Does the current flow from the bottom left pin to the bottom right pin, or from the bottom pins to the cap on top?
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It's an 811 power triode. There is no cathode per se as it's also the heater filament.
I believe that's a 4 pin triode. The camera angle makes it look like 2 pins. The top connector is usually a connector for the plate/anode. You would need three pins for the heater/cathode and one pin for the grid, similar to this.
Operation is (simplified) heat up the negatively charged cathode to boil off electrons, which are attracted to the positively charged plate. Modulate the stream of electrons by varying the voltage on the grid.