Deltaspecialforce:
You have a .38 Military & Police Model of 1905 4th Change, manufactured 1919/1920.
Heat treatment of cylinders began in September 1919 at serial number 316648, serial number 358xxx shipped in December 1920. so late 1919 seems likely.
It is the predecessor to the Model 10, but most parts will not interchange.
The change in color of the cylinder bluing is referred to as going 'plum'.
Various reasons have been given on gun forums, including poor bluing salts, poor temperature control on the bluing bath and too much nickel in the steel.
The grips are not original, they are post war Magna grips.
The gun predates the positive internal hammer block introduced after a fatality with a dropped gun in WWII. Treat it as a five shooter, leaving the chamber under the hammer empty.