After some digging, I know officially what my lathe is

Elgin EL-5C.Wood bench

TT Tap Collets are used in the Hardinge® TT-5/8 and TT-3/4 Tap Holders. These collets are stocked in ANSI (USA) and ISO (England) standards. The ANSI Inch-series tap collets relate to taps manufactured in the United States. Metric collets manufactured in the United States have the same shank sizes as those used for the inch series. The metric collets manufactured to the ISO standard have different shank sizes than the ANSI series metric collets.

0.141  = #0-#6
??? In chuck
0.194 = #10
0.220 = #12
0.255 = 1/4″
0.312 = 1/8″ P
0.323 = 7/16″
0.367 = 1/2″
0.381 =3/8″