Marks on barrel of m1865 carbine

[Pinfire]

I have a model 1865 carbine, serial #13563 that is correct in all respects except for the barrel band which of the M1860 type.  It has no cartouches.  The marks shown on the metal parts are 1/16 size M,E, AND Ws' which I understand from Roy Marcots' book are assembly marks.  My interest is in the marks on top of the barrel under the barrel band.  The marks are an M.M. About 1/8" in size and what appears to be a letter struck out followed by a 3/16" size P.  Any information on these marks would be appreciated as it could show were it was used. The    Butt stock shows marks on the left side of carbine sling usage.  Pinfire