If anyone has a copy of "American Cartridges and Their Handguns" by Charles Suydam refer to pp. 192-3 for the.41 Smith & Wesson cartridge. Very little is known about it and at the time the book was written (Original (C) 1977) only two revolvers chambered for this cartridge were known to exist. These were a NM#3 Single Action and NM#3 Double Action. This may be a 3rd example. All the visual queues are there for an experimental revolver between the late 1880s and ca. 1896, before the first Hand Ejector was introduced, before they had decided on all future revolvers being double-action. Had this been built after the M&P, is there any doubt it would have looked just like the 1899 and been double-action? Definitely a candidate for a letter from Roy, there has to be something about it in the archives.
Reportedly an experimental cartridge sometime around the turn of the century. Per dimensions in Suydam the case is the came diameter as the .41 LC, slightly larger rim and length in-between the heel-based and inside lubricated variations of the .41 LC. The .41 S&W was one of several experimental cartridges S&W worked on between 1890-1910. Possibly the .38 Special was one too, and the only one to see production! Or, maybe, the .44 Special also.
And, yes, S&W did build pistols with no serial number. Tool room models and guns intended strictly for in-house testing that were never intended to see the light of day outside the factory fall in this group. I have seen one in 1974, a Model 39 used for test-firing spare magazines. When magazines needed to be shipped and there were no M-39s in production they shot every magazine through this gun. How is that for QC, test-firing magazines! Betcha you didn't know that!