Act 1 scene 1
The very first two questions that Richard asks in the play, about what Bolingbroke's motivations, is a mystery we will be trying to answer throughout the entire play. Why does Bolingbroke have to accuse Mowbray? Obviously, he cannot accuse Richard, the King, of being a traitor. But since Gloucester, next youngest brother to Edward the Black Prince, and therefore heir to Richard unless he had a son to inherit the crown, has been murdered, the crime is treason. Since Mowbray was the actual instrument used by Richard, Bolingbroke accuses him. In the second scene, The Duchess of Gloucester admonishes Gaunt as one of Gloucester's brothers for not avenging the murder of Gloucester. With Gloucester dead, were Richard to be found guilty of treason, Gaunt would be the next in line for the kingship. And since we find out later in the play that Gaunt does not have long to live, Bolingbroke would be next. So Bolingbroke may have ambition as one of the motivating factors for this accusation of Mowbray.
These first speeches between Bolingbroke and Mowbray are very formal and ritualistic in this very public court scene where Richard as King acts as the judge. As Bolingbroke throws down his gage and Mowbray stoops to pick it up, Shakespeare begins the motif of stooping and standing straight, of being up or down, literally as well as symbolically. Since this is a rise and fall structure, we might expect high and low symbolism. Actually we see that as Richard falls, Bolingbroke rises, so that they actually change places by the end of the play.
This accusation seems definitely exaggerated, unless we understand that Bolingbroke is really accusing Richard, not just of the death of Gloucester, but of all the problems of the kingdom since Richard took the throne as a young man.
There are several possible interpretations for this line: 1) first that Bolingbroke is speaking in a higher pitch, possibly even getting louder, and Richard may be telling him to settle down; 2) he may understand the Bolingbroke is actually accusing him of the death of Gloucester and he may be commenting on how high in the sense of power Bolingbroke may be aiming with his accusations.
This line begins the motif of Richard seeing himself as a physician able to cure the disease of dissention within England. The irony of this, of course, as we find out later, is that Richard is actually himself the disease.
Richard loves to use the Great Chain of Being language associating himself with the sun, the higher levels of everything, including the lion as king of beasts.
Shakespeare often comes back to this theme of reputation, especially in both Cassio's and Iago's speeches in Othello.
Though, of course, Shakespeare was writing in the Renaissance, he was writing about the medieval times in England when jousts were used to determine who was telling the truth or was in the right. It was believed that God would fight on the side of the right, strengthening the arm of the good guy and making his opponent weaker due to his knowledge that he was wrong. Richard, since he cannot arbitrate between the two opponents and talk them into forgetting their conflict, he says he will let God decide between the two.