The reality is that gold jewelry is not "withdrawn" from the system but is part of it, just as much as that double eagle.
As inflation increases and savings shrink because the dollars that comprise savings lose value, jewelry begins to be converted back into bullion. Jewelry, especially gold and diamonds are subconsciously, sometimes explicitly, bought in part as a store of wealth.
Such processes are not as smooth and appropriate as theory indicates and has high transaction costs which limit their effectiveness. Classical economics had a consistent and exhaustive theory that predicted events but turned out not to do so.
But their is no way I would agree to linking the United States money supply to the decisions of gold speculators, third world political vagaries, financial decisions of other governments or the desire of Rap stars, Chinese and Indians for blinge.