Thanks for reaching out! Your balances appear to be the discontinued crossbow style balance. The good news is that they can potentially be converted to our Series 795 Channel Balances.
To confirm that they will be a situatable replacement, you'll need to obtain a few measurements from your existing balances in addition to the length of the balances. You'll need to double check the diameter of the balance spring/channel. This measurement should be 1/2"; but let me know if it is 3/8" as this will need to be a custom assembly. Please also confirm the width of the bottom T-shaped attachment (it will either be 1" or 1-1/4" across the bottom of the T shape) as well as the exact weight of each window. We'll need this to select the correct stamp option.
Take a look at the video below for instructions on this balance conversion and the information you'll need to determine the correct balances. Let me know if you have any questions.
Yes, you are correct, we can use the height of the glass to attempt to determine the length of the balance. Although, I cannot make any guarantees.
With that said, based on the dimensions for the height of the visible glass and the sash weight, we believe the 31-1/8" sash weighing 18.3 lbs. will use S795-34 with a 34B stamp for a sash weighing between 16-22 lbs.
For the 29-1/8" sash weighing 16.7 lbs., you can use the S795-32 with a 32B stamp for a sash weighing between 14-20 lbs.
Since your has a 1" T shape, you'll need the 15-194 T-Lock Balance shoe. Our balances come equipped with a 1-1/4" shoe but you'll be able to swap them out. Take a look at the video below for reference.