The acorn valves were designed to have low capacitances and therefore work to higher frequencies than the normal valves. The DS310 was designed for the low UHF region at about 300 MHz. The two Volt heater would indicate use in portable equipment. The DS311 had a 12.6 Volt heater for vehicle or mains use.
The stamp BA 4721 would be a Wehrmacht approval mark.
The base showing the pins passing through the glass. Each pin is a composite of up to three metals.
The base section showing the evacuation seal and the connection to the heater wires.
The acorn envelope is 14 mm in diameter and, including the base pins, is 42 mm tall.
Reference: Datasheet. Type DS310 was first introduced in 1938.