I'm working on an old (early '70's) Sunshine front hub and these are the lock nuts being used. The concave side is toward the dropout. I'm not sure if these are proper for use as a lock nut or if they are from another use.

If the conclave side is towards the frame, I suspect someone put them together backwards. The lip on the concave side should fit around a spacer and the flat side should be towards the frame.

I had those on a late 1970s bike, nice large flange hubs with cutouts like Campy of that era. The concave side is the one that grips the dropout - rather than using a toothed face that grips well but can chew the frame ends, these just reduce the contact area to increase grip pressure.

Yes this! For front wheels running the locknuts backwards, so the flat face contacts the dropout's inner face, isn't too big a booboo. But for the rear and a horizontal drop out the flat against flat interface can be too slippery to keep the wheel from shifting due to pedaling forces. Same reason why some lock nuts have a serrated or notched outer face, like many Campys have. Andy

Thanks All! After having a wheel fall off (my fault) a while back, I try to be careful.

It looks like a recess to hold a captive washer, like those on track bikes.