Very interesting. The style suggests late 20's or early 30's; its a vaguely curvex-style watch. The movement is very nice. The swiss cross normally denotes a patent number, and there IS a swiss patent 2001 that I found, but I'm not convinced its actually relevent to the watch. A german reader might be able to tell you more: Espacenet - Original document
Odd thing is that the patent was registered in 1890. That's really pushing the time-frame, since I think patents are only valid for 25 years. But the german nature of the patent does match up with the lack of any obvious "swiss made" markings.
I'm with Rob on the dating as perhaps early 1930's as it has a round movement placed into the (then) newly fashionable rectangular case. It is likely a ladies watch movement, so your search should be restricted to the smaller calibres. From the wear to the case (which could be just reflection of your fingers) I'd be suspicious that the dial has been repainted at some point which might explain the lack of name. Given that even if you find the manufacturer of the calibre you may never know who assembled the watch as a whole. Ladies watches are not especially collected so I have doubts you'll find a picture of the calibre online easily - chances are you need someone with a movement parts catalogue and for that you will probably need the dial removed for a photo of the setting parts (and it may well be stamped under there by the manufacturer).
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