Aqualung, that serial number puts your grandfather's gun somewhere around 1907-1908.
If a gun seems loose, one of the things that can be of benefit is a good cleaning. You may have some grime stuck in the housing for the front locking lug that keeps the plunger there from completely engaging the end of the ejector rod. Drizzle some penetrating oil in there and let it sit, then blow it out with canned or compressed air. Repeat a couple of times until oil comes out clean. Do the same thing to the lockwork with the grips removed. If you are comfortable taking the action out of the gun completely, that's the best way to clean it up internally. But if you don't want to do that, just soak down the action, let it sit, blow it out, and repeat a couple of times.
Also run some oil down the shaft through the cylinder from both ends.