This is a Remington -Hepburn #3 Match B

Selected Walnut Checkered stocks , cheekpiece and hooked butt , Mid-range Soule vernier tang sight , and windgage front sight with spirit level ,  that takes interchangable aperture inserts , half round 30 ” barrel all were standard with the Match B , but the D.S.T was an option .

  This Model was the midrange offhand Schuetzen.($60) It was also offered in more affordable versions such as Match A,($45) and the standard sporting rifle,($25) but also as the long range Creedmoor with 36″ bbl with long range sights sometimes mounted back on the stock near butt for the lying back position for 1000 yards (Hepburns competition choice)

This one was origininally made in 32-40 in 1897,  But sent back later to factory for re-bore to 38-55

Nice accurate old target Rifle, but not a real threat to the 1885 right Bert? 

However interesting history. Designed by famous long range target shooter Louis L. Hepburn as an improvement on the Remington Rolling Blocks , for his Creedmoor competion shooting. Introduced in 1880 so pre-dating the Win 1885 and produced till 1905