It is an "autoportrait" selftimer with a curved mirror. After setting the timer, the photographer puts in his place and he can see his own reflection in the mirror.
Known numbers:
2817____Alain Berry collection.
5086____PYC. collection.
5654____Jacques M. collection.
5752____seen on eBay.
8083-------Jim McGee
9944____Bill Parkinson collection
11508___seen on eBay.