You have a Smith & Wesson .22 Single Shot, Third Model. These were made from about 1909 to 1923, when the model was retired. About 7,000 of this model were produced. They resemble the earlier second model but the parts are not interchangeable.

That is a custom wood grip on your gun; I have never seen one exactly like it. If you take it off, you may find a maker's ID inside, or some feature that will help you identify it further. You should also find the gun's serial number stamped on the butt of the gun. I presume 7918 is the frame number as well as the latch number, because at a certain point in the manufacturing process the gun's frame number was used on other parts to keep them together after they had gone through the fitting process but before they were blued.

Those are in-demand guns in collectors' eyes. Congratulations on having it in the family.

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David Wilson