Remington 30S Rifle from early 1030s
The scope is a Zeiss Zielvier 4x. There are holes that I'm confident were drilled by the gunsmith for these mounts but there are two holes in the side of the bridge, near the cut-out portions of the stock that were for a receiver sight. Some of the models came from the factory with receiver sights so it is quite possible that these holes were done at the factory. The stock of the 30S is straighter and has less drop than the 30 but otherwise they are interchangeable. this rifle happens to be a 257 Roberts and while it is way over built for such a light cartridge, it is very pleasant to shoot.