Robert M. Reilly, American Socket Bayonets and Scabbards; "Based on the extreme variations in the bore diameters on extant specimens, it appears that this firm endeavored to provide a bayonet for many of the different firearms of the period.  Their time of manufacture is not precisely known, but was probably between 1850 and 1860.  Indeed, daguerrotypes exist showing Horstmann bayonets affixed to Model 1841 rifles in the hands of Union soldiers.  They have not only been fitted to these Mississippi rifles, but are known to perfectly fit Model 1842 muskets as well.  Other firearms were unquestionably involved."

Were these pictured weapons just props for the soldier to hold while taking the picture or were they actually issued and used during the Civil War?  It seems that no one truly knows for certain but clearly some variations of this bayonet does fit the US Model 1841 "Mississippi" Rifle.  Reilly was also certain that some fit the Model 1842 musket as well.

If these bayonets were also made for the Turner Society then they could have been made for any pre-war civilian militia carrying all sorts of rifles, including custom made rifles.  Pre-existing examples made to fit unknown rifles may have been modified to fit the Model 1841 rifle or Model 1842 Musket.     

Hopefully, as additional information is recorded, the answers we seek will become clearer to understand.  For now, it is still uncertain as to which rifle(s) these bayonets were originally made.