2690 31 marked on the balance

Both our S380-27 and S385-27 channel balances look very similar to your balances. The only difference between these two balances is the depth measurement of the bottom shoe. For the Series 380, the depth measurement is 1" and for the Series 385 is 1-3/32". Measure the depth of your bottom shoe, like in the diagram below, to determine which balance will make the best match. Since your stamping does not match up with any of ours, you will need to weigh your sash and refer to the sash weight chart located on the store pages of the balances. 

Alternate view of 15-004

If it less than an inch, could you get back to us with the exact measurement you're getting? 

Yea they would still work. You would just have to shave down the bottom shoe a little, not much.