We were led to awareness of and belief in this [second anomaly] by the observations of lunar positions recorded by Hipparchus, and also by our own observations, which were made by means of an instrument which we constructed for this purpose.<\/p><\/blockquote>\n
That instrument was, at the time, called an “astrolabe” which simply means “for taking the [position of] stars,”<\/span>1<\/sup><\/a><\/span> but today we would call it an armillary sphere. Ptolemy describes how one should be constructed which is what we’ll be exploring in this post. To help us, here’s the image of one labeled from Toomer’s translation<\/span>2<\/sup><\/a><\/span>.<\/span><\/p>\n Ptolemy begins with ring $3$ and $4$ here, which are joined at right angles to one another. Ring $3$ represents the ecliptic and ring $4$ is the meridian through the celestial poles. You’ll notice that there two rings are fixed with relation to one another as there are not pins joining them like at points d<\/em> and e<\/em>.<\/p>\n From ring $4$ which was the meridian, pegs at e<\/em> were inserted, diametrically opposite one another and placed such that they are the poles of the ecliptic. Mounted on those ring is ring, $5$, which is able to rotate freely. As such it is not<\/em> joined to ring $3$ and rotates around it.<\/p>\n Those same pegs at the ecliptic poles also extend to the interior of ring $4$, and on them, ring $2$ is placed which, again rotates freely inside of ring $3$. As you can see in the illustration, rings $2$ and $3$ were both marked with divisions totalling $360\u00ba$.<\/p>\n Interior to ring $2$ a more narrow ring, $1$ was inserted, on which were mounted a pair of diametrically opposing pinnules (b<\/em>) which could be used to sight stars. This ring is able to rotate inside ring $2$ in the same plane. Recalling that ring $2$ is rotating on the pins at\u00a0e<\/em> which were ate the ecliptic poles, the increments on ring $2$ indicate the ecliptic latitude. So $0\u00ba$ would be located where it met ring $3$ and $90\u00ba$ would be at the pins,\u00a0e<\/em>. Unsurprisingly, since ring $3$ indicates the ecliptic, the divisions on ring it therefore indicate the ecliptic longitude.<\/p>\n However, this would be quite unwieldy to use since the ecliptic poles do not retain a fixed point relative to the observer like the equatorial poles. As such, we need to be able to have that as a fixed point of reference. To do so, Ptolemy places another set of pegs (d<\/em>) such that the arc along ring $4$ from\u00a0e<\/em> to\u00a0d<\/em> is the obliquity of the ecliptic<\/span>3<\/sup><\/a><\/span>. These pegs extend into ring $6$ which represents the meridian of the equatorial system.<\/p>\n You’ll notice that this drawing has the $6$ going through two rings – the one we just discussed and an outer ring. The reason is not explained but I suspect it’s an artifact of Toomer using a reproduction of a diagram from another source in which the outer ring was labeled as ring $7$. Although I can’t fully understand the paper, my suspicion is that ring $6$ is allowed to rotate inside ring $7$ in the same plane much like ring $1$ inside ring $2$. This would allow for the instrument to be used at any latitude on Earth. This is because the pegs\u00a0d<\/em> need to be aligned to the celestial equatorial poles. Since these change relative to the horizon, having ring $6$ rotate in this way would allow for these to be adjusted to the correct altitude above the horizon.<\/p>\n To me, this does not really come from my reading of the Almagest<\/em>, as Ptolemy only says these need to be aligned for “an elevation of the pole appropriate for the place in question, as well as parallel to the plane of the actual meridian.” That could be read to indicate that ring $6$ was fixed and the instrument was not designed to be moved.<\/p>\n Regardless, that covers the primary components of this instrument. To summarize, a ring that is the meridian of the equatorial coordinate system ($6$) has, placed inside it, another ring ($4$), which carries two rings at right angles representing the ecliptic ($3$) and the meridian of the ecliptic coordinate system ($2$).<\/p>\n In the next post, we’ll explore how Ptolemy says to use such an instrument to make observations. But before leaving off, a few notes about this instrument. Firstly, Tycho Brahe owned several armillary spheres as described in his book,\u00a0Astronomiae Instaurate Mechanica<\/em><\/a>, and a modern version of one based on Tycho’s design was installed in 2018 on the campus of St. James College in Santa Fe, New Mexico<\/a>. It’s the only functional armillary sphere of its kind in the world so it’s definitely on my list of places to visit at some point. It’s only an hour or so out of the way on a drive to\u00a0Estrella War, so maybe there’s a good reason for me to go!<\/p>\n![\"\"](\"https:\/\/i0.wp.com\/jonvoisey.net\/blog\/wp-content\/uploads\/2020\/09\/AlmagestFig5-F.png?resize=269%2C300&ssl=1\")
<\/a><\/p>\n
\n
![\"\"](\"https:\/\/i0.wp.com\/jonvoisey.net\/blog\/wp-content\/uploads\/2020\/09\/Almagest-Progress-20200905-2.png?resize=300%2C131&ssl=1\")
<\/a><\/p>\n