lathe/4th axis conversion question

[m_c]

I was going to suggest if it's that old, it might be something totally random, but a search suggests the Morse Taper has existed since 1864.

19.23 would put it around MT2, which the mouth should officially be 0.7" or 17.78mm. MT3 should be 0.938" or 23.83mm.

Best option would probably be to find something cheap that has an MT2 taper, and try it for fit. Have a search for a drill (if you know any local engineers/blacksmiths, they may have some broken drills), reducer adapter, or dead centre.