What is “knocking their rings on tables” supposed to mean?
Naval Academy grads are famous for proudly wearing their class rings at all times.
Ring Knocking is either an attention getting technique or a nervous habit (maybe both).
If used as an attention getting technique; during a meeting turn the class ring over so the jewel is on the palm side and knock it against the table like a gavel.
If a nervous habit simply tapping or knocking the ring against the table rhythmically.
In the service, all officers in the same grade are equal, but academy (West Point, Annapolis) grads are a little more equal than everyone else. As stated, during a meeting, the ring knockers will sound off to remind the other of this fact.