This watch is rather special and distinctive for a number of reasons: it's very early for a (man's) wristwatch - the hallmark in the case (London / "P") dates it to 1910/11. It wasn't made for military use as the numbers are not coated with the radioactive lume to allow it to be seen in the dark.
The crown and seconds layout is rather unconventional (again because it's early for a wristwatch the convention for putting the crown on the right hasn't been established yet). It's from a precurser to the Heuer company: "Rose Watch Co" was a trading name they used for a few years in the early part of the 20th century.
Finally it's in pretty much unworn condition - it's doubtful that it was every retailed at the time that it was made (possibly it started to look dated after a few years: men's watches were generally around 33mm diameter in the 1910s / 1920s and this is rather oversized at 40mm). It's in perfect working order as you can see in the video below.
Even as a chronograph (chronograph means it works as a stopwatch as well as displaying the time) it's rather unusual having no way of recording elapsed minutes, meaning that it's a stopwatch designed to time events lasting under sixty seconds.
I brought this at auction with only minimal information: it was sold through Fellows in Birmingham and they don't include pictures of the movement, nor do they date the watches from the hallmarks (although they mentioned that it was hallmarked). I thought at the very least it was an interesting and unusual transitional watch in the shift from pocket to wrist timepieces. It wasn't especially expensive, at around £200, but I think I got a bargain!
I did a little research online and found some more examples of Rose Watch Co watches (and also learnt of the link to Heuer). The watches that I have found online are all called "Pulseographe" which was a trade name for the chronographs designed . The Pulsographe has a scale around the edge of the dial to allow the calculation of heart rate from the time taken to count twenty heartbeats (so no requirement for tracking elapsed minutes on the chronograph).
An ebay pulsographe next to my 1910 Chronograph (auction photo from Fellows)
another Pulsograph movement found online
I've not cleaned the watch (nor do I plan to!), basically I can only make it worse - it's in full running order as it left the factory and I certainly don't plan to spend a lot of time wearing it. The movement is beautifully finished - nice mix of grained and highly polished parts.