I presume there is no letter on the bottom of the butt...
In that case you have a Smith & Wesson .38 1905 Hand Ejector (Military & Police Model) 3rd Chg. These were made between 1909 and 1915, within a serial number range going from 146,900 to 241,703. Your revolver would probable date from around 1913. It would have been originally chambered in .38 Special, not .38 S&W. Given its age, only shoot standad .38 Special cartridges, not those marked a Plus-P. Also as it doesn't have an independent hammer block, carry the hammer down on an empty chamber. Probably not necessary, but it's best to be careful. Someone in the past cut back a longer barrel and replaced the front sight with one with the one it has now. The stocks are also aftermarket replacements.
Given this gun's history within your family, I suggest that you get it "lettered." To do so you will need a snapshot of the gun, a full description including the serial number on the butt, and a check in the amount of $30.00 made out to Smith & Wesson. In exchange the company's historian, Roy G. Jinks, will research the original records (which are not computerized by the way) and send you a letter containing the details of what he finds.
This comprehensive document will contain an overview of the model’s history, followed by the details of your particular gun. This usually includes the caliber, barrel length, finish, and the exact date it was shipped from the factory, and to what distributor or dealer. If there are any special features they will be listed too. This information is often invaluable to both you and future generations.
Additional information on a historical letter will be found at the Smith & Wesson company website at:
www.smith-wesson.com