What is this electrical device?

[amecks]

Looks like a soldering iron, sorta.  No markings that I can see.  The alligator clip is stamped with a + mark.

[bonneyman]

The compressed carbon tip makes me think a low voltage arc welder (or spot welder) for tight spots. Maybe for in the field, emergency repairs? Clip onto the car battery and weld away?

[amecks]

Yes, it looks like something from a vintage JC Whitney catalog.  You hook it up, do a roadside repair, then your car won't start cuz you drained the battery!

[lptools]

Pretty cool looking tool! Have you drained a battery yet?

[bonneyman]

Yes, it looks like something from a vintage JC Whitney catalog.  You hook it up, do a roadside repair, then your car won't start cuz you drained the battery!

Oh, the old JC Whitney catalogs! How I used to go thru those and dream about someday having a car and putting all those cool accessories on!

[p_toad]

Them or Warshawsky

[papadan]

Yep, small DC carbon arc torch. Handy for soldering hose necks back onto radiators. Back when everything was brass instead of aluminum and plastic. 

[Lostmind]

I worked at an ignition/electrical shop in the 60's.
We used a similar piece to solder brushes in starters.

[amecks]

I'm guessing there was a lead filler rod or wire solder that you fed into the arc, sorta like a crude heliarc welder?

[Catch22!]

We used to make these out of an old D cell battery core and a jumper cable.   It will work for a while if you need to weld something away from the house.