A micrometer needs two reference surfaces – on a standard tool they are the fixed and the moving anvil.
What is the second reference surface on the one you have? My guess is the cylindrical face of the part in which the arm slides.
There appears to be a domed item on the end of the graduated barrel – is that relevant, or is it just a screw?
When the dial is set to zero, what is the relationship (measurement) between the face of the arm and the face of the cylinder? When the dial is set to 1″ what is the relationship? Are the scales zero left or zero right?