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looking at a 1948ish catalog it may be 4809. it wants a 17mm band. When I asked for one for my similar 1948 Tudor at the jewelers the lady insisted there was no such thing... she actually ended up yelling at me when I said I had both 17 and 19mm bands for watches.
My Tudor has an FHF30 movement marked caliber 59. Most sources list this movement as a Tudor movement, but some insist it was also in some Canadian market Rolex stuff through the WW2 period.
Tisk tisk to her
Could be a 4444 from around 1958
Here's mine
There are quite a few 59 calibre watches in circulation, so routine service should not be a major issue if the main parts are in decent condition. If this is not known, I would be wary. The price seems a bit high, as one that is in good shape with a serviced movement would be in the $1000-1500 range. The dial on the watch you are looking at seems pretty good but I suspect the hands may have been swapped at some point. The the shape looks a little odd for the style and both the second and minute hands, go slightly past the second track. Compare the one you are looking at to the photo of Smurfdivers. A generic replacement crystal can probably be sourced in the vintage NOS or aftermarket parts supplies.
Here is a link to a Solar Aqua on Derek Diers website for comparison, although neither is the same model you are looking at. The 30-31mm is often called boys size, so unless you have tried one one, people are often disappointed with these cases. I had a Solar brand watch fron the 1950's that I gave my daugher and she loves it. If I had kept it, I would have it on a bundt strap, which wears a tad bigger.
https://watchestobuy.com/shop/solar-aqua-watch/
Great to know! Yeah I passed on this one. I know what you mean about smaller watches. But I am starting to get used to and prefer them. I can get down to 33-34mm comfortably but I did buy a 50s Oris military it's like 31ish. Still taking some getting used too but I am suprised at how quickly I warmed up to the smaller sizes.

I don't own a Patek because I would want one that was at least 35mm, and I don't want to make the necessary investment to buy a good one of that size. But at the 31mm-32mm size, they are a relative bargain, and it would be cool to have a Patek. 馃槈