Looks like a 38 Safety, 2nd Model, but you did not supply a serial number? The S&W logo did not appear on any models made prior to 1896, except for the hard rubber stocks that started around 1879. The 2nd Model ran from 1887 to 1890. You may or may not have caliber stamping on the barrel as that was another later era stamping on these guns.

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Gary
SWCA 2515