You need to get an idea of the thread pitch. I would stick something like a match stick down the hole, and then the right diameter small screwdriver down the hole alongside it to squeeze it against the thread. Remove the screwdriver and then the match stick, and with luck, there will be an impression of the thread for you to measure the pitch.

David

As Brown and Sharpe is an American company I'd expect American threads. 1/4" ANC / UNC has a core diameter of 0.1887" which is in reasonable agreement with your 0.19" measurement and is 20 TPI.

Standard US countersunk machine screw head for 1/4" is 0.507" diameter but, as I'm sure you have already found elsewhere normal practice for this sort of equipment was to use smaller diameter heads with a parallel portion above the countersink cone. Tricky bit is whether they are 80° or 100° nominal countersink angle.

Yup les crazy yanks used both!

I'd be unsurprised to discover that the basic dimensions were basically as per the Slotted Undercut Oval Countersunk Head Machine Screw but of reduced diameter with a flat, rather than oval top. So the countersink angle would be 80° nominal and overall head height about 0.18" and diameter 0.30" or a shade under. If the dividing head is was old as I think probably 19/64" diameter.

Machinery's Handbook is your Frenemy for this sort of thing. Nearly everything is in there but finding it is different matter! As is making sense of what it all means when you have found it!

Clive