As promised, I found my Hepburn photos and "internet-sized them". They are kind of lousy photos (see a pattern here?) and it looks much better in person.This is one of the very rare Hepburn models and was only made during the E. Remington & Sons period and then in a most limited way. I show one example, serial number 223, that must have been made well before 1885 and may have been the first one produced. The barrel on this rifle is fully round: later examples are round with a flat section on both sides, just in front of the breech. The catalog listed the barrel length as 32", but all that I have seen are 34". All that I have discovered, I believe, are chambered for the .44-2 6/10" but as the barrel marking is covered by the stock, and the mark is difficult to access, this may be incorrect. The catalog states that there is a special form of rifling. I have not noticed a difference from the found in Creedmoor rifles.
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This rifle was designed as an American version of the British Military Creedmoor. The MBL (Military Breech Loader) was a rifle style that saw considerable success in England for military style matches. The British rules stated that the trigger pull had to be 6 pounds, be fitted with military sights, and cound not weigh over 10 pounds. the rifle had to be fired without cleaning between shots.
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It was used in some International competitions which were reported in Shooting & Fishing and undoubtedly in other places. This was a sport with very limited participation for the general run of target shooters.
As far as the rifling goes I count 6 lands/grooves.
I don't remember seeing those markings under the barrel but will pull the stock and check again. I'll let you know what I find.
The more intriguing markings are on the side of the barrel where it is stamped, "L N Walker", who I believe was the head gunsmith at Remington at this time. I don't know if all of them are stamped with his name or if this was his personal gun.
Here is a link that contains these pics as well as other misc. detailed pics:
http://www.arcaneiron.com/firearms/remington/hepburn/
Well, that's about all I know about this rifle, and maybe a little more.
Best regards,
-Ron