The 2X2 is an EHT half wave rectifier. We also have the later 2X2A vibration resistant variant in the museum.
The 2.5 volt heater indicates that it would be powered by a special heater winding of high insulation. Such a valve would have found application in oscilloscopes or in multiplier chains for higher voltages.
The identification is etched around the fluted top cap.
The anode bell - trying to see inside was blocked by the gettering.
The classic envelope is 38 mm in diameter and, excluding the UX4 base pins, is 98 mm tall.
References: Data-sheet, 3002 & 1043. Type 2X2 was first introduced in 1939.