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Most people seem to want to believe it does. 
Glass is a liquid, and naturally flows, rightNo.

Why the Myth Doesn't Make Sense 
There are at least four or five reasons why the myth doesn't make sense.

Although the individual pieces of glass in a window may be uneven in
thickness, and noticeably wavy, these effects result simply from the way
the glasses were made.

One also wonders why this alleged thickening is confined to the glass in cathedral windows.

Why don't we find that Egyptian cored vessels or Hellenistic and Roman bowls have sagged and become misshapen after lying for centuries in tombs or in the ground?

Speaking of time, just how long should it take—theoretically—for windows to thicken to any observable extent? The calculation showed that the time required for the glass to flow down so as to thicken 10 angstrom units at the bottom (a change the size of only a few atoms) would theoretically be about the same as the age of the universe: close to ten billion years.

This brings us to the subject of viscosity. The viscosity of a liquid is a measure of its resistance to flow. Estimates of the viscosity of glasses at room temperature run as high as 10 to the 20th power (1020), that is to say, something like 100,000,000,000,000,000,000 poises, As for cathedral windows, it is hard to believe that anything that viscous is going to flow at all.

It is worth noting, too, that at room temperature the viscosity of metallic lead has been estimated to be about a billion times more fluid than glass. Presumably, then, the lead came that holds stained glass pieces in place should have flowed a billion times more readily than the glass. While lead came often bends and buckles under the enormous architectural stresses imposed on it, one never hears that the lead has flowed like a liquid.

Glass Doesn't Flow 
When all is said and done, the story about stained glass windows flowing—just because glasses have certain liquid-like characteristics—is an appealing notion, but in reality it just isn't so.

The full article by Robert H. Brill, Research Scientist, Corning Museum of Glass can be found at:http://www.cmog.org/dynamic.aspx?id=5728.

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