BS87 -
The unknown tool is a Saw-Set. Back when handsaws were in primary use, the carpenter would sharpen his own saws. There would be one in every toolbox, or back at his bench at home next to his saw vise.
The saw-set was used to re-set the angle of the teeth on the saw to allow for a kerf, and to keep the saw from binding. There should be a dial, or some sort of adjustment on it (the front thumbscrew) to create a shallow or deeper angle. The tool would then be placed on the blade, centered on a tooth, and then squeezed to bend the tooth to the correct angle. All before the file was used to sharpen the teeth. The saw teeth would be alternated left/right to keep the sawdust from choking the teeth, and make a kerf wider than the width of the saw.
I used one
once, just for the experience. I'd rather pay someone to sharpen and tune my saws after that.
A cool, but forgotten tool.