BOOKREVIEW: The Easter Calculator of the Strasbourg clock

[Fortunat Mueller-Maerki]

BOOKREVIEW by Denis Roegel
roegel@loria.fr
Posted with permission of the reviewer


Joseph Flores, Denis Kleinknecht, Marc Augereau:

Le comput ecclésiastique de Frédéric Klinghammer,


Besançon: AFAHA (Association Française des Amateurs d'Horlogerie Ancienne),
2007, 160 pages and a CD with a 58 minutes movie. 40 euros, shipping
included to France. Order at AFAHA, BP 33, 25012 Besançon, France, phone:
(33)3 81 82 26 74. 1700 copies printed, including 1300 offered
to the AFAHA members.



The Strasbourg cathedral houses one of the most famous, perhaps even the most famous, astronomical clock in the world. The current clock, which is
actually the third, was designed by Jean-Baptiste Schwilgué (1776-1856)
and built from 1838 to 1843. It improved the previous clock from the
16th century in every possible way, be it on astronomical matters with
for instance intricate mechanisms for obtaining the real positions
of the Sun and the Moon, or on calendrical matters with what was
probably the first perpetual and mechanical Church calendar able to
compute automatically the date of Easter Sunday.

Easter has been following an apparently simple rule for almost
2000 years, namely that Easter is defined as the Sunday following
the first full moon in the Spring, starting on March 21. If for
instance there is a full moon on March 26 and this is a Wednesday,
Easter will take place on March 30. Now, since the motion
of the Moon is very complex, approximations of its motion have
been used since the dawn of time. The moon alluded to in the definition
of Easter is therefore not the real astronomical moon, but some
approximation which tries to follow the real moon as best as it can,
but without making things too complex, and in such a way that
Easter becomes predictible.

Before 1582, when the Julian calendar was still effective,
Easter was following a simple pattern, and repeating itself
after 532 years. The Julian calendar, however, was somewhat defective,
and it is well known that the Julian year being slightly too long
with respect to the tropical year (the year of the seasons),
the error accumulated and amounted to about 10 days in 1582.
The calendar was modified under Pope Gregory XIII and in addition
to dropping 10 days, the reform also made the Gregorian year slightly shorter
than the Julian one, by removing three days out of 400 years:
years such as 1700, 1800, 1900, which would have been leap years
in the Julian calendar, were no longer so in the Gregorian calendar.
This was the most obvious change introduced by the Gregorian
reform, but there was another change, that went by almost unnoticed,
and it concerned the cycles of the Moon. In the Julian calendar,
the approximation used for the Moon was based on the Golden Number,
a lunar cycle of 19 years known for more than 2000 years. Incidentally,
the word ``Golden Number'' is much more recent than the cycle itself.

In the Gregorian calendar, the cycle of the Moon was made more accurate
and based on the calculation of the Epact, which is approximately
the age of the Moon (the number of days since last new Moon)
on December 31st of the previous year. In 2008, for instance,
the Epact is 22, and this means that there was approximately
a new moon on December 9, 2007. An examination of ephemerides
shows that there was indeed one on that day, but there might
have been a difference of up to two days between the real
astronomical moon and the ecclesiastical moon.

Computing Easter is not very difficult using tables, but there are
a number of tricky issues, like those of the secular leap years,
and a special case for the Epact 25. One can for instance
compute the dominical letter (a letter from A to G specifying where
are the Sundays in the year), and then the Epact. The latter, sometimes
aided by the Golden Number, provides the position of the first
full moon of Spring. It is then straightforward to find Easter, by hand,
that is. But the complexity of the calculation is apparent when
one considers that the cycle of Easter is now no longer a mere 532 years,
but 5700000 years!

The first known mechanization of the Gregorian Easter calculation,
the so-called ``computus paschalis,'' seems to have been that of
Jean-Baptiste Schwilgué in 1821, after an idea that first
occurred to him in 1816. Schwilgué built a small model which was
able to compute the Solar Cycle (a cycle of 28 years in the Julian
Calendar), the Dominical Letter, the Epact, the Golden Number,
the Roman Indiction (a cycle of 15 years unrelated to Easter),
and finally Easter Sunday, for any year in the Gregorian calendar.
20 years later, Schwilgué built this mechanism, with only few
modifications except size, into the Strasbourg astronomical clock.
The computus is triggered by the clock on New Year's Eve, and
after a few minutes, it sets Easter (and the associated feasts
such as Passion Sunday, Pentecost, etc.) on a nearby calendar dial.

Schwilgué's prototype was unfortunately stolen around 1945 and
has not been recovered since. In the 1970s, however,
Frédéric Klinghammer (1908-2006), a former employee of the Ungerer company that used to take care of the Strasbourg clock, and who was instrumental in the construction of the great astronomical clock in Messina (1933), built a new replica of Schwilgué's computus.
Klinghammer's computus was recently restored by Joseph Flores,
from the French AFAHA group, and he, together with Denis Kleinknecht
and Marc Augereau, describe this model in the book which we are
reviewing.

We will say little on the mechanism itself, because it would
obviously take a long time to explain all its details. Flores's
book is 160 pages long, but still leaves a number of questions
unanswered. Our purpose, in this review, is not so much to describe
the computus, than the book on the computus. The computus itself
is a marvelous little jewel. There is unfortunately scarce
information in English on how it works, but the most complete
published sources on the Strasbourg clock so far are the books
by Alfred and Théodore Ungerer ``L'horloge astronomique
de la cathédrale de Strasbourg'' (1922) and by
Henri Bach and Jean-Pierre Rieb ``Les trois horloges astronomiques
de la cathédrale de Strasbourg'' (1992). The latter was also published
in German. There is a small booklet written by Théodore
Ungerer, which has been published in English, and gives
a technical overview of the clock, including its computus. To my knowledge,
there isn't anything else.

Flores's book is a very welcome addition, and I must stress right
away that even if you don't read French, interest in the Strasbourg
clock alone makes this a necessary buy. You won't regret it.
Flores gives a first hand overview of the structure of the computus,
and the included CD (by Denis Kleinknecht)
shows you how it works in practice. You can follow
several year changes and analyze the motion of all the parts
by slow motion. Although the accompanying text is read in French,
I believe the images are mostly self sufficient.

If the book had been perfect, I would probably stop here, and wish
you a happy reading. Alas, reading the book has left me with very
mixed feelings. First, the book is obviously concentrating
too much on the structure of the computus, and is not, in my
opinion, enough pedagogical. Understanding such a mechanism
makes it necessary to have first a good understanding of the
Gregorian calendar, which few readers will have, at least as far
as the lunar part is concerned. The book contains indeed an introduction
to the Gregorian calendar, by Denis Kleinknecht, but this introduction
is more of an appendix than an introduction, and is certainly
not well interleaved with the study of the mechanism itself, although
Flores refers here or there to Kleinknecht's part. It is possible
to understand how the computus works using this book, but the reader
will have to do a lot of back and forths from Flores's part,
to Kleinknecht's, and to the CD. How many readers will really complete
this mission is not clear. Probably not that many!

The book is supplemented with an appendix by Marc Augereau
computing various gear ratios, but this part can be totally skipped.
It is badly typeset, contains mostly irrelevant material
that seems to have landed here just because this author
was asked to compute all possible ratios. Actually, only a few of
the calculations are needed, but they are hidden in a jungle
of formulae that are not well explained, and probably inscrutable
for most readers, besides containing a number of typos.
The main text doesn't make use of Augereau's part at all.

It would have been nice to find some historical material on
the mechanical side of things. One wonders, for instance, what other clocks
have had a computus, before or after Schwilgué's clock, but
Flores has unfortunately done no historical research at all.
He therefore does not even seem to know that there are two
related mechanisms only a few miles from where he lives and
examined the computus, next to the Swiss border. Such oversights
are surprising for someone who got a Gaïa prize in the
historical category. Nor does Flores offer much
information on the development of Klinghammer's computus itself,
and he fails to notice that the computus was at some point
modified, as for instance the examination of the pictures
published in the 1992 book by Bach and Rieb shows.
Lack of historical research also leads Flores to attribute
some features to Klinghammer, when they were actually
already present in Schwilgué's model.

Many other problems could be mentionned, among them the rather
surprising fact that Flores alone appears on the front cover,
when he basically only dismantled and described the computus,
but did no historical research, whereas Denis Kleinknecht
researched on the Gregorian calendar and made the accompanying CD.

But what I have come to regret most is the too AFAHA-oriented
documentation. This is a book which was written for the AFAHA members
and they are probably happy with it. However, when someone has the
privilege of being able to dismantle and document such a rare
mechanism, knowing that not many people will have that opportunity,
I believe there is a duty towards the scientific community,
which far extends a group such as the AFAHA. Now, how could these
two aims have been reconciled? The scope of the current book
could have been kept as it is, provided the author made for instance
clear that all historical research were to appear elsewhere, as well
as all details that could not fit in the current work. Among
the missing details, for instance, are those of the two weight-engines.
The number of teeth are never given, although some of them can be
obtained or guessed from the pictures. Why they were not given is
a mystery, and it would have helped for a more complete comparison
with Schwilgué's computus. A companion volume, written by Flores,
or by someone else, should have been planed simultaneously,
and it could have contained, in a more archivistic manner,
all the things that would perhaps have bored the casual reader.
I have for instance in mind the kind of documentation which
was made in the 1980s by Ludwig Oechslin for the clock of Bernardo
Facini, or more recently for the clock by Johann Wolfgang Hartich (2007).
In both cases, Oechslin shows every part in isolation, on graph paper.
No such thing was made by Flores, at least not in his book.

Scientific rigor is no waste of time, and it should be the aim
of every author, whether the author writes for children or
for scholars. An author should always state why he writes this,
what are his sources, or, perhaps, state why he doesn't give them.
He should not be oblivious of his duties towards the scientific
community, and keep an open mind. An author should not write
only for him, not write only for his group, he should write for
all, or start some kind of collaboration to make this possible.
None of this was attempted by Mr. Flores, and the book eventually
appears very amateurish. It reminds me of what Anthony Turner
and Emmanuel Poulle wrote on Baillie, Lloyd, and Ward's ``The Planetarium
of Giovanni de Dondi'' (1974) which published the translation of
a 14th century manuscript, but as a collage of several translations
and drawings coming from at least three different sources,
the translations being accompanied by no critical commentary and
being practically useless, at least at the time of publication.
Poulle wrote that this book made public the amateurism of
the team that produced it, and turned to their confusion.
In some way, this is what now happens with Mr. Flores.

Denis Roegel, January 23, 2008.

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