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The old styles of rimless and semi-rimless glasses made around 1900-1930 by American Optical (and maybe others?) all seem to have the same screw. They measure about .045 inches diameter and the thread is 90 tpi. (The US dime in these photos is 18mm diameter.)

I made some out of brass and steel, and they came out great. The first operation is cutting the thread, body, and the bottom and outside diameter of the head. Then I parted them with a jeweler's saw. (The bottom screw in this first photo is a too-short original.)

Then, I turned them around and held them in a #11 WW collet to finish the head and cut the slot. The slots were cut with a screwhead file clamped atop an adjustable parallel on the cross-slide.