemy says that the northern rim, which is not bright, is defined by 1. The southern one, much brighter, by 2, 3 and 4. Ptolemy’s star choices seem to enhance the contrast between both limit of the Milky Way. While it is true that there is a general noticeable difference between them, the three stars he selected for the southern rim are precisely at a particularly bright spot in that region, as it can be seen in Pannekoek’s diagram, where it is labelled with a “32”. The rest of the description is accurate, inasmuch as all the stars he lists are between the two limits he indicated.
Auriga.
Auriga is the next constellation, “[…] displaying a thinner consistency. The star on the left shoulder, called Capella, and the two stars on the right forearm fall just short of touching the north-eastern rim of the milk, while the small star over the left foot in the lower hem define the south-western edge.” In Ptolemy’s catalogue Capella is XII 3. The two stars he refers to are XII 5 and 6 (ν and θ Aur), respectively. The one that defines the southern rim is probably XII 14 (14 Aur, although the identification is not certain28). “The star over the right foot lies half a degree within the same edge, and the two stars close together on the left forearm, called Haedi, lie in the middle of the belt.” The first of these three is, XII 12 (χ Aur), and the Haedi are XII 8 and 9 (η and ζ Aur), respectively.
Refer to Figure 17 and Figure 18. Both the photograph and Pannekoek’s diagram supports Ptolemy’s assertion that the Milky Way is at this point much dimmer. In fact, Capella’s galactic longitude is about 160°, which explains the low density of stars in Auriga. Capella is just to the north of the limit Pannekoek determines, as does Ptolemy. Ptolemy seems to recognize that the milk makes a little turn to the north, because he says that 3 and 4 are within it, almost touching the border, even if they are both to the north of Capella. The southern rim also shows a coincidence between both authors.
As in other instances, Ptolemy’s measurements regarding the distance of a star to a rim of the milk are unsatisfactory: 5 is at least three times away from the southern rim than what Ptolemy indicates. The reference to the Haedi lying “in the middle of the belt” is rather ambiguous. Although it is not easy to determine this with certainty, it would seem, nevertheless, that they are almost on the southern rim.
Gemini.
Ptolemy then says “Next the milk goes through the legs of Gemini, displaying a certain amount of density in elongated form just over the stars at the ends of the legs. Now the advance edge of the milk is defined by the rearmost of the three stars on a straight line under the right foot of Auriga, by the rearmost star of the two in the staff of Orion and by the northernmost of the four stars on his [Orion’s] hand […]” The stars that define the southern rim are XXIV 19 (1 Gem), and XXXV 12 and 9 (χ2 and 72 Ori), respectively. He then continues “[…] the brilliant star under the right hand of Auriga and the star in the rear foot of the rear twin are approximately 1° inside the rear edge, while the stars in the other feet lie in the midst of the milk.” The two stars 1° inside the milk are XXIV 20 and 18 (κ Aur and ξ Gem), respectively. The stars in the other feet are XXIV 17, 16, 15 and 14 (γ, ν, μ and η Gem, respectively).
Refer to Figure 19 and Figure 20. According to Ptolemy, there is a particular dense region around 5-9. If compared to Auriga, the cloud of relative brightness in that region is more continuous, thus justifying the “elongated form” Ptolemy refers to. However, we do not find any particularly bright spot in these parts. The southern limit is defined, according to Ptolemy, by 1-3. Both Figures indicate that this is probably too septentrional. Ptolemy’s location of 4 and 5 as being “1° inside” the northern edge is also incorrect. In both cases, it seems that he is narrowing the width of the milk. This may be due to the fact that, at this point, we are again approaching the southernmost point of the Milky Way (SP in Figure 1), although we are still not within the “15° of maximum altitude” zone (i.e, the zone between I and II in Figure 1).
Ptolemy also says that stars 6-9 are “in midst of the milk”, a comment which is difficult to understand, given that they are located at a similar galactic longitude than 5, and the milk is fairly consistent in its width all across the constellation.
Canis Minor and Major.
The Almagest then says that “[…] the belt passes by Canis Minor and Canis Major: it leaves the whole of Canis Minor outside the milk no small distance to the east, and leaves Canis Major too outside to the west, almost in its entirety; for the star on its ears is caught by a sort of cloud which projects and which then almost touches the three stars in the neck of Canis Major next to that [star] towards the ear, while the lone star over the head of Canis Major, outside it and at some distance, is about 2 ½° inside the eastern rim. The consistency in this whole region is somewhat thinner” The star “on its ears” is XXXVIII 2 (θ CMa), and the three stars in the neck are XXXVIII 3, 4 and 5 (μ, γ and ι CMa, respectively). Finally, the “lone star” may be XXXVIII 19 (δ Mon29).
Refer to Figure 21 and Figure 22. Canis Minor (Procyon) is indeed well outside the milk, as is Canis Major (Sirius). It is not clear what is the shape of the cloud which projects towards 4, 5 and 6. Nevertheless, Pannekoek’s diagram shows an increased brightness around 3, one which could be seen as coming from the north. The location of 7 2;30° within the milk is approximately accurate.
Argo.
“After that the milk passes through Argo. The western rim of the belt is defined by the northernmost and most advanced of the stars in the little shield in the poop.” This is XL 5 (m Pup). And continues: “The star in the middle of the little shield, the two stars close together under it, the bright star at the beginning of the deck near the steering-oar and the midmost of the three stars in the keel are just shorth of touching the same [southern] edge.” These five stars are XL 6 (k Pup), XL 8 and 9 (3 and 1 Pup), XL 17 (ζ Pup) and XL 38 (δ Vel). “The northernmost of the three stars in the mast-holder defined the eastern rim, while the bright star in the stern-ornament is 1° within the same edge, and the bright star under the rearmost little shield in the deck is the same amount, 1°, outside the same edge.” These are XL 22, 2 and 31 (NY Vel, ρ Pup and λ Vel, respectively). Ptolemy then says that “[t]he southernmost of the two brilliant stars in the middle of the mast touches the same edge, and the two bright stars at the point where the keel is cut off are about 2° inside the advance rim. At that point the milk joins the belt through the legs of Centaurus.” The stars are, in the order they are referenced: XL 27 (β Pyx) and XL 35 and 36 (γ Vel and χ Car). Finally, he closes the section by indicating that “[t]he consistency in this area too, throughout Argo, is somewhat rarefied, but the sections of it around the little shield, the mast-holder and the point where the keel is cut off are more dense.”30
Refer to Figure 23 and Figure 24. As in other cases, Ptolemy seems to be defining the limit of the belt with a brightness that is around the value 20 in Pannekoek’s system: stars 1 to 5 are indeed at or close to that line. Stars 6 and 9 are also close to the limit, but on the other side, although Pannekoek locates them a bit inside the “20” limit. The positions of 7 and 8 as being 1° on each side of the northern limit are not accurate: the figure should be three or four times greater. The location of 10 as being about 2° inside the southern belt is a good one, although it is strange that he says the same about 11, which is clearly much farther away from the milk, as it can be seen in both figures.
Ptolemy’s commentary that the regions close to 2, 6 and 10-11 are broadly true, as Pannekoek’s diagram shows (again, the inclusion of 11 does not entirely fit).
The northern belt: Scorpius, Ophiuchus, Serpens.
After the description of the southern belt, Ptolemy goes back to his original division, and describes the northern, curved belt seen in the direction of the galactic center. As I said earlier, this northern belt is divided in two by what Ptolemy describes as a “[…] considerable gap of open space […]”31, which is the dark cloud we know today as the Great Rift. We will begin by looking at the first half of the description Ptolemy makes of this part of the Milky Way.
Ptolemy begins by indicating that “[…] it encloses the three joints of Scorpius nearest the body, but leaves the rearmost star of the three in the body 1° outside its western rim. The star in the fourth joint lies in the open space between the two belts, about the same distance from each, a little more than 1°.”32 These stars in Scorpius are easily identifiable as XXIX 12, 13, 14, 9 and 16. Their modern names are ε, μ, ζ, τ and η Sco, respectively.
He continues: “After that the advance belt turns aside to the east, in the shape of a segment of a circle, defining the advance edge of the milk by the star on the right knee of Ophiuchus, and the rear edge by the star on the same [right] shin, while the most advanced of the stars at the end of the same [right] leg touches the same edge. Subsequently the western rim is defined by the star under the right elbow of Ophiuchus, and the eastern rim by the more advanced of the two stars in the same [right] hand.”33 The knee of Ophiuchus is XIII 12 (η Oph), and its shin is XIII 13 (ξ Oph). The advanced star in the right leg is XIII 14 (36 Oph). The stars that define the two rims are XIII 9 (μ Oph) and 10 (ν Oph), respectively.
Ptolemy ends with this section with the indication that “[f]rom that point on there is a considerable gap of open space, in which lie the two stars on the tail of Serpens next to the star in the tip [of the tail]. The whole of the section of this belt which we have [just] finished describing consists of an extremely fine and almost aery substance, except for the area enclosing the three joints [of Scorpius], which is somewhat more concentrated.”34 The three stars on the tail of Serpens are XIV 16 (ζ Ser), 17 (η Ser) and 18 (θ Ser).
Refer to Figure 25 and Figure 26. Both images confirm the inclusion of Scorpius’ joints 1 to 3 beings inside the milk. His indication that 4 is 1° to the north of it is exaggerated. While the 1° which supposedly separates 5 from both belts is uncertain, the photograph clearly shows that he is right in putting it in the darkness between both.
The shape of this section of the milk is indeed curved. The indication that 6, and 7-8 mark the northern and southern limits is very accurate. Stars 9 and 10, however, seem to be well outside the milk, beyond its end-limits. The indication that 11, 12 and 13 are within the Great Rift is also accurate. Ptolemy’s comment that the area around 1-3 is more concentrated than the rest of this curved section does not seem to have much grounding.
The northern belt: Cygnus.
In this section we will look at the last part of Ptolemy’s description of the Milky Way, which is focused on the part of the northern belt on the other side of the Great Rift. Ptolemy says “After the gap the milk again makes a fresh beginning at the four stars to the rear of the right shoulder of Ophiuchus. The eastern rim of this belt is defined (being just grazed) by the lone brilliant star under the tail of Aquila, while the opposite rim is defined by the star which is some distance to the north of the four just mentioned.”35 The set of four stars is comprised of XIII 25, 26, 27, 28 (66, 67, 68 and 70 Oph, respectively). The brilliant star which defines one rim is XVI 9 (ζ Aql), and the star that defines the other one is XIII 29 (72 Oph).
Ptolemy continues: “From there on this belt, besides being rarefied, is also contracted into a narrow space in the area which is in advance of the star in the beak of Cygnus, so as to produce the appearance of a gap. However, the remained of it, from the star in the beak up to the star in the breast of Cygnus, is wider and considerably denser. The star in the neck of Cygnus lies in the middle of the dense section. A rarefied section branches off to the north from the star in the breast as far as the star in the shoulder of the right wing and the two stars close together in the right foot. From this point, as we said, occurs a clear gap to the other belt, stretching from the above-mentioned stars in Cygnus up to the bright star in the rump.”36 The star in the beak of Cygnus is IX 1 (β Cyg) and the one in the breast is IX 4 (γ Cyg). The stars in the neck and the right wing are IX 3 and 6 (η and δ Cyg, respectively), and the two stars in the right foot are IX 15 and 16 (ο1 and ο2 Cyg, respectively). Finally, the star in the rump is IX 5 (α Cyg).
Refer to Figure 27 and Figure 28. Ptolemy’s indication that the group 1-4 marks the beginning of this part of the northern milk is accurate, as is the indication that 5 “just grazes” its southern rim. The indication that 6 defines the northern rim is also supported by both figures.
Ptolemy then says that the belt rarifies and contracts in the area in advance of 7. This description is both subtle, and accurate. He then says that at this point a much wider and denser region begins, from 7 up to 8. He is referring to the modern Cygnus Star Cloud, one of the most striking features of the Milky Way for modern boreal observers. Star 9 is indeed right in the middle of the star cloud. The following part of the text is not so clear: it is possible that Ptolemy was looking at the set of 8, 10 and 11 as the markers of a part of the cloud which has the shape of an inverted “L”. Indeed, while 10 and 11 are connected by a soft stripe of the milk, the section between 8 and 12 is clearly occupied by a dark spot. This spot marks, as Ptolemy says, the division between this section of the northern belt, and the much larger and continuous southern belt.
Conclusion.
A description of the Milky Way is something of a surprising element in a work such as the Almagest. While the rest of the work is devoted to themes which are potentially tractable via precise mathematical tools, in this chapter he is dealing with something that, to an extent, escapes this approach. Here Ptolemy uses the coordinates of stars to locate the limits of the Milky Way, or to point to this or that of its features. But this is only part of the work. Given that the Milky Way has a complex structure, with different densities and variable shapes along its path, Ptolemy has to combine his mathematical skills with qualitative visual descriptions, in order to convey an appropriate image of his subject. There is here no theory of the Milky Way, no attempt at investigating its nature. He is aware that he is looking at something that “[…] is very apparent even to the casual eye […]”37, and his aim seems to be just to give this phenomenon its proper place within the wider astronomical framework he is developing, by describing it to a certain level of detail and fixing it with respect to the star catalogue he had already given.
The mixed nature of the work is comparable to his geographical books, where we can find the subtle descriptions of borders between regions together with the mathematical discussions about, and determinations of, geographical coordinates of many locations.38 The result of this application of dual skills to the Milky Way is, if not superb, at least with some notorious merits.
Ptolemy recognized many of the main features of the Milky Way: not only the more obvious divisions at Ara and Cygnus, but also possibly the nebulae in Crux and Carina (“near the hind legs of the Centaur”), the Large Sagittarius Star Cloud, the Great Rift and the Cygnus Star Cloud. The use of stars to determine the limits of the milk and areas of particular interest are, in most cases, very accurate. There are, however, exceptions. To see the most salient discrepancies we must look at the positions Ptolemy indicated for τ and σ Cyg in the Cygnus/Cepheus section, of χ Aur in Auriga, ρ Pup and λ Vel in the region of Argo.
As I repeated throughout the paper, it seems that Ptolemy generally considered the rims of the Milky Way to be located at the level of brightness which Pannekoek labels with a “20”. There is, nevertheless, a pattern of deviation from this general value. As the belt gets closer to the center, Ptolemy tends to diminish its width to Pannekoek’s value of 30 and even 40. This may have something to do with the fact that there is a high contrast between the very bright clouds in Sagittarius, and the dark clouds which are intertwined with them. Also, it is possible that the low altitude this area had as seen from Alexandria at the time, with the high effect that extinction had because of this, tended to lower the apparent brightness of the region. As we saw in the cases of Lupus and Ara, this should not be discarded. Pannekoek himself points to this difficulty related to altitude: “It can be seen from this description that Ptolemy did not notice the Coalsack nor the division into two streams in α Cen, which is understandable given the low altitude of those parts above the Alexandrian horizon. For him the bifurcation only begins in Ara-Norma.” (Pannekoek, 1928: A63). Whatever the case, Ptolemy’s description conveys a good image of both the general structure of the Milky Way and a good amount of its fine details.
Acknowledgments.
I would like to thank Aníbal Szapiro, Diego Pelegrin, Christián Carman, and to the two anonymous referees for reading previous versions of this paper. Also, I would like to thank Serge Brunier for kindly providing a high-resolution version of the Milky Way photograph. Finally, I wish to thank the Stanford University Library for their help with scanned versions of Pannekoek´s diagrams.
Funding.
PICT (2019-01532 ) Astronomía pre-Newtoniana: aspectos históricos (segunda etapa).
Notes
1 Because our understanding of the Milky Way has changed so much between Ptolemy and us, the use of terms such as “Milky Way”, “galactic belt” or “galactic center” is ambiguous. While for Ptolemy the Milky Way was a whitish band that crosses the celestial sphere, for us it is the galaxy in which we are located. Both meanings are of course related.
2 Toomer, 1984: 404.
3 Toomer’s translation lists the constellations of the catalogue in Roman numerals, and then each star with Arabic numerals. Even more, Toomer himself gives catalogue identifications of the stars in the Milky Way description.
4 A map, in this case of a section of the sky, where lines of equal luminance are determined.
5 My use of the image is in compliance with ESO’s conditions (https://www.eso.org/public/outreach/copyright/). Therefore, I incur in no copyright infringement.
6 Toomer, 1984: 400.
7 Toomer, 1984: 400.
8 Toomer, 1984: 400.
9 Toomer, 1984: 400.
10 Toomer, 1984: 400
11 Toomer, 1984: 395.
12 Toomer, 1984: 400.
13 Pannekoek’s representations with isophotic lines indicate the limits of the most luminous parts with a thick solid red curved line. These lines can be distinguished in here even if they are black and white. As the decreasing luminosity of the Milky Way is in most places gradual, this limit is certainly arbitrary: in Pannekoek’s drawings it is loosely defined by the number 20. Gradual changes inside and outside this region are also indicated, only with other types of lines.
14 See Pannekoek A63.
15 Toomer, 1984: 400.
16 Toomer, 1984: 400.
17 Toomer, 1984: 400.
18 Ptolemy’s location of the object suggests that he was looking at G Sco, which is a giant star closer to the sting. The qualification as “νεφελοειδῆ”, though, indicates that maybe he was also describing M7. For our purposes, the discussion is not too relevant.
19 Toomer, 1984: 400-401.
20 Toomer, 1984: 401.
21 Toomer, 1984: 401.
22 Toomer, 1984: 401.
23 Toomer, 1984: 401.
24 There is no easy identification in this case. The stars must be approximately in line with α Aql, and that line has to be approximately parallel to the southern rim of the Milky Way. I think that Toomer’s proposal –which is the one I follow here– is the most convincing one (see Toomer, 1984: 401 note 164).
25 Toomer, 1984: 401-402.
26 Toomer, 1984: 402.
27 In Lattusek (2014, 174) it is shown that Bayer’s Uranometria (1603) describes it the other way around, indicating a “void” in the middle of the constellation, and rather brighter rims, and that the error is traceable to what was likely one of Bayer’s sources, Peuerbach’s and Regiomontanus’ Epytoma Almagesti (1496).
28 See Toomer, 1984: 354, note 148.
29 This identification is very doubtful. There is no star of that brightness close to the coordinates given by Ptolemy’s catalogue. δ Mon is the best candidate, but it had a longitude of about 83;40°, and a southern latitude of about 23°, instead of the 79;30° and 25;15° indicated by the Almagest (Toomer, 1984: 387).
30 Toomer, 1984: 403.
31 Toomer, 1984: 404.
32 Toomer, 1984: 403.
33 Toomer, 1984: 403.
34 Toomer, 1984: 404.
35 Toomer, 1984: 404.
36 Toomer, 1984: 404.
37 Toomer, 1984: 400.
38 Berggren & Jones, 2000.
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