The features that made these guns so desirable were the grade of wood and the wide "Knick" rib.
Add in the fact that the gun above is a very early in production pre-war gun, makes it qualify as a "Grail" gun.
The T's and S's shared the rib style with Knick single barrel trap gun. These guns were made by people that were craftsmen. Due to labor cost these guns today, would be prohibitively expensive. The ribs were all soldered on by hand and the barrels are not "Hot Blued". The same with the solid rib guns, soft soldered on. Cannot be hot blued or the rib will come off.
Here is a high condition 16ga 37S. (he might be priced a bit high, it has been out there a while, just an example to share what an "S" looks like)
If you click on the photos, they will open in another window and then if you keep clicking, it will walk you through all the photos like a slide show.
http://www.gunsinternational.com/Ithaca-37-S-rare-16-gauge-Skeet-grade.cfm?gun_id=100194663
These below are the Knick SBT (short for Knickerbocker) (none of these are mine, just examples showing what I mean).
http://www.gunsinternational.com/It...-Shot-12ga-Knickerbocker.cfm?gun_id=100522708
http://www.gunsinternational.com/It...p-12-Gauge-2-3-4-Chamber.cfm?gun_id=100399552
http://www.gunsinternational.com/ITHACA-SINGLE-BARREL-TRAP-4E-KNICK-.cfm?gun_id=100423867
Back in the day that these guns came from, Ithaca, Remington, Winchester et al, built works of art, examples of the gun making craft that could hold their own with the guns made in Europe.
Notice the screw heads on the Knicks. As they came from the factory, the slots were all "timed" to run with the axis of the gun. You can tell if one has been taken apart as most folks simply don't take the time to learn how to retime a screw.