What plan does Polonius concoct to prove that Hamlet is mad for love at Ophelia?

Polonius tells the king and queen, in a very roundabout way, that he has discovered Hamlet’s foiled love of Ophelia, and that he believes this lost love to be the root cause of Hamlet’s madness. Claudius asks how they might prove this to be the case. Polonius has a plan. He offers to loose Ophelia on Hamlet while he is reading alone in the library. Meanwhile, he suggests, he and Claudius could hide behind a tapestry and observe the meeting. Claudius agrees.