Monday, 29 February 2016

Leap years and astrolabes

Since today is 29th February, a leap-year-themed post is in order.  This one answers the question you've all been asking: how are leap years represented on astrolabes?

Astrolabe-equatorium at Merton College, Oxford
First, a word about the Julian calendar.  Most astrolabes were made before the Gregorian calendar reform (1582), and that made life a bit simpler for instrument-makers.  In the Julian calendar, leap years happen every four years, without exception.  On the other hand, the Gregorian calendar got rid of 3 leap days in every 400 years, by decreeing that centurial years (1700, 1800, 1900...) would not be leap years, unless they were divisible by 400.  That's why 2000 was a leap year, but 2100 won't be.

Still, astrolabes have to deal with the fact that one year in four has an extra day.  And astrolabes basically only map celestial motions over a single year.  So how did makers handle the irregularity?

This astrolabe at the Oxford Museum of the History
of Science says it has 28 days in February, but there
seem to be 29. A mistake?
They certainly knew about it.  For the most part they made their instruments to be correct 2 years after a leap year, thus averaging out the errors (which were insignificant anyway).  But that approximation didn't satisfy everyone.

Jean Fusoris, the Parisian craftsman - and alleged English spy - whose trial for treason was taking place exactly 600 years ago, wrote in detail about astrolabe calendars.  He argued that
"Their major defect is that they assume that the Sun on its deferent circle traverses the entire zodiac in precisely 365 days, which is not true."
Fusoris proposed that marks could be added to an astrolabe's alidade (the rule used to read information between the solar and Julian calendars), so that the calendar could be read differently for different years in the leap cycle.

But this still doesn't solve the problem of the Julian calendar.  Fusoris was well aware that one leap day every four years was too much - it meant the Sun effectively moved 1 minute and 46 seconds too far every four years (there are 60 minutes in a degree).  So he suggested you could customise your astrolabe to keep it up to date.

How?  Simple.  Just file down the alidade a tiny bit:
"In this way the instrument will show the true place of the Sun precisely for the lifetime of a man and more, so it is a good way of putting the motion of the Sun on the back of an astrolabe.  It can be done just as the zodiac of the rete of an astrolabe is commonly filed down."
It's important to remember that instruments were frequently customised in this way - they weren't kept in pristine condition as museum pieces, but were designed to be working objects, to be altered and added to just as you might buy a new case for your smartphone.  (Though it may be fair to say that most medieval astrolabe-owners were about as capable of performing these kinds of upgrades as most people today are of repairing their phones.)

However, some instruments were designed to make leap year calculation easy.  The instrument pictured at the top of this post is a combination astrolabe-equatorium from Merton College, Oxford.  It was made around 1350, when Merton was Europe's centre of astronomical and mathematical learning.  The picture just above shows a segment of the same instrument's solar and Julian calendars.  (They're usually on the back of an astrolabe, but they're on the front of this instrument in order to make space on the back for a planetary equatorium.)  Above where it says "Pisces" in the middle of the picture, you can see there are four curves arcing across the photo from the top-left corner to the lower-right side.  They're crossed at an angle by more-or-less vertical lines.  Those allow the calendars to be read differently in different years.  Depending on which year you were at in the leap cycle, you simply read from the calendar to the solar longitude (or vice versa) using a different one of the four circles.

It's an ingenious solution to what was a pretty complex problem.  Of course the results weren't exact, but they never were with these instruments.  That wasn't the point.  Astrolabes - not unlike like your smartphone today - were designed to be quick and clear, convenient and user-friendly.  And attractive of course.  This one's designer succeeded admirably.


  1. This is a great article! I recently created my own planisphere, and wrestled with the same question. I settled on the middle year solution, but found it a bit unsatisfactory. I'll have to see if I can adapt the Merton concept. Thank yoU!

    1. Thanks! I'd be interested to hear how you get on (and see pictures). I love your photos, by the way!

    2. I've placed the ecliptic right on the planisphere star map, which makes showing multiple years solar positions problematic. The Merton solution was to mark the solar position on the perimeter, which in my case would require a straight edge from the pivot to the perimeter to find the solar position. But I want to be able to, for example, place the solar position on the planisphere's horizon, to predict local sunrise/sunset. This would be inconvenient with a straight edge.

      I tried creating tick marks on the ecliptic to show the solar position in each of the leap year cycle years. That was horrible. I couldn't figure out which set of tick marks I should use, and I'm the one that created them. I figured anyone else would be hopelessly lost.

      So, I'm considering moving the ecliptic to a transparent overlay that can be fixed to the planisphere sky map. This would allow me to print one for each of the leap year cycle years. It's less convenient for sure, but allows me to predict the solar position/altitude directly on the ecliptic.

      Ugh! I've spent far more time on the ecliptic than I did on the remainder of the planisphere! Check

    3. Very interesting! I think transparent overlays have real potential to do things that couldn't be done with brass. It can be fiddly to change them around, but then you could say the same about the latitude plates that were very common. I hope you manage to find a solution that works for you!

    4. I've arrived at the realization that both my ecliptic and peripheral date scale need to be adjusted for proper position in each of the four leap year cycles. To me the best way to do this is to produce four star maps, each with the appropriately positioned date and ecliptic scale. The trick then is to make them easily interchangeable. Again, we can do this because we're not working in brass! This eliminates the clear overlay for the ecliptic.

  2. I'm sure you've come across this---But just in case you haven't (I was so {unscientifically} tickled to find it, myself): Tractatus de Conclusionibus Astrolabii, Geoffrey Chaucer

    Lyte Lowys my sone, I aperceyve wel by certeyne evydences thyn abilite to lerne sciences touching nombres and proporciouns; and as wel considre I thy besy praier in special to lerne the tretys of the Astrelabie. Than for as moche as a philosofre saith, “he wrappith him in his frend, that condescendith to the rightfulle praiers of his frend,” therfore have I yeven the a suffisant Astrolabie as for oure orizonte, compowned after the latitude of Oxenforde; upon which, by mediacioun of this litel tretys, I purpose to teche the a certein nombre of conclusions aperteynyng to the same instrument.

    1. Oh yes! A lot of people are surprised to find Chaucer wrote a treatise on the astrolabe, but it was very popular (it survives in more than 30 manuscripts). In fact the "Equatorie of the Planetis" manuscript, which I've been researching, cites Chaucer's Treatise on the Astrolabe and was obviously influenced by Chaucer's approach.

      There's no contradiction between Chaucer the poet and Chaucer the astronomer. His preface, where he lays out the plan of his writing and explains why he was writing in English instead of Latin, is always worth a read, and the treatise as a whole is still a clear and readable guide to the astrolabe, more than 700 years after it was written. (You can find it online at

  3. Cool website! I'm in the design phase of a 14th-century-style astrolabe, so I would love to hear more about medieval house systems! Everything I've seen only goes back to Regiomontanus. Is there a good bibliography you could recommend for 14th century sources on astrology or astrolabes?

    Thanks again for the website and, in advance, for your consideration! :)

    1. Glad you like it! I'm on holiday at the moment so only time for a quick reply, but the absolute best book on medieval astrology is "Horoscopes and History" by John North. It's hard to find, but worth the effort, and will tell you loads about medieval house systems. North's work also covers astrolabes (there's a great explanation of how they worked in "Chaucer's Universe"), but once you've mastered the functions (which it sounds like you have), I'd say the best thing is just to look at lots of examples (I can't think of any book that systematically compares different astrolabe layouts). is a good catalogue with great images, if you've not already found that. Good luck!

    2. Thank you very much for your quick reply! Both John North and Chaucer's Universe look like great resources-- I'll have to track them down somehow :) The main resource I've used so far is James Morrison's Astrolabe book, which is pretty systematic. 14th C is pretty early for most western astrolabe systems, so tracking down resources has been challenging.

      Thank you again for your help; I look forward to seeing more posts on your page in the future :)



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