How does Hamlet try to appeal to his mother in Scene III?

At first, Hamlet appeals to his mother through anger against her marriage to Claudius. He holds up to pictures, one of his father and the other of his uncle. He accuses his mother of letting her passion overcome her reason. Gertrude sees her guilt and begs Hamlet to stop, but he continues berating her. He accuses her of incest with “A murderer and a villain, / A slave that is not twentieth part the tithe / Of your precedent lord, a vice of kings, / A cutpurse of the empire and the rule, . . . ” He probably would have gone on chastising his mother except the ghost reappears. Only Hamlet can see the ghost so Gertrude is frightened that her son is speaking to “th’ incorporal air.” But the ghost reminds Hamlet that he is not to take revenge on his mother. Then Hamlet's tone changes to a softer approach. He tells his mother not to worry, that he is not crazy. Then he asks her to “Confess [herself] to heaven, / Repent what’s past, avoid what is tocome. . . . ” He asks her to refrain from sleeping with Claudius that night, “And that shall lend a kind of easiness / To the next abstinence. . . . ” He then asks his mother not to reveal his lack of madness to Claudius and reassures her that when he is sent to England he will outsmart Rosencrantz, Guildenstern and Claudius. This appeal to motherly love and protection obviously works because in the next scene, Gertrude lies to Claudius and calls her son mad even though she knows he isn't.