It sounds like a Model 1902 AKA the 2nd Model M&P. It should have a round butt and be stamped on the left side of the barrel "38 S&W SPecial and U.S. Service CTG". There should be a locking lug under the barrel for the ejector rod and the knurled end should look like a mushroom. These revolvers were made in 1902 and 1903.

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Guy
SWHF #474 SWCA LM#2629