Well Eric I can tell you how I did it when I attempted a lamina engine.
Hopefully some that knows the proper way will step in to correct me.
I chucked the test tube up in the 3 jaw of my lathe padded with thin strips
of rubber. Then I mounted a cheap hand glass cutter in the tool post and slowly
advanced it until there was a good even scribe line cut into the glass.
A few very patient light taps around that line with a piece of 1/4" brass stock
broke it through. It wasn't as clean of a break as I had hoped for but a little
working over some 220 grit emery cloth taped to the work table and nobody would
Brass I just saw this on Ebay. I can remember back in the 1980's when Ronco, Ginsu or one of those exuberant TV sales mavens once offered a bottle cutting kit for making artsy crafty creations. It wouldn't very be hard to make one of these for cutting a test tube, or even the main cylinder for a stirling.
I found these cheap chinese diamond discs on a market stall for about $15 for 8 ,they are 50mm dia., they also had 75mm ones, I have a little Proxxon table saw so I re-drilled one to fit ,they are the bees-knees for cutting test tubes and the sides work a treat for the edges of glass plate, for cutting a circle you could roughly cut with a normal glass cutter first and make a little jig with a pin somehow superglued to the centre of the disc to turn it against the diamond wheel to clean up the rough edge, you could even mount it in a Dremel. I'm sure they can be found on ebay or somwhere.