This is an interesting early watch, dating to 1910. This style of watch, with a smaller glass cover is called a half hunter. It's worth explaining a bit where this name comes from: huntsmen (i.e. men on horseback in pursuit of a fox) and their requirements for a watch: early pocket watches were open faced - so they had a glass face that was easily cracked in the melee of a fox hunt. A Hunter pocket watch had a sold cover over the face, depressing a button on the winding crown would cause the cover to pop open so you could check the time (this could be done one handed by the huntsman). A variation of this was introduced which had a smaller glass face in the centre of the protective cover, so you could see the time without opening the cover.
Ok, so this is a half-hunter wristwatch. It dates from 1910, so pretty early for a watch and doesn't have the luminous hands and numerals that would imply it was for military use. The dial is marked Sir John Bennet Ltd who was a London retailer. Sir John Bennett was the first London 'watchmaker' to begin importing Swiss watches. then casing and signing them in London. The dial is nice because it's clearly the original - made to work with the half-hunter case. The hands look to be original as well because they are the correct size for the opening on the face.
The movement is marked S&Co for Stauffer & Co who were the importers of IWC watches at this time (although this isn't an IWC movement). This tallies with the hallmark on the case back: C.N was Charles Nicolet, a partner and later director of Stauffer & Co. The movement is nicely finished and responded to cleaning very well. I'm not sure how many times the watch has been serviced - it was in pretty tidy order and there aren't any repairer's marks on the inside of the caseback.
The watch is pinset, meaning that you need to push in the little pin above the winder and then turn the crown in order to set the time. The combined hand setting and winding system (that was invented by Patek Philippe in 1845) had not found universal acceptance at this time (or maybe the watch was made down to a price). The importance / desire to make watch cases water tight received considerable impetus in the first world war and naturally there was a move to reduce to a minimum the number of openings in the case. The winding crown may very well be original as well (it's basically a pocket watch crown), it certainly looks right with the case.
The watch once back together isn't running very strongly and has a tendency to stop, looking again at the jewels I think there may be a crack to one of the pallet jewels. Anyway it will go to RE for expert diagnosis.