This one most closely resembles a President Madison....close but no cigar. White case has enameled highlights on the lugs, in the middle of the vertical sides and an odd "propeller" pattern engraving around face with a repeating chevron engraving on sides. Numbers on face are black and slightly raised like a radium dial. Hands are black. No sign of Radium.
Movement is 1930 and single hinge case is 1931. Face seconds track and number layout doesn't match case opening and is likely a swap.
No reference to gold content on inside of caseback (Marked Bulova Quality and Pat. Jan. 1927) and nothing on slightly curved case back exterior.
I have no idea what this is. Dust cover and ring over movement intact. Running and keeping time.
In reply to We have the same watch here, by Geoff Baker
It appears to have a cylinder crystal which I think it distorting the dial but I also note that it's likely a replacement dial as the minute track is oval as opposed to rectangular like the case and the numerals seem to be out of place. That could account for the movement being replaced as well.