coil spring and pivot shoe for a reynold double hung window

Hi there!

Thanks for reaching out to us. This looks like a spiral balance for a tilt window. I recommend the 3/8" Series 900 or 9/16" Series 600 depending on the tube diameter. 

We're happy to help with the pivot shoe but I'm afraid it's too damaged. Can you show us photos of an intact version along with the written-out thickness and width?