The Harrington & Richardsons of the era yours was made were respectable little critters that didn't get near enough love
.
Note the pinned barrel like an early S&W, and the Rugeresque lack of side plates. Primary lockup is at the crane in a semi-Dan-Wessonish manner, but different
. This gun and the Charter Undercover were great designs backed by small companies that didn't survive rough times. Quality control on H&Rs was more even than Charter's, which went up and down like a yoyo. (Mine is excellent, others were ghastly.)
I've seen them in 38Spl and 22, but not in 32S&W - that's an oddball. It can probably take 32S&WLong. Unfortunately, defensive ammo for that isn't going to be available, you'd have to handload 60gr JHPs meant for 32ACP in 32S&WLong cases.
Huh.
You know...
If we knew the Rockwell numbers for the 38 variant and then tested your cylinder, we might find that the heat-treat is the same. Your gun pre-dates the 32Magnum being popular, I think. I wonder if it's safe to ream that cylinder a tad deeper?
After all, the 32Mag is technically the 32H&RMag, the only caliber that company designed I think?