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You have a .38 Military & Police model from
about 1916. The B on the barrel flat simply means it left the factory with a blue finish. The B is not part of the serial number, which is why it does not appear on the butt.
The stocks appear to be original. The serial number would have been written on the inside of the right panel with a pencil. It may no longer be legible, but it might show up if you shine a bright flashlight on it at an oblique angle.
Nice older revolver.
Added: Jeff got in just before me! Quickdraw Jeff.
