Just to add to this ...

Guns that are truly "factory engraved" are fairly scarce, but it's worth defining this term more specifically since there's some grey area here.

It's possible to have two identical Smith & Wesson guns, both with correct period engraving from a notable like Gustav Young or Louis Nimschke. The only difference would be that one gun would have had the engraving commissioned by the factory before it was shipped to the wholesaler, and the other would have had the same engraving commissioned by the wholesaler (or by the retail establishment, or by the end consumer). To the customer buying the guns they would appear to be identical (and they indeed would be), but only one will show up in the books as "factory engraved."

As others have said, it's impossible to ascertain whether a gun was "factory engraved" without a historical letter.

But -- if the gun isn't factory engraved, it doesn't mean that it wasn't engraved by one of the notable engravers of the time. And that's a much more difficult thing to ascertain, since many of these guns weren't signed and it means that someone really knowledgeable about this stuff (I can think of maybe a half-dozen people in the world) who would have to really study the gun to develop an opinion.

And with that said, welcome to the murky waters of engraved guns. :-)

... and I agree with the consensus that these guns are all engraved in the New York style, but only the third shows anything resembling the level of detail that I'd expect to see from one of the notable New York engravers. I'd need to put the gun under my stereoscope to develop any more accurate opinion than "maybe."

Mike