The Martin Band Instrument Company in Elkhart, Indiana was established in the early 1900s by Henry Charles Martin, a former Conn employee, and several of his family members.  By 1910 the firm was producing a sizeable quantity of instruments, among them some interesting cornet and trumpet designs.  They were able to make a dent in the market, and their product line included alto/tenor horns alongside cornets, trumpets, and more.  

The less-common model 1 cornet piece has a "deep cup" and "medium rim", as stated in its 1948 catalog appearance.  The mouthpiece exteriors shown include both the 1930s version seen here and the 1940s "Schilke" avant-garde type.  Only two models are listed, 1 & 10, but the implication might be that other sizes exist between those points [1980s Conn catalogs did the same thing], and other sizes definitely exist.

This sequential numbering system appears on earlier-looking Martin pieces, and higher numbers appear to have smaller cup volumes.  This system was used until the end of Wurlitzer's ownership with sale to LeBlanc in 1971.  However, the model 7 seems to have been the main [or only] design by that point.

The 1 was also the basis for the stock mouthpiece included with the unique, semi-cornet wrap Imperial & Committee Martin flugelhorns of the 1950s-1960s.  

By the Richards-RMC era catalogs, the mouthpieces shown are the Roth-Reynolds lightweight type, both with the Martin-branded horns and the Reynolds-branded Emperor & Contempora equivalents.  

This example is in good shape, with the usual nicks and a few light scratches one would expect for an item of this age.  The rim and cup are in nice playable condition.  There is plating loss on the shank, and while the opening is pretty round, it's a bit rough.  While not radically different than Morse shank tapers, due to manufacturing variability, we can't guarantee the taper will be perfectly matched for every receiver.

Sold as-is, no returns, pay within 3 days.  US shipping free - caveat emptor as we cannot take responsibility for any mishandling/loss on the part of the courier at any point - this is FOB shipping point.  By buying, you [the buyer] agree to the potential risk of the package not arriving due to courier mishap - be aware of these conditions.

Usually we get the item in the mail within 1-2 days.

Please note shipping delays may still occur.  It could take ~an extra week in some cases.