Help identifiyng an Omega pocket watch from the 1900's.

Dear Forum community,

I come before you seeking help with the identification of an Omega pocket watch that belonged to my great grand-father.
My mother recently handed me this watch which was in a drawer for more than three decades. This watch was supposedly bought in Italy in the beggining of the century and ended in Brazil where it remained until now.
I have opened it to inspect the different pieces and found that the balance spring is broken. In order to be able to eventually find a replacement for the spring, I think it would be nice to (at least try) to identify it correctly.
Here you have some photos and some informations concerning the case and the mouvement:

- case number 3915095
- caliber number 2971795

Any help would be much appreciated.
Thank you in advance.

Rebutini

Dear all,

First of all thank you very much for the advices.

Indeed, the dial is in pretty bad shape. Nevertheless I was not planning on restoring it, I would like to enjoy it just like my great-grandfather left it. The only thing I am planning to do is to have it working again.
All the other pieces (of the movement), except for the hands (missing) and the broken hairspring, are present and in good condition. I have disassembled the watch, cleaned it and checked all the pieces under a microscope. After assembling it, and after giving it a little winding, the pallet fork shows clear signs that there is tensions. So, the only thing missing is a functionning balance wheel.
That is why I would like to find (if possible) the exact model to maybe try and find a donor movement before an eventual and very difficult endeavour (maybe impossible) of repairing the balance wheel and hairspring.

Any (more) help would be very much appreciated.
Thank you!

It might be easier to measure the diameter of the mechanism and find a replacement on ebay of the same diameter.
May be https://ranfft.org/caliber/8370-Omega-19LB