The correct answer is B) steam pressure sensing device with linkage to the damper air vanes. In an automatically fired auxiliary boiler, the fuel oil metering valve is controlled by a steam pressure sensing device. This device monitors the steam pressure in the boiler and uses a linkage mechanism to adjust the damper air vanes accordingly. This allows the fuel oil supply to be regulated based on the steam demand, maintaining the desired pressure in the boiler. The other options are incorrect because they do not accurately describe the control mechanism for the fuel oil metering valve in an automatically fired auxiliary boiler. Option A refers to a pressure magnifying device in the steam coil outlet, which is not the control mechanism for the fuel oil metering valve. Option C describes a metering device in the air supply line, which is not the primary control mechanism. Option D refers to a signal from the feed water electrode, which is not directly involved in controlling the fuel oil metering valve.