Or could it be a Gillette New Short Comb, from the late 1930s? The tabs on the top cap and the single groove instead of three holes make me say this. I have an Old Type, and that baseplate has three holes instead of a groove.
As @chuckd says above it's a Gillette New Short Comb, most definitely. Gold plating is gone, at least on the top cap, but seems to be in good shape otherwise. Those ball-end handles usually have a crack in the tube.
