How to predict an eclipse

Who's read Prisoners of the Sun?  In this enthralling Tintin story our hero is captured by a group of Inca who have survived in secret.  He and Captain Haddock are sentenced to be burned alive; their pyre is to be set alight by the rays of the sun.  Tintin is allowed to choose his time of death and cleverly picks the execution to coincide with a solar eclipse.  The amazed tribesmen believe he can command the sun god and immediately set him free.

This trick is not entirely fictional: Christopher Columbus pulled off something similar.  His son Fernando (considered a fairly reliable biographer) writes that in 1504 Columbus, stranded on Jamaica and undermined by mutiny, needed more supplies.  So he invited the local chiefs to a feast and, according to Fernando,

told the gathering [that] God was very angry with them for neglecting to bring us food ... and had determined to punish them with famine and pestilence...  They should therefore attend that night the rising of the moon: She would rise inflamed with wrath, signifying the chastisement God would visit upon them... At the rising of the moon the eclipse began, and the higher it rose the more complete the eclipse became, at which the Indians grew so frightened that with great howling and lamentation they came running from all directions to the ships, laden with provisions, and praying the Admiral [Columbus] to intercede with God. (p. 261)

Useful party piece, eh?  Well, you'll be pleased to know that you can pull this one off using your own planetary equatorium, which you've built using the instructions provided on this very blog.  In the last post I explained how to find the Moon's longitude.  If you're looking for the planets, longitude is usually enough, because they stick fairly close to the Sun in its annual journey (the ecliptic) across the background of fixed stars.  But for an eclipse, "fairly close" is not enough.  The Moon's latitude can be ±5° (celestial latitude is measured from the ecliptic), but an eclipse will only take place when it is 0° - that's why the ecliptic is called the ecliptic!  So in this case latitude is rather important to us, and to medieval astronomers.

Fortunately, it's quite easy to predict.  Here's what you do.  You need two pieces of information: the Moon's true motus, and the true motus of Caput Draconis.  Caput Draconis (which of course means the head of the dragon) is one of the two lunar nodes (the other, directly opposite it, is called Cauda [tail] Draconis) - the two places where the Moon's inclined orbit intersects with the ecliptic.  The nodes move steadily through the sky at a rate of about 19° a year, and their true motus is listed in any good set of astronomical tables like the one in our manuscript.

The Moon's true motus crops up naturally in the process described in my last post.  In the picture on the right, the green thread has been used to mark the Moon's mean motus (which we took from our tables), and the white thread has been stretched across the pole (middle) of the epicycle from the centrum oppositum.  The angle between the green and white thread is called the equation of centre, and that angle plus the mean motus is the true motus.

Now all we have to do is find the difference between the two true motuses.  (If it's more than 90° we may have to fiddle the figures a little, but that's not too tricky.)  Then find that number on the face of your equatorium, and stretch a thread horizontally across to the other side (as I've done in the photo below).  In the middle it will cross a line which our author has called line alhudda.  When we marked up the face, we divided that line into five (corresponding to the Moon's full range of latitude), so we can simply read off the point where our thread crosses the line.  In the case pictured below, it's about 2.6°.  Whether it's positive or negative will depend on whether we subtracted the true motus of the Moon from that of Caput/Cauda Draconis, or vice versa.

That's it!  As I said, if the Moon's latitude is 0° (and its longitude is either the same as the Sun's or 180° away), we'll have a lovely eclipse.  Remember that, it may save you from execution...

 

The Moon on a stick*

*well, on a disc of MDF, anyway.  

Want to know how to find the moon?  Of course you do!

So far on this blog I have constructed and calibrated a medieval planetary equatorium, and shown you how to use it to find the longitudes of the planets (most recently Mercury).  Now it's the turn of the Moon.

This will be a two-part post, because - unlike for the planets - our equatorium will not only tell us the longitude of the Moon, but also its latitude.

Celestial longitude is measured on the ecliptic, which is a circle in the sky angled at about 23½° to the celestial equator (the projection of the earth's equator outwards onto the sky).  Throughout the year, the Sun, Moon and planets move steadily around the ecliptic.  The Sun, by definition, sits on it; the Moon and planets may stray a little from it, but won't go far.  That's why medieval astronomers didn't worry about the planets' latitude (which is a measure of angle above or below the ecliptic).

The Moon, though, is different.  Classical and medieval astronomers were certainly interested in knowing its latitude.  Can anyone guess why?  (Feel free to comment; you may even win a prize.)  So our equatorium will tell us the Moon's latitude, and that will be the subject of my next post.

But let's talk about longitude now.  The Moon's longitude was modelled by Ptolemy in broadly the same way as for the planets, with a deferent and epicycle (for a refresher, read my explanation here).  There's one crucial difference, though: there's no equant.  Remember that the equant point was the centre of the motion of the epicycle around the deferent, which helped to model the irregular motion of the planets.  But since, for obvious reasons, the Moon's motion as seen from Earth is much more regular, there's no need for an equant point.

But we do still have a rather complicated setup with a moving deferent centre.  This accounts for the fact that, for medieval astronomers, the Moon's movement still seemed somehow to be linked to the Sun's.  (Hardly surprising to us, since the Earth orbits the Sun and the Moon orbits the Earth, but not so obvious to medieval scholars.)  In order to find the Moon's deferent, we need to look up the Moon's mean motus (the location of the centre of the epicycle, as measured from the constellation Aries) in our tables.  From this, we subtract the Sun's mean motus to find the deferent centre (if you get a negative answer, add 360°).

The deferent centre thus moves in a circle around the Earth.  Opposite it on that circle is another point known as the centrum oppositum.  We'll make use of that in a minute.

So, once we've worked out the location of those two points and marked them with our black and white string (pictured right), we get out our big Epicycle.  We put it with its common centre deferent reference point on the Moon's deferent centre.  Then:

1. As with the planets, we move the "black" string to mark the Moon's mean motus on the edge of the face of the equatorium.
2. We move the centre ("pole") of the big Epicycle so it's under the black string, while keeping the common centre deferent in place.  Note: we haven't done the trick with the parallel white string - remember there's no equant this time.  (This change seems to have flummoxed the author of the Equatorie of the Planetis manuscript I'm studying - he was a bit confused on this point.)

Step 3

3.  Run your white string from the centrum oppositum, over the pole of the Epicycle, to the far side of the Epicycle (see picture).
4.  Starting from where the white string crosses the far side of the Epicycle, turn the movable pointer ("label") clockwise [unlike with the planets where we turn it anticlockwise] to mark out the number of degrees corresponding to the Moon's mean argument, which we find in our tables.
5.  As with the planets, stretch the black thread to the mark for the Moon on the label (see below).
6.  Where the black thread crosses the edge of the face, is the Moon's true place (longitude).

And that's it!  Now you can find the Moon, even on a cloudy night.  In the next post, we'll learn how to use the equatorium to find its latitude.  Don't pretend you're not excited...

Mercury's meandering deferent

This week I'm back with my equatorium, trying to pin down precisely how well it models Ptolemy's planetary theories (and, in turn, finding out the strengths and weaknesses of those theories in predicting the locations of the planets in the night sky).  Today it's the turn of the Winged Messenger, Mercury.

In my last "medieval craftsmanship" post I described the procedure for using the Equatorie of the Planetis to find the longitude of most planets.  I mentioned that the procedures for the Sun, Moon and Mercury vary to a greater or lesser extent from this basic procedure.

So here's how it works for Mercury.

Let's first discuss why the Ptolemaic model doesn't work as well for Mercury as the other planets.  Note: the simplest way for me to explain this is by referring to modern astronomical theories.  Before I do, I should stress that the success or failure of medieval theories was obviously not judged by how well they approximated modern astronomy; instead, their success was measured, in good empirical fashion, by how closely they matched observed data.  Ptolemy's genius - building on the work of earlier, less celebrated men such as Apollonius and Hipparchus - was to devise theories for each planet that produced predicted locations that would match observations to an astounding degree of accuracy.

To recap: deferent=big dashed circle
centred on X; equant=big black dot;
epicycle=little dashed circle.

So, that said, what's up with Mercury?  Well, as you may have read in one of my previous posts, the Ptolemaic system of planetary motion is based on two circles for each planet, the deferent and epicycle.  Together these model the movement of the planets as observed from the earth.  In other words, [ANACHRONISM ALERT] they account for both the earth's and the planets' motion around the sun.  But if you're familiar with the basics of modern astronomy you may be aware that, according to Kepler's first law of planetary motion, the planets' (and earth's) motion around the Sun is elliptical, not circular.  How can we make circles into ellipses?

We get a pretty good approximation of one ellipse from the fact that (a) the deferent is not centred on the earth, and (b) the centre of the epicycle moves around the deferent at a constant speed relative to another point, the equant.  But the epicycle is still a circle, and the planet is assumed to move around it at a constant speed.  Problem, no?

Well, no, not really.  Why not?  Precisely because Ptolemy was not trying to model modern systems: the deferent and epicycle are not pretending to be two ellipses; they're just accounting for what we see in the sky.  As it happens, in the case of Venus, Mars, Jupiter and Saturn, the location of the deferent and equant can effectively factor in a bit of extra eccentricity, so the epicycle doesn't need it.  The resulting level of (in)accuracy will vary depending on the orbits of the various heavenly bodies, but this system gives us a maximum inaccuracy of about 9 minutes of arc (three-twentieths of a degree) for Mars, and is even better for the other planets.

But not for Mercury, though - with this system the locations for Mercury might be almost a degree out.  You might think that's still pretty accurate (remember that we're talking about naked-eye observation here), but it wasn't good enough for Ptolemy.  Here's his solution:

You may remember I mentioned before that we have to mark an aux, or apogee, for each planet; I drew a line (sometimes called the line of apsides) through earth, the deferent centre and equant, out to the rim of the equatorium.  Because the deferent centre is on this line, the aux is the point on the deferent circle that is furthest from earth.  With all the other planets, as the diagram above shows, the centre of the deferent is halfway between earth and the equant point.  But Mercury's deferent centre (D) moves: it can be any point on a circle which straddles the line of apsides, goes through the equant (E), and has a radius equal to the distance from earth to E.  You can see this little circle in the photo below: the pin is at the centre of earth, and E is on the right of the little circle, nearest the pin.

OK then.  We start, as we did before, by finding the mean motus (let's call it λ) of Mercury in our handy astronomical tables.  As usual, we find the point on the rim of the equatorium that is λ° round anticlockwise from the vernal equinox.  Now we subtract the value of the aux from the mean motus; if we get a negative answer, we add 360°.  Let's call the result ψ (technically, it's known as the mean centre).  Now, to find your deferent centre, count clockwise ψ° from the point on the little circle opposite E (on the left on the picture above, furthest from the pin, where I've unhelpfully marked a tiny D).  You might be able to see a little dashed line on the picture above, showing a value of 79° for ψ (as it was on 31 December 1392).

That's it - once you have the location of your deferent centre, you can go ahead with the method as I described before, laying out your parallel threads, placing the common centre deferent of the Epicycle on D, and so on.

I hope all that makes sense!  Next time I'll explain the (much simpler) procedure for the Sun.  Then it's the Moon, which will raise the question of latitude for the first time.  Please visit again soon!

Croissants and Communication at the Catalan Congress

"my" globe

I have just returned from the XII Trobada (twelfth congress) of the Societat Catalana d'Història de la Ciència i de la Tècnica (SCHCT - Catalan Society for the History of Science and Technology).  This conference was held in Valencia, Spain, and I was honoured to be able to attend and present a paper on a globe in the collection of the Whipple Museum here in Cambridge.

I thought I would post some thoughts on this conference while it is still fresh in my mind.  It was my first academic conference, so I can make no direct comparisons, but I still came away with some strong impressions.

First and foremost, I thought it was a well organised, wide-ranging conference.  The venues were ideal and the hospitality arrangements were excellent: good accommodation and plentiful refreshments (hence the title of this post) certainly made a favourable impression on me! The talks were well scheduled and, although the focus was naturally on Iberian (and especially Catalan) subjects, impressively wide-ranging.  Most speakers managed to produce succinct, interesting 15-minute talks, though a disappointing number of people chose to read from pre-prepared scripts and PowerPoint was not always well used!  Here and there there were stimulating questions that led to interesting discussions.  Overall, then, I had a fantastic time and got a great deal out of the experience.

The striking (and controversial) Ciutat de les Arts i les Ciències

All that said, here's what this blog post is really about: the issue of language, which is undoubtedly where the conference made its strongest impression on me.  Since this was the Catalan Society of the History of Science and Technology, you probably won't be surprised by the following breakdown of languages: of 104 presentations at the conference, 66 were in Catalan, 33 (including mine) were in Spanish, and 5 were in English.  Also probably unsurprising is the fact that 40 of the presentations were given by representatives of just two universities: the University of Barcelona and the Autonomous University of Barcelona.

Now, I'm really not sure what I think about this.  Of course I'm in favour of cultural diversity and I'm aware that languages are becoming extinct at an alarming rate (check out the World Oral Literature Project, based at Cambridge and Yale, if this is a subject that interests you).  I'm also aware that Catalan language and culture, in particular, were suppressed for forty years during the dictatorship of Francisco Franco.  It is surely positive for people to be able to present papers at academic conferences in their native language, and for a language to be used in the full range of possible registers and settings (rather than narrow domestic, non-literary settings, as might happen).

But the fact is that there was no-one at that conference who spoke Catalan but not Spanish; all 66 of those talks could have been in Castilian.  Now, most people who speak Spanish can probably follow the general gist of a presentation in Catalan (especially the relatively comprehensible Valencian dialect; not so much the Barcelona accent, and much less the dense Balearic version), but it is certainly going to limit their ability to grasp its finer points, and particicipate in discussions.  If the organisers are proud of the growing international nature of their conference (there were speakers from the Czech Republic, Mexico, Portugal and the UK) and want that trend to continue, wouldn't they be better off encouraging presentations to be given in Castilian?  Wouldn't it better serve the purpose of breaking down barriers between academics, promoting the history of science and publicising their impressive research achievements?

Still, members of the Catalan Society are rightly proud of their achievements: by all accounts it is thriving, more active than its Spanish counterpart.  If they can't give presentations in Catalan at their own biennial conference, when can they?  At a time when Catalan independence is very much in the news, this is clearly a live political issue - apparently the hostel I was due to stay in cancelled the Society's booking when they heard who had made it.

What do you think?  Is it bigoted of me even to raise the issue?  I should emphasize that in general I was content to listen to talks in Catalan (I tweeted from many of them; they're collated here), though I obviously got more out of those in Spanish.  There was just once I found it a little irritating: after a talk in Catalan, I asked a question in my competent but obviously accented Spanish.  The speaker replied in Catalan.  To me, that was just plain rude, but it was the exception: most conference-goers were happy to speak Spanish or even English, and there were some native speakers of Catalan who gave their presentations in Castilian.

In the Friday evening plenary, Charles Withers of Edinburgh University presented a talk entitled "Place, Space, Nation, Globe: Thinking about the Geographies of Science."  Using the examples of the Scottish Enlightenment, the development of Scottish identity through map-making, and the late-nineteenth-century prime meridian debates, he argued that we need to understand the importance of place and space (in both literal and figurative senses) to the development of knowledge; not only how knowledge is made in certain places and situations, but also the transactions between them.  These ideas are hardly revolutionary - Withers acknowledged his debt to a range of thinkers, from Bruno Latour to Jim Secord - but the talk certainly got me thinking about the ways that science and its history are communicated, not to mention the multi-layered geographies of Spain.

That's enough from me - I look forward to your comments.  I'm off to listen to the new BBC Radio 4 series "The Invention of Spain".  Its webpage quotes historian Felipe Fernández Armesto: "I can't imagine Spain ever cohering.  If it did, it wouldn't be Spain."

Tweets from the Catalan Congress

At the weekend I attended my first ever academic conference, the XII Trobada (twelfth congress) of the Societat Catalana d'Història de la Ciència i de la Tècnica (Catalan Society for the History of Science and Technology).  I had a wonderful time, enjoyed making a presentation about this globe, met some very friendly fellow historians of science, and learned a lot.

I will post more of my thoughts about the conference soon, but for now, here are some tweets.  I've just joined Twitter (as @astrolabestuff) and thought I would tweet my thoughts on the conference (or at least summaries of the talks) as it progressed.  Here's what I wrote...

Medieval Craftsmanship, Part 3

[Drumroll] Ladies and gentlemen, I shall now demonstrate the use of a medieval planetary equatorium!

In the first two posts in this series (here and here) I described how I made the physical structure of an equatorium according to the instructions in a fourteenth-century manuscript, and explained how I marked out the equatorium so that it could be used to find the location of the sun, the moon and the planets.

(Technical point: skip this paragraph if you're not interested.)  To be precise, the "location" is what medieval astronomers called the true place, which is more or less the same as the planet's longitude.  Celestial longitude is measured as an angle along the ecliptic (the path traced against the background of fixed stars by the sun in the course of the year) between the planet or star you're measuring and the vernal equinox (traditionally the first point of the constellation Aries, though a phenomenon called precession means this no longer corresponds to the true spring equinox).  We can also measure the celestial latitude, the angular distance above or below the ecliptic, but since the planets orbit broadly in the same plane as the sun, it doesn't vary much.

As I've suggested, an equatorium is a sort of analogue computer: you input information and it uses that information to give you another piece of information.  Unlike, say, an astrolabe, an equatorium can't be used for observation.  What it does is simply and speed up calculations; you could calculate the planets' positions geometrically, but it would be much more difficult and time-consuming.

In the last post I explained how Ptolemy modelled the planets' motion using two circles: the deferent and epicycle.  So in order to use the equatorium, we need to input two pieces of information: the planet's position on the epicycle, and the position of the centre of the epicycle on the deferent.  These were called the mean argument and mean motus, respectively.

There's one more piece of information, which I should have mentioned last time, as it involved marking my apparatus.  Of course we need to know the relative sizes of the two circles.  Fortunately the standard tables used by medieval astronomers (about which more later) included lists of the radii of the planets' epicycles.  Following the manuscript instructions, I marked the radius of each planet on the label [pointer] that spins around the Epicycle (I'll use a capital E to distinguish this bit of wood from the theoretical epicycle I've just been talking about).

Now to the fun stuff.  Here's how you find a planet:
1.  Look up the mean motus and mean argument of a planet in your tables.
2.  Lay a black thread in a straight line from the centre to the edge of the face, at the point equivalent to the mean motus.
3.  Lay a white thread parallel to the black thread, with one end at the equant point for the planet.
4.  Place the common centre deferent (a sort of reference point at the top) of the Epicycle on the deferent centre of the planet whose location you want to calculate.
5.  Turn the whole Epicycle so its centre lies over the white thread

This is what your equatorium will look like after step 4.  I couldn't find black thread, so I used green twine instead.

Almost there - just a few more steps...
6.  Starting from the white thread, turn the label anticlockwise the number of degrees equivalent to the mean argument.
7.  Now move your black thread to line up with the planet’s mark on the label
8.  The place where the black thread crosses the edge of the face is the planet’s true place.

This is what it will look like after stage 8.  I used it to work out the location of Mars, for a mean motus of 40° and mean argument of 100°, and got the result 84°.

That's all there is to it.  I've simplified the method slightly, but the whole process takes just a few minutes, even allowing plenty of time to get the threads nice and straight and parallel.  I think you'll agree that, once you've got your head around the terminology, it's remarkably straightforward.  It's also a very accurate representation of the theory (and the theory does a great job of modelling planetary motion).  The biggest causes of inaccuracy are undoubtedly the way I've marked the degrees on the equatorium, and my (in)ability to get the threads straight and parallel.

So that's how you find the location of Venus, Mars, Jupiter or Saturn.  The method varies somewhat for the Sun, Moon and Mercury, but I probably won't post about that for a while, as all this has raised plenty of questions for me!  Many of the questions are about the astronomical tables, which I keep referring to rather breezily, but about which I know very little.  I'll blog about them as I learn more.

It's been fun making this model, and I've learned a lot, starting from a position of almost total ignorance about medieval astronomy in general and equatoria in particular.  There's a long way to go!  Thanks for reading.

Medieval Craftsmanship, Part 2

In my first post I described how I began making an equatorium according to the instructions in the fourteenth-century manuscript I'm researching.  Since writing that post, I discovered a full-size replica made in the 1950s (you can read about that here).  Needless to say, that replica is far more attractive and probably more accurate than anything I can make at home with my saw and pencil, but I never said beauty or accuracy were priorities of mine.  So I went ahead with my own model anyway.  In this post I'll describe how I finished making it; the process of using it will have to wait for a future post.

Here's what I made earlier: (1) the "face" - a three-foot disc of MDF; (2) the "epicycle" - a circle three feet in external diameter and 34 inches in internal diameter with a half-inch bar across the middle (patched up with some gaffer tape); and (3) the "label" - a pointer three feet long, fixed to the middle of the epicycle but free to turn around its circle.

My first task was to divide both the face and epicycle into 12 (zodiac) signs, 360 degrees, and 21,600 minutes.  Yes, you read that correctly: the Middle English manuscript can be vague, but here it is quite explicit that "everi degre shal be devided in 60 mi."  This is staggeringly ambitious: even if the the equatorium is made on the six-foot scale demanded by the manuscript, its circumference would only be 18' 10" (5.745m), which would demand almost four minute marks to be squeezed into every millimetre around the instrument (95 minutes to each inch).  It's that kind of unrealistic demand that makes you suspect that the author of the manuscript was describing an ideal instrument, and never expected his instructions to be followed literally.

For me, of course, making a half-size instrument, it's quite enough to divide the face and epicycle into degrees (which works out at 3 degrees to the inch).  But even that is a tricky proposition: dividing a circle into equal divisions is notoriously difficult and time-consuming.  (It was a problem that exercised instrument-makers, astronomers and navigators right up to the eighteenth century - the dividing engine devised by Jesse Ramsden to mark circles mechanically is arguably one of the key inventions of the Industrial Revolution.)  I had a head-start: I bought a cheap protractor and used it to mark out the degrees.  But that circle of dots was obviously quite small; when I tried to extend it by drawing lines from the centre, through each dot, to the rim of the circle, I realised how hopelessly inaccurate this method was.  A tiny error in placing my home-made ruler at the centre of the face could make my markings on the rim as much as a centimetre out.

Accepting that my divisions were bound to be pathetically inaccurate, I proceeded to mark the face of the equatorium for the sun, the moon and each planet.  Because, from our perspective, the sun does not move at a constant speed around the zodiac throughout the year (the number of days between solstices and equinoxes is not equal), the sun's path has to be marked as a slightly eccentric circle (i.e. a circle whose centre is not quite at the centre of the face of the equatorium).

The procedure for the planets is a little more complicated.  If you track the progress of the planets through the sky, they all move gradually eastward around the zodiac, night after night.  But there are some nights when they appear to move back towards the west, in what is called retrograde motion.  (If you believe that the earth is going round the sun, and not the other way around, you can explain this by thinking about the different relative speeds of the earth and planets.)  Medieval astronomers modelled this, and the changing apparent speeds (as viewed from earth) of the planets, using two circles: a deferent and an epicycle.  According to the theory, which medieval astronomers took from the ancient Greek mathematician, geographer, astronomer and general genius Ptolemy, each planet moves at constant speed around the epicycle, but the centre of the epicycle itself moves around the deferent circle (see the diagram on the right).  Ptolemy added a refinement to earlier theories: not only is the deferent eccentric to the earth, but the centre of the epicycle moves round the deferent at a constant speed relative to a point that is not at the deferent's centre; instead, it is the same distance as the earth from the centre of the deferent, but in the opposite direction.  In other words, the earth, the centre of the deferent, and the centre of the epicycle's motion (known as the equant point) lie on a straight line, with the centre of the deferent exactly in the middle of the other two.  (The situation is a little different for Mercury, but we won't worry about that for now.)

Is that all clear now?  It doesn't really matter: what's important for our fourteenth-century instrument maker is to know that for each planet he has to mark an equant point, and midway between the equant point and the centre of the face he has to mark the centre of the deferent.  The placement of these marks depends on two bits of astronomical data: the constants of eccentricity for each planet, which tell our instrument maker how far from the centre of the face to put the centre of the deferent; and the direction of the aux (roughly similar to the planet's apogee in modern terms), which tells him in which direction to place the deferent and equant.  The first of these figures was constant and had been calculated pretty accurately by Ptolemy; the second shifts slowly (by about a degree every 136 years) and would have to be kept up to date.  But it was not necessary for our instrument maker to do any calculation: he could lift the necessary data directly from the tables which accompanied the manuscript.  These list auges for each planet, for 31 December 1392.

Having marked up the face and epicycle with signs and degrees, deferents, equants and auges, we are now ready to start calculating the positions of the planets.  The picture on the right will give you a flavour of how it works; for a full description, watch this space!

Igniting interest in science

Great day out in Nottingham yesterday.  It's always fun to be a shameless tourist but the highlight was not one of the usual sights (though I did enjoy Ye Olde Trip to Jerusalem) but, instead, something claiming to be The World's 1st Science Pop-up Shop.

A group called Ignite! had taken over an empty unit in the Broadmarsh shopping centre.  SG and I wandered in off the street and found a bunch of enthusiastic students, teachers and other volunteers sharing their passion for all kinds of science to curious passersby.

Plenty of parents and children on half-term stopped to check out an eclectic mix of experiments and demonstrations, focused on pointing out the amazing phenomena of everyday life.  Did you know that if you whip Marmite it goes white?  Or that if you put your thumb over a straw you can stab it straight through a potato?

The Ignite! folks were also joined by people from creative collective Hackspace, who were letting kids loose with soldering irons - I had a go and even got to make a flashing robot badge.

The walls and floor of the shop were decorated with fun facts and quizzes like the one on the left (see below for answer),which were arousing plenty of discussion among visitors.

Of course it's not a new idea to strip all the off-putting formulae and unhelpful abstractions out of science, and remove the distinctions between different scientific disciplines.  (It reminded me of many happy childhood visits to the Science Museum's basement "Launch Pad".)  What was great was to see it sandwiched in among Poundland, Argos and Wimpy.

The pop-up shop is a four-week project.  Could it work in the longer term?  It would be hard to keep fresh - they'd need to keep changing the decoration and activities if they wanted people to come back for repeat visits.  I guess they're getting the space rent-free too, which is doable with so many recession-hit units standing empty, but might not be possible indefinitely.  On the other hand, if we're all shopping online and in malls, and retailers are abandoning city centres, maybe this is the future of the high-street experience.  Saturday afternoon in town for coffee and chemistry, anyone?

(Apparently frogs' bones grow in visible rings, just like trees - so you can tell their age by cutting them open.  But bad luck on the frog...)

A Spanish "Encyglobedia"

Just published a new article on the Whipple Museum's "Explore Collections" site.  Here it is:

http://www.hps.cam.ac.uk/whipple/explore/globes/aspanishencyglobedia/

Not about an astrolabe this time, but a curious globe - here's a picture:

How I found King Arthur's Round Table

I've just started a research project focusing on a medieval manuscript, The Equatorie of the Planetis.  This manuscript describes the construction and use of a curious astronomical instrument, and my previous post was about the first stages in my attempt to reconstruct that instrument, in order to better understand the manuscript.

I'm still working on that, and will write all about the fun I had trying to divide a three-foot circle into 360 equal degrees very soon.  Before that, though, here's a tale of intrigue to liven up your weekend...

I'm not the first person to study The Equatorie of the Planetis, or indeed to make a replica of it.  The great historian of science Derek de Solla Price researched it for his (second) PhD in the 1950s, and published an edition of the manuscript, complete with detailed commentaries in which, among other topics, he put forward his argument that the manuscript was by Geoffrey Chaucer, and indeed had been written in Chaucer's own handwriting.  Price was friends with the Nobel Prize-winning physicist Lawrence Bragg, who by the 1950s was running Cambridge University's Cavendish Laboratory, and Bragg arranged for the Cavendish technicians to make a full-size replica of the Equatorie.

I had read that Bragg's gift was "to be hung in a place of honour on the end wall of the big room" of the fabulous Whipple Museum of the History of Science in Cambridge.*  But none of the Whipple's current staff was aware it existed, let alone where it might be now; and the quote above could conceivably have meant that the equatorium was intended to be hung in the Whipple, but never actually made it there.  So I wasn't very confident, but decided I'd have a go at finding out what happened to the mysterious equatorium.  I thought I might at least be able to find some of the paperwork connected with its production at the Cavendish, and maybe some hints about its fate.

I made an appointment to check out the Whipple's archives and, when I met up with the archivists, explained to them what the equatorium was and what the replica might have looked like: a six-foot wooden circle with a similarly-sized brass ring attached.  They looked at each other for a moment, then one said "do you think it might look a bit like this?"  On the computer screen they showed me a museum database record for an unidentified object.  Although I'd obviously never seen the Equatorie, I instantly recognised from the photo that this mystery object must be Price's replica.  The object was described accurately in the database record but the cataloguer, not knowing precisely what it was, had apparently struggled to come up with a title for the record.  So this six-foot wooden circle had been officially named King Arthur's Table!

We went out to the stores and, as carefully as we could given its size, wheeled it out from its resting-place behind a large storage cupboard.  It was dusty and a bit scratched, but unmistakable.

Dining space for about eight guests

I'm now gradually piecing together the story of this remarkable item.  It was made in 1952 and soon afterwards given to the museum, where it hung happily for a few years.  However, as both the museum collection and the Cambridge University Department of History and Philosophy of Science expanded, it seems there was not room to display it, or to store it on the premises.  It was moved to a storage facility for about a decade.  In the 1970s, the Whipple's curator wanted to move some items out of that facility, but, he told me, the stairs were so rickety that no contractor would take the job.  So he did it all himself.  Unfortunately, the Equatorie was too big to fit in his car so it lingered in the same storage facility for another few years!  Finally it was moved into the Whipple's current store in the 1980s.

Hopefully it will soon be back on display in the Whipple Museum.  However, it may have to lose its splendid Arthurian name, which would be a slight pity as it does capture the romance of the Whipple's early years (not to mention my own quest).  I think I know why they called it Camelot now...

(* The quote is from the Whipple's 60th anniversary publication, an excellent collection of essays on a range of subjects associated with the museum.)

My weekend as a medieval craftsman

With a free weekend, and fine autumn weather forecast, it seemed a good time to try making my own planetary equatorium.

I'm studying a manuscript called The Equatorie of the Planetis, which belongs to Peterhouse, Cambridge.  Much more about that in future posts; for now it's enough to say that it's a fourteenth-century instruction manual for the construction and use of a planetary equatorium, a device to compute the position of the planets.

Helpful handyman hints from our Swedish friends

Now, I'm no DIY expert, but I pride myself on being able to follow Ikea instructions without breaking anything, or myself, or having to call them for help (see right).  So I thought I'd have a go at following the instructions in "my" manuscript, and making my own equatorium.

This was not just an excuse to buy some new tools and hang out in the garden on a sunny(ish) afternoon; I was also trying to understand some of the practical issues involved in making a medieval instrument: the choices, the difficulties and perhaps the pleasures, too.

So on Saturday afternoon I headed down to Homebase and bought myself an 8 x 4-foot sheet of 6mm MDF, as well as some upholstery nails, two balls of twine, a coping saw and three rasps (I only wanted one, but it was a choice between a three-pack at Homebase and a nine-pack at B&Q...).  The friendly guys at Homebase kindly cut my board in half, and then chopped 11 inches off each half, leaving me with two large not-quite-squares, and two useful off-cuts.

Task #1: make a pair of compasses capable of drawing a three-foot circle.  This wasn't too difficult once I'd realised that they only needed to span the 18-inch radius, not the full 3-feet diameter.  (They appear on the blue towel in the second picture below.)

Task #2: draw the big circle and then cut it out of my squarish bit of MDF (twice).  Now, you may be thinking that three feet in diameter (that's 91.4 cm to those of you in civilised countries) is rather large for an astronomical instrument (though perhaps not by the standards of the Square Kilometre Array).  In fact, the original instructions call for a full six feet of circular precision, so my reproduction is a humble half-size replica.  (More about the issue of scale in future posts.)

Cutting out the circles, with appropriate canine supervision

 At this point I realised that sawing in precise circles is actually quite hard.  Granted, your medieval craftsman might have had years to hone his art (and probably had a better workbench than mine - a toolbox, if you're wondering), but then my saw is probably sharper than his.  And I'm not sure when MDF was invented, but I guess he wouldn't have had the luxury of starting with a slim, smooth, knot-free sheet of board, either.

Task #3: cut out a smaller circle inside one of the larger ones, to leave a one-inch wide ring of wood.  This "epicicle", as it's named in the manuscript (not to be confused with the epicycle of Ptolemaic theory), is supposed to be made of metal, but I'm sticking with MDF for now.  The instructions call for a bar to be soldered across the middle, but I just cut out two semicircles, leaving a half-inch strip intact.

(The picture above left shows me marking out the semicircles by the light of a handy headtorch; you'll see I tried it out in paper first, on a 1cm:4" scale.)

Unfortunately (a) my sawing wasn't very straight, and (b) a three-foot-long, half-inch-wide, six-millimetre-thick strip of MDF is not very strong.  Never mind, there's nothing a bit of gaffer tap and some strategic rasping can't fix.  (What those medieval craftsmen did without gaffer tape, I have no idea.)

 Task #4: Make a "label" [pointer] for my epicicle.  This is also supposed to be made of metal (the author specifies latoun, i.e. brass), but, you guessed it, I'm sticking with MDF.  The label is a pointer, a full three feet in length, which is fixed to the centre of the epicicle and spins round (that's what the upholstery nails were for).  As you'll see in the photo (right), the label has a little kink in the middle, as is traditional (see below, from a fourteenth-century astrolabe at the fantastic Whipple Museum).

So, after all that, I now have a lovely smooth three-foot disc, which is the face of my equatorium, and a similarly sized epicicle, complete with revolving label (see below).  Now all I need to do is to precisely mark out the zodiac signs, degrees and minutes round the outside; as well as the centre of the deferent circle and the equant point for each planet.

More about all that in a future post.  Check back here if you want to know more, or to find out why I bought those two balls of twine!

(Thanks to my wonderful housemate for some of the photos.)