Yeah, that compound looks kinda wimpy, I thought the 12" Logans had compound dials that you could actually read.
I've had several Logan lathes and they often come 'mix and match' between models. But usually with another lathe of the same size. Rare to see accessories and parts from a 10"on a 12". But, maybe people tried to make do with what they had or could find.
Logan has some old catalogs on their website, and vintage machinery may have some too. Heck, may be some here in the if you look in the downloads section. Take a look and compare to your machine.