Nice find, eastbank; if you've not played around with a .32-20 before, I think you'll find it an interesting caliber...and that Smith, the ideal way to begin. You might give Ken Water's "Pet Loads" book a look-see; he had many good things to say about his Smith, and some tricks for getting it to perk with handloads....I've got what I think is a H-E 4th change...Mike, what do you think? Serial 1346xx, produced in 1938? I missed the matching gun in .32 Long for lack of funds...both were in 'as new' condition, back in '97.
It's a good piece and really hums with Lyman's #311008, sized .312" and pushed along by 4.0 to 4.4 gr of Win 231. From a good sitting rest at 25 yds, it'll group 5 shots in 1.2 to 1.5", and right to the sights as well!!!
.32-20 is a good caliber, a bit finicky to load for (the neck brass is thin on R-P and Win but better with Starline when you can find it). And damned if you don't look like Indiana Jones confronting that whirling dervish in the casbah scene when toting it in a good, period correct holster. It's a nice woods loafing combination when paired with a good Winchester M-92 rifle or carbine, and you've taken the time to match up the loads for good performance in each.
Pic below. Good shootin', I predict you'll like it. Best Regards, Rodfac