If you look at the link of the pocketwatch database for the serial number and you go to the parts list you can go to Springs and I snipped out an image. So we have an Elgin part number and a strength as an added bonus you click on the part number and you get this link
Fortunately it looks like that particular hairspring goes in a lot of different watches. That's the good news the bad news is we still have to find one and you're going to have to play with the screws to bring it in to time. When I get a chance I'll go look at my Elgin parts catalog and see what it says about the hairspring if there's any other additional information.
Then that is assuming that it just needs a hairspring and that it doesn't have a broken balance staff more than likely it's going to need a main spraying and if you're lucky that's all that's going to be wrong with. I don't like when parts are missing like any parts it suggests other things could be missing were not even right. As one of the cautions of buying off of eBay it might look nice and pretty in the picture but in real life that doesn't always agree with the pictures. On the other hand the watch that I bought that wasn't quite what should be scrapped for parts because I really needed one of the parts off the watch so it worked out at the end.
Dr ranfft shows 18 size HS to have come both in flat and berguet.
Will you show a side view close up of the balance?
I suppose you can go by serial No as well to find out the hairspring type.
Building the complete balance on these is challanging.
In case anyone is having trouble curing their UV cure products, check the UV curing light. Most nail curing lights are using UVA leds with a wavelength of 365 to 405nm. These tend to have a low output and some manufacturers apply higher currents than recommended to increase output. This unfortunately will shorten the lifespan of the LED. The bad news is it will still lights up but the useful UVA part of the spectrum is gone. Hence your varnish or glue won't cure properly.
Another problem is using a dental curing light for curing UV gels. Our dental curing lights are actually using blue light with a wavelength of 450nm. There is absolutely no no UVA. It is designed to be safer for eyes.
Hope this info helps.
Yes that is a problem but unlike when I try to point out that swapping hairsprings is a bad idea and it typically falls on deaf ears on this group this is an American pocket watch. Providing nothing else is wrong and if the hairspring truly is missing it's not like it fell out all by itself which then makes other things suspicious that they could be bad. But providing it's the only thing that's gone missing in this watch it can be replaced. American pocket watches were some of a few watches that hairsprings are available as a separate component. Although finding one and the associated timing screws to bring it in to time will be an interesting challenge but not impossible.
Then it's a shame it wasn't a 16 size? 16 size is a much better watch to start playing with 18 size has some interesting challenges but still a watch somebody can still taken apart with caution and before the original poster does so I will explain some cautions before taking it apart to avoid unpleasant surprises and damage.