If you don't remove the air in such a column, you're likely to get shot that is more raindrop-shaped than sphere-shaped. BTW, I believe an analogous method has been used to fabricate spherical items in space orbit. So *that's* what Galileo was really doing on the Tower of Pisa: making musket balls and cannon balls! Unfortunately, Galileo was about 100 years later -- almost 1600. So we have a very interesting question: is it possible that da Vinci considered the same idea for making spherical glass objects? The problem with glass is that unless it is extremely hot, it will take quite a while to "relax" into a spherical shape during the fall. A slightly more modern Galileo might have used an elevator, part of whose travel was in free fall, because an elevator would eliminate the airflow problem. BTW, now that we have really, really tall buildings, where are the *free fall* elevators? Why do we have to go to Magic Mountain (N. of Los Angeles) to find a free fall ride? At 10:19 AM 10/22/2017, you wrote:

The usual method for producing spherical lead shot was as follows:

1. Position a large container of cold water at the bottom of a tower.

2. Stand at the top of the tower.

3. Drop a volume of molten lead, in freefall, from the tower.

4. Appeal to the isoperimetric inequality.

Best wishes,

Adam P. Goucher

...

Sent: Sunday, October 22, 2017 at 5:03 PM From: "Henry Baker" <hbaker1@pipeline.com> To: math-fun@mailman.xmission.com Subject: [math-fun] Fabricating a glass/crystal sphere circa 1500

It's the year 1500, and some wealthy patron wants a transparent glass and/or rock crystal sphere perhaps 6-8" in diameter.

How would you fabricate it?

I don't know how they actually did it, but here are some of my speculations:

1. To make a solid glass sphere, one might make a spherical mold, melt glass into it, and then polish the result.

2. To make a rock crystal sphere, one might build a lathe, and then utilize a semicircle guide to cut a rough crystal block into nearly spherical shape, and then polish the result.

One might even take the glass from the mold & mount it onto a lathe for the polishing step.

Clearly (!), one could continually reposition the sphere in the lathe to work on different axes to attempt to make the sphere as precisely spherical as possible.

Are there more elegant methods?

Using just the technology available in 1500, what kind of precision could be achieved?

[BTW, a similar problem arose in the 19th Century when *ball bearings* became important. Apparently, the longevity of various kinds of engines depended critically on making the bearings as spherical as possible. I don't know enough about how this precision was achieved, but during WWII, bearing manufacturing plants were heavily targeted for bombing.]