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.

Medieval (g)astronomy: my PhD in biscuit form

The Equatorie of the Planetis, from
Peterhouse, Cambridge MS 75.I, f. 74r

I submitted my PhD thesis last week (and now have a little more time to post on this blog).  In large part it's a study of this fascinating instrument.

If you've read this blog before, you'll know I've studied a 1950s replica of this equatorium, made my own replica - and then made it again in a smaller form and (slightly) more authentic materials.


But until now, I'd never made an edible equatorium.

I made the face out of chocolate shortbread (an adaptation of Jamie Oliver's recipe, with 3 tbsp of cocoa added per equatorium).  The epicycle was gingerbread.

It was a bit tricky to get everything the right shape, and the gingerbread expanded more than I had expected in the oven, but it all came out pretty well...

Add a screw and nut to hold the rule to the epicycle, position them correctly, and here's your complete equatorium!

Masculine Mars? Planetary degrees in medieval astrology

I handed in my PhD thesis earlier this week, so I finally have time for a new blog post.  It's another small step towards the blogging task I've been putting off for months: using my son's horoscope as a way in to understanding medieval astrology.

This chart has been pinned above my desk for some months:

Horoscope from Peterhouse 75.I, f. 64v

Much of my research investigates how medieval astronomers found the locations of the planets, using instruments and tables.  I explained in an earlier post how, in order to cast a nativity (an astrological analysis of the moment when someone was born), the first step was usually to find the locations of the planets in the 12 astrological houses.  The chart above is a traditional layout (here's the same layout used in a 9th-century horoscope, copied in the 14th-century manuscript at the centre of my research). It shows the cusps (boundaries) of the houses, and the locations of the planets within them.  They start in the middle on the left, and go round anticlockwise.  So in my chart, the first house starts at the 4th degree of Capricorn, the second house starts at the 16th degree of Aquarius, and Mars was at the 29th degree of Capricorn.

Now, the location of the planets in the zodiac was thought to determine the strength and nature of their influence.  But this basic astrological axiom could be interpreted in many ways.

The Declarations, a brief manual written for "The Queen" (probably Philippa of Hainault, the wife of Edward III) by the great astronomer Richard of Wallingford, who was Abbot of St Albans 1327-36, begins thus:

If there be a question made of the nativity of a man, and the planets be in masculine degrees, that shall be to him a strength.  And if there be a question made of the nativity of a woman, and the planets be in feminine degrees, that shall be to her a strength.

What are masculine and feminine degrees?  Ptolemy (whose Tetrabiblos is as important a text in astrology as his Almagest is in astronomy) had written that the stars were masculine when they rose and set before the Sun, and feminine when they followed it.  But here we see a different doctrine, in which certain degrees within each sign are assigned one or other sex.

Here, as on so many other topics, medieval astrologers were following the authority they knew as Alkabucius or Alchabitius.  This was (Abu as-Saqr 'Abd al-'Aziz ibn Uthman ibn 'Ali) al-Qabisi, a 10th-century Syrian who, along with the 9th-century Persian Albumasar (Abu Ma'shar), wrote the works of astrological theory that were most popular in the Middle Ages.  Al-Qabisi stated that the first 11° of Capricorn were masculine; the next 8° feminine; and the last 11° masculine again.  Each sign was divided in a similar way (but always in different proportions) into between 3 and 7 groupings of masculine and feminine degrees.

Opening of the Declarations, in Wellcome Library 8004, f. 31v

You'll already have worked out that for my little boy, Mars was in a masculine degree on the day of his birth.  (Matters weren't always this easy: in a table found with one copy of Richard of Wallingford's Declarations, individual hours of the week were assigned sexes.  On the other hand, the 11th-century Persian scholar al-Biruni thought the whole idea of masculine and feminine degrees was confused and lacking in substance.)

Anyway, if I use al-Qabisi's layout for little ADJF's horoscope, Mercury is also masculine; all the others (the Moon, Jupiter, Saturn, the Sun and Venus) are feminine.

This could be interpreted in a number of ways, depending on what we're interested in: are we investigating the subject's health, wealth, chances in life and love?  And how do we balance this information against other data in the horoscope concerning the Signs and planets?  I'll explain some of this in the next post (coming soon!), when I talk about the very important doctrine of planetary dignities, which considers the locations of the planets in the Signs and their relationships with each other.

For now, though, we can say that Mars and Mercury are strong in my son's nativity.  Mars, according to al-Qabisi,

indicates tyranny, bloodshed, conquering, highway-robbery, wrongful seizure, the leadership of armies, haste, inconstancy, smallness of shame, journeys, absence, indulgence in love-making, miscarriages, middle brothers, and the management of riding animals. (translation by Burnett, Yamamoto and Yano)

 Meanwhile Mercury suggests

public address, rhetoric, and activities which arise in mathematics like business, calculation, geometry, philosophy, taking omens, sorcery, writing, poetry, and all kinds of calculation . . . It indicates fear, fighting, killing, enmity, tyranny, opposition, prosperity, craftsmanship, kindness in deed, investigation, and everything else concerning commerce and contentions.

Does this mean that little A is going to be a tyrannical accountant? Well, it does run in the family.  But the more important point is that it took an experienced astrologer to interpret all the data in a horoscope.  This whole post is based on just the first two sentences of Richard of Wallingford's Declarations, and already we have a bewildering array of options.  What I thought was a simple little square diagram turns out to be surprisingly complex - in my attempts to read it, I'm beginning to understand why astrology was thought to be such an advanced science in the Middle Ages.