Why Does a Circa 1905 Solenoid Have Two Different Wires?

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In post #28 you show pair of back-to-back Zener diodes on an AC supply. You also show data for a MOV = metal oxide varistor.
Since you have a DC supply you only requires one power diode to suppress the flyback arc.

A single diode would keep the current flowing for longer after the contacts open because the reverse voltage across the coil would be less than with a MOV or the Zeners. Just make sure the diode and battery polarity are correct so it does not normally conduct.

The shorted coil would waste energy while turning on and extend the field while turning off. If you disconnected or removed the shorted coil, the single diode would go some way to compensating for the removal of the shorted coil.
 
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Perhaps it is to get rid of DC flux when driven by a directly connected (non-capacitive) connection? One would use a serial capacitor now as a DC block, but I imagine wire was cheaper than capacitors in those days.