Grainger2,
The 16 means it is 16 ga.,the 16 in a circle means it has the standard 16ga. chamber, which is 65 mm (2 1/2-2 9/16") instead of the current American depth of 70mm (2 3/4"). The crown S means it was proofed for shot, the crown W means the barrel is choked, but doesn't indicate the amount of constriction. The crown U under the two Imperial eagles shows it was View proofed after withstanding the Definitive proof. The view proof is basically a detailed inspection after the proof including verification of dimensions. The 62,78 is the bore (not groove or bullet) diameter, expressed in gauge measurement. This would translate to 10,67mm. The Germans used a , where we would use a . in numbers. The crown G means it was proofed to fire a single projectile (bullet). The crown U under two Imperial eagles has the same meaning as on the shotgun barrel. Whether the cartridge for the rifle barrel is 10,75x70 Collath or not depends on a detailed comparison of a chamber cast with dimensions of the cartridge. It must be taken into account that the chamber must be larger than the cartridge to allow chambering. Chamber diameters are commonly .005" larger, but in older rifles are sometimes as much as .015" larger. Black powder rifles commonly have groove diameters larger than actual bullet diameter and sometimes the bore diameter is larger. Obturation of the lead bullet by the black powder was depended on to fit it to the barrel. Personally, I usually use "nitro for black" loads in my old rifles and nitro powder will not always reliably obturate the bullets, especially if cast of a harder alloy. This sometimes requires using special procedures to use bullets otherwise too large to chamber.
The gun was made between early 1893, when the 1891 proof law came into effect and 1912 when the bore diameters started being marked in millimeters in accordance with the 1911 improvements to the 1891 law. Hemmerling in Magdeburg would not likely be the owner, but more likely the marketer of the gun. It was, and still is common for local gunsmiths to guy the guns from manufacturers in various stages of completion and finish them before selling them. These were made "for the trade" and sometimes incorrectly called Guild guns if bought complete from the manufacturer and not marked by the marketer. Horn was commonly used to cover forearms, such as yours, but it could be something else. If you heat a pin until it changes color and touch it to a hidden place on the material, it will smell like burning hair if a natural organic material such as horn or less commonly bone.
I hope this helps.
Mike