Hello. Welcome to the forum. That looks like a .38 Military & Police (M&P) Model of 1905 - fourth change.
I would guess the revolver has been refinished based upon the trigger and hammer being nickel plated as that is not the original finish for the trigger and hammer. The grips are not original. None the less it is an attractive piece. Congratulations.
Here's what the SCSW (Standard Catalog of Smith and Wesson) says:
.38 Special Hand Ejector M&P
1915-1942 241704-700000
Extrapolating I would venture a guess that your revolver dates to the 1920's or early 1930's?
What you have is a Model 1905 4th Change .38 Hand Ejector known as the Military and Police or M&P. It was manufactured probably late 1920 to early 1921. It has been re-finished, which explains the condition of the finish. It does look to be an excellent job though. The Mother-of-Pearl stocks are probably after-market and not of S&W manufacture. Very pretty!
Concur on the 1920-21 dating. I list one with a slightly higher serial number which shipped in January 1921. From the picture, it appears the trigger and hammer are also plated. S&W didn't do that, a pretty good indication of a non-factory plating job. Also, it looks too good.