At the walls of the Tower, Richard coaches Buckingham in acting distraught. Buckingham assures him "ghastly looks are at my service, like enforced smiles." Catesby enters with the Lord Mayor followed by Ratcliffe and Lovel with Hastings' head. Richard affects despair that his beloved Hastings turned out to be a villain. Buckingham backs Richard up. The two convince the Mayor that Hastings deserved death, that it's too bad the Mayor couldn't hear "the traitor speak" before he was beheaded, and that the Mayor must spread word of Hastings' treachery and rightful execution to his citizens so that no one mourns his death. The mayor exits.
Here Richard's directorial role is more explicit than ever – he openly treats Buckingham as an actor and coaches him on how to act convincingly. As Richard's trusty sidekick, Buckingham is as comfortable faking emotions as Richard is. They put on a show of grief in front of the mayor in order to manipulate the mayor into getting the general population on Richard's side. Richard wants to make sure the power of the common people stands behind him, not Hastings.
Richard sends Buckingham after the Lord Mayor to spread rumors amongst the citizenry that young Edward Prince of Wales and the Duke of York are illegitimate, that the late King Edward was a relentless lecher, and that the late King was himself also illegitimate, unrelated to his and Clarence's father. Buckingham exits and Richard sends Lovel and Catesby off too. Alone, Richard says he's going to hide Clarence's children, Edward Plantagenet and Margaret Plantagenet, and isolate Edward Prince of Wales and the Duke of York so no one can access them.
Not trusting the mayor alone to win public support for Richard, Richard plans a slander campaign to influence the public in his favor by spreading lies about his brother Edward. If King Edward and his sons really were illegitimate, they would have no real right to rule England. Richard hopes to convince everyone that that's indeed the case, allowing him not just to take the throne but for the public to think that his doing so is perfectly legitimate.