Looks like a .38 M&P first model of 1899, from the lack of locking lug. Manufactured sometime around the turn of the century. One of the first “Hand Ejector” models S&W made, a nice heirloom if you ask me.
Welcome to the forums from the Wiregrass! Your heirloom is S&W's first .38 Special hand ejector created to shoot the new .38 S&W Special cartridge (CTG). It was known as the .38 Military & Police revolver, Model 1899. Your gun was likely manufactured in 1900. They only made the Model 1899 for 4 years from 1899 to 1902. It appears to be complete and may be all original.