The pictures help, as do the patent dates on top of the barrel.
You have a
Smith & Wesson Military & Police revolver, also known as the .
38 Hand Ejector, Model of 1905, 4th change.
These were a mainstay bread & butter model in Smith & Wesson's product line, and remains the most popular production revolver ever made. Your Great-Grandma's gun was made during the middle 1920's.
Specifications: .38 Special (Standard loads only), 6-shot, 4" barrel. Apparently the original checkered walnut stocks were replaced with aftermarket mother-of-pearl ones. Nickel plate was a standard factory option.
I you want more detailed information, Smith & Wesson will for a $50.00 research fee, go back through their old hand-written records and find out whatever was recorded on serial number 441523. Usually this will include the finish, barrel length, type of stocks, and the exact date it was shipped from the factory, and to what distributor or dealer. All of this will be sent to you in an official letter from the company.
To learn more, and the process and requirements to obtain an "historical letter," go to:
www.smith-wesson.com