If your gun is a .38 special (it would say so on the barrel), it's a Hand Ejector M&P, 4th change, probably from the period 1915-20. I have a late 20s version of the same, I just found some hard black rubber grips for it on Gunbroker. In addition to rubber, they also came from the factory with walnut grips according to the Standard Catalog of S&W.
Note that the cylinder on your gun is NOT heat treated, that didn't start until serial #316648.
My guns include S&W and Colt revolvers, Colt and Ruger pistols, Remington 870 shotgun, Henry and Marlin .22LR rifles, Hi-Point 9mm carbine and Lancaster Arms AK. I reload handgun rounds with a Lee hand press, over 18K rounds since Nov. 2009 with nary a squib nor kaboom.