Please let me know if you need any other information. Thank you!
Hello! I do recognize this spring system, yes. This is a very, very old type of balance that hasn't been made for the better part of the last century. The good news is that we have a more modern equivalent that should work just as well with minor alterations. See our Series 500 spiral balance. This can install in the track at the top with a screw, and then mount to the bottom of the sash using our 17-012 bracket (non-refundable).
Your next step is to determine size. First, measure the space available to confirm that you can fit a 9/16" diameter tube where it needs to go. Next, to determine length, measure the height of the visible glass and add 3" for the bottom sash and only 1" if it's the top sash. For example if the visible glass on your bottom sash is 20", you want a 23" long balance; if the top sash visible glass is also 20", you only want 21".
Lastly, to determine the proper spring calibration, you will need to weigh your sash on a scale. We have a chart on every Series 500 store page that tells how much weight each option supports, so all you have to do is pick accordingly.