Yes, it is a "J" frame, and older one. Al. frame, the original "light weight". These are usually not recommended for +P ammo, although they take occasional use (lets call it "bussiness" use). Had one for a couple of decades, no problem.
I have a 37-2 Airweight. This is a model sold briefly a few years back. Rumor was, they were overruns on a foreign order, or perhaps the result of a contract cancellation. They are the only guns ever issued by S&W, so far, with a hammer bobbed at the factory, and they have no lock. If, by chance, yours is one of these, S&W confirmed for me that these were +P rated, same as all there more recent production.
Now, if the one you're lookung at is an older Model 37, S&W will not say it is +P rated. Some have fired many, many rounds of +P ammo through them without apparent harm, but if I had an older one I believe I would stick to using standard pressure ammo about 90% of the time. This actually makes the gun comfortable to shoot, and there are some very effective standard-presssure self-defense loads on the market; frankly, you don't lose a whole lot by dropping down from +P to standard ammo.
They are wonderful, lightweight, reliable little guns, and very nice for carry.
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