Cathedral glass does not flow: it would need 414 degrees held for eight centuries
There is one explanation that keeps coming back around Gothic stained glass: the panes are thicker at the bottom than at the top because glass is a liquid. A very viscous one, granted, but a liquid, sagging under its own weight for eight centuries. The explanation has everything going for it. It is visual, it hangs on an observation anyone believes they could make for themselves, and it grants glass a secret life. It is false. What makes it interesting is not only that it is false: it is that in 1997, when a researcher set out to check it, he found, to his knowledge, no published calculation on the question.
A myth whose source nobody knew
When he published on the subject, Edgar Dutra Zanotto signed from the materials engineering department of the Federal University of São Carlos, in Brazil. He recounts being asked the question by students and colleagues several times over his two decades of teaching, because of twelfth-century cathedral windows reputed to be thicker at the bottom. He notes one detail worth as much as the rest: nobody knew where the information came from.
He first took it for a Brazilian myth, then discovered that a colleague had heard the same story in Argentina, and a referee for the American Journal of Physics confirmed that it circulated in the United States. It surfaces in print as well. Zanotto points to a textbook, Materials Science, Testing and Properties by W. O. Fellers (Prentice-Hall, 1990, page 204), and to the Encyclopedia Britannica, entry "Viscosity", volume 23, page 198, William Benton edition of 1966. Both of them, he says, claim that pieces of glass kept bent for several months at ordinary temperature do not return to their original shape.
His paper, Do cathedral glasses flow?, received on 23 April 1997 and accepted on 27 October of the same year, appeared in the American Journal of Physics, volume 66, number 5, May 1998, pages 392 to 395. In it he writes that to his knowledge no calculation had been published on the subject, a cautious phrase and rightly so: the following year he would cite a text by Roy G. Newton, published in Glass Technology in 1996, which had already raised the question. His method: rather than argue, work out how long it would take glass to flow.
What a visible flow costs: 414 degrees
The relaxation time of a glass is its viscosity divided by the shear modulus at infinite frequency. For common window glass compositions, Zanotto takes about 30 GPa for that modulus, from absolute zero up to the glass transition range. That is the easy constant. Viscosity, on the other hand, depends violently on composition and temperature.
His table starts from real compositions. A modern window glass: 73.2% SiO2, 13.4% Na2O, 10.6% CaO, 1.3% Al2O3, 0.8% K2O. Medieval glasses refuse to be summed up: silica ranges from 45 to 75%, potash from 2 to 25%, soda from 0.1 to 18%, lime from 1 to 25%. They are rich in potassium where the modern ones are rich in sodium, and loaded with iron impurities (0.3 to 2.1% Fe2O3) and manganese (0.3 to 2.3% MnO). Those ranges come from a study of roughly 350 ancient glasses, by W. Müller, M. Torge and K. Adam in the Glastechnische Berichte in 1994.
To turn a composition into a viscosity curve, Zanotto uses the formulas published by T. Lakatos, L.-G. Johansson and B. Simmingsköld in Glass Technology in 1972, which relate the contents of SiO2, Al2O3, Na2O, K2O, CaO and MgO to the three parameters of the Vogel, Fulcher and Tammann law. For a yellow potassium glass from Saint-Gatien cathedral in Tours, he obtains A = -4.22, B = 5460.9 and T0 = 196.3 degrees Celsius. He points out that the procedure ignores minor impurities and probably overestimates the viscosity a little, with no consequence for an order-of-magnitude calculation.
From there falls the first number. For a typical medieval glass to show significant flow over 800 years, it would have to be brought to about 414 degrees Celsius. Not a spike, not a fire: a furnace temperature, held for the whole eight centuries. The windows, for their part, stayed at ordinary temperatures, several hundred degrees below.
Ten to the thirty-second, then ten to the twenty-third
One problem remains, and Zanotto raises it himself. The Vogel, Fulcher and Tammann law diverges at T0, that is 180 to 360 degrees depending on the glass, so well above room temperature. It predicts an infinite viscosity at 20 degrees, which is not an answer but a refusal to answer.
He gets around it by a detour. Silica, germanium oxide and P2O5 are among the very few network-forming oxides whose structure does not depend on temperature, and whose viscosity therefore follows a true Arrhenius law, one that can be extrapolated. GeO2 glass has a transition temperature equivalent to that of window glass, and its viscosity is written with A = -9.94, B = 17962 and T0 = 0. Following that curve down to room temperature, he obtains a relaxation time of 10 to the power 32 years, which he presents as a lower bound for cathedral windows. The paper supplies the scale that fits: the age of the Universe is on the order of 10 to the power 10 years.
This is where the story gets better than its short version. The paper made noise, and Prabhat K. Gupta, of Ohio State University, objected that the extrapolated equilibrium viscosity does not provide a lower bound on the relaxation time, but an upper bound. The relevant quantity is the isostructural viscosity, that of a glass whose structure is frozen, and it stays finite at room temperature. Zanotto and Gupta redid the calculation together in Do cathedral glasses flow? Additional remarks, American Journal of Physics, volume 67, number 3, March 1999, pages 260 to 262. The revised result, about 2 times 10 to the power 23 years, is nearly nine orders of magnitude below the first, and it leaves the conclusion untouched: still thirteen orders of magnitude beyond the age of the Universe. Between the two papers, Jay M. Pasachoff had published a comment in the same journal, in November 1998, which we come back to below.
Westminster, measured in 2017
Twenty years later, the case was taken up again with means Zanotto did not have. Ozgur Gulbiten, John C. Mauro, Xiaoju Guo and Olus N. Boratav published Viscous flow of medieval cathedral glass in the Journal of the American Ceramic Society: posted online on 3 August 2017, the article occupies pages 5 to 11 of volume 101, number 1, dated January 2018. They work on a medieval composition of the kind used at Westminster Abbey, and lean on a measurement rather than on a single empirical formula.
Their result is friendlier to the myth than the 1998 one, and that is exactly what makes it convincing. Depending on the thermal history of the glass, its viscosity at room temperature sits around 10 to the power 24 to 10 to the power 25 pascal-seconds, roughly sixteen orders of magnitude lower than an earlier study on a soda-lime glass had given. Medieval glass is therefore far less stiff than that value suggested. Even so, describing the flow of glass down a wall, the authors arrive at a maximum displacement of about 1 nanometre in a billion years.
The workshop hypothesis: a furnace six feet by four
If glass does not flow, where does the uneven thickness attributed to these windows come from? A first caution: in 1999, Zanotto and Gupta speak of "suggested" non-uniformities, without treating them as established. A second caution, about the cause: here we leave calculation for hypothesis, and Zanotto is the first to write that he is speculating. His proposal: old window glass was blown into cylinders, split, then flattened by hand, so that the sheets were not of uniform thickness and some lower portions could end up thicker than the upper ones.
The process itself is documented by the practitioner. In the treatise De diversis artibus, attributed to the monk Theophilus and generally dated to the early twelfth century, book II details the glassmaker's workshop. Chapter III calls for a third furnace, six feet long, four wide, three high, described as the furnace for spreading and flattening, equipped with an iron rod two ells long and as thick as a thumb, two iron tongs flattened at one end, and two trowels. Chapter VI describes the blowing: the gather is beaten on a flat stone so that it hangs evenly on every side, then blown until the piece looks like a long bladder, then the end is opened in the flame. Chapter IX gives the ending: the piece is split with a hot iron, laid on the floor of the glowing furnace, and once it softens it is opened on the split side, spread out and evened with the tongs, as one pleases. Then it is stood against the wall of the annealing furnace, a second beside it, a third, and once they have cooled they are cut up to make the windows.
A plate evened out with tongs has no reason to be the same thickness everywhere. What remains to be explained is why the thick side would end up at the bottom, and no source demonstrates it. In 1999, Zanotto and Gupta add a second lead, the crown process, where the thickness decreases as you move away from the centre, then suggest that glaziers may have set the pieces thick side down, crediting that suggestion to a personal communication. Pasachoff's 1998 comment went the same way, quoting a letter from John P. Hoxie, a consultant to Corning Glass Works: before 1890, window glass was mostly blown into cylinders that were split and flattened, a process that invariably gave sheets of varying thickness, and the panes of a single sash had to be mounted with the thick edge all facing the same way, downward for instance, otherwise the distant horizon appeared as a broken line. A workshop practice, then, rather than a law of matter, and attested for the nineteenth century far more than for Gothic building sites. Zanotto finally files one material observation: glass vessels thousands of years old are kept undeformed in museums the world over.
Why the story still holds
The myth survived because it combined a true observation with a seductive explanation. Panes of uneven thickness do exist. Glass really is an amorphous solid, with no crystalline structure, which makes the frozen liquid idea comfortable. And eight centuries is a span large enough to seem capable of anything, while remaining imaginable.
That is exactly the blind spot. Eight centuries look enormous to anyone comparing them to a lifetime, and negligible to anyone comparing them to 10 to the power 23 years. Zanotto concluded in 1998 that medieval and modern window glasses alike cannot flow at room temperature on human timescales, and the revised 1999 calculation, far lower though it was, did not touch that sentence by a single word. It took four pages and a table of compositions to settle a question the Encyclopedia Britannica had let through, then three more pages, the following year, to correct the number without touching the answer.