Meanwhile, back at Gloucester's castle, Edmund's evil plan is progressing nicely. (Cue the evil smirk and hand-rubbing gesture.) He has told Cornwall about his father's forbidden allegiance to Lear and has also showed Cornwall the incriminating, anti-Cornwall letter. (Remember the letter Gloucester showed Edmund back in Act 3, Scene 3?)
Edmund humbly suggests that he's made a great sacrifice by placing his loyalty to Cornwall above his filial duty (to his father, Gloucester).
Cornwall concludes that it now seems like Edgar's "plot" to kill his father was kind of just, Gloucester being such wicked guy and all.
Edmund holds up the incriminating letter and says something like: "It's just so awful that I have to tell on my own father, who is clearly a spy and informant for France."
Cornwall swears he will punish Gloucester for his treason and then promises Edmund that he will become the new Earl of Gloucester.
Cornwall sends Edmund off to find Gloucester and bring him back for punishment.
Edmund hopes that when he finds his father, the man will be comforting Lear, because then Gloucester will be doubly implicated for crimes.