Drifter, in adding to Sam's observation:
Your rifle started it's life as a #1 Musket, full length stock, 3 bands with a 35.25" barrel. Stock cut down to look like a 'sporting' rifle with only one band left on the wood
Your sight looks to be the 500yd sight, not the M1879 1400m sight.
You might want to look on the metal, including the patent date for any additional stamped marks. On the wood, any cartouches or a rack number. This can tell the model year and the country/contract the rifle was produced for. Forget about the numbers on the upper and lower tang, they are just Remington batch numbers for the receivers. And the 'P' on the barrel just means it was inspected at the the Remington factory
Here's a couple of recipes you might want to try:
With the military sights and many sighter adjustments, this load produced at 1000yds
* Starline 50-70 Brass, annealed
* Lee 515-450F, 1:20, (actual weight 457gr) 40:40:20 mix of mutton tallow-paraffin-beeswax
* Resized 511 using Lee bottom push lube/sizer. Rifle groove is 507
* CCI BR2 Primer
* 70gr Swiss FFg
* 0.075 Hard unlubed Felt Wad
* 1263 AV with a 13.8 SD
Haven't shot this one yet, so no fps or SD ...
* Lee 515-500-F ... resized to 0.510, 1:20, homemade lube - BC 0.283
* Starline Brass
* Remington 9.5 LR Primers
* 70grs DuPont Fg (vintage pre 70's) or any vendor's Fg powder
* 0.030 Fiber Wad
* 0.040 Mutton Tallow Lubed Felt Wad
Seated out to 3rd GG band