Howdy
Definitely a Third Model Russian. The large head knurled screw on the top strap is indicative of the Third Model. Also, the front sight will be forged from the same piece of metal as the barrel. The 2nd Model Russian did not have the large knurled screw on top, just a small screw with a regular style head. Front sight on the 2nd Model was a separate piece, pinned to the barrel. Standard barrel length for the 3rd Model was 6 1/2", standard barrel length for the 3rd Model was 7". The proportions of the large lug under the barrel (ejector housing) are different with the two models too. The 2nd Model had a longer ejector housing than the 3rd Model.
Here is a photo of my 2nd Model for comparison.
According to Supica and Nahas, the 3rd Model Russian was only produced from 1874 to 1878. Most were chambered for the 44 Russian round, a few were chambered for the 44 Henry Rimfire round. The rimfire version will have a different type of hammer, so the rim of the cartridge can be struck.
Russian contract numbers can be difficult to track down because it is believed that each contract started over again with the number 1.