Assuming 2nd model, I just cant find the serial number

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Im assuming this is a 2nd model 6 shot E. Remingtons Ilian N.Y W.S. Smooth Oct. 21 1873 on top of barrel. Im selling off my father's rather large Rifle, ammo,and pistol collection dating mid 1800's up to pre 64, mostly Winchester's and remington but other rifles also and some older pistols. Im just having trouble finding the serial number. I thought it would be in the same place as the 1872 #306 was on the Colt house Cloverfield pistol but cant find a number. Im assuming this is a 2nd generation