Nostalgia overcame my better judgment and I decided I couldn't live without a couple of old school combat planes.  I got a couple of Fox 36X's, one ball bearing and one needle.  I need a back plate for one.  Someone must have a spare can live without.  Please PM me if you have one.  Oh yeah, I got a couple of piston and liner sets from Brian Gardner so I'll be good to go.  Hopefully I can stay married after this.

Historical value makes no difference to me.  I have them both apart and in a tub to clean, the only difference I see is the type of bearing in each. I can't tell which needs the back plate.  One of them came with a back plate that was a lot smaller in diameter so it rattles around.  The bolt pattern is OK, but it just doesn't look right.  Maybe it is?

I went through my handful of pics showing some of my 35X/36X stuff and here's the best picture I have of the back plates for a 36X needle bearing engine. Hard to tell here, but yes, the outside diameter of the back plate is less than the inside diameter of the case, so there is "slop" when the back plate is in place sans screws. (I used to wrap the NB back plate with flexible 1/16" balsa to fill the void.) Also note the long protrusion that was cast on that was to be drilled-out and a pressure fitting installed if case pressure was desired.

The later back plates for the 36X BB was a closer fit inside the case and lacked the protrusion to the rear for the pressure fitting.

I suspect you have a back plate for a needle bearing 36X.