In Act IV Scene iii, lines 107-123 how do Brutus and Cassius reconcile? In what ways is Brutus being fair to Cassius in this argument?

In this part of Scene III, Brutus comes to Cassius expressing his regret at being too hasty in his words.  Brutus first tells Cassius to "[b]e angry when you will, it shall have scope"(l.108), acknowledging that Cassius should has every right to be angry.  Brutus goes on to explain that he is a "lamb" who is quick to anger, but also quick to return to good humour.  Cassius responds by asking if he is all mirth and smiles, even when he is vexed or "ill temper'd."  Had he not been angry before as well?

Hearing this, Brutus quickly admits that he was "ill-temper'd" when he said what he did.  From this point in the conversation (approx. l.114), they quickly reach a place of reconciliation.  They each take the other's hand, and Brutus asks Cassius if he cares (has love enough) to put up with him, even when he forgets himself (because of the anger he has inherited from his mother).  This passage is somewhat surprising given the nature of their prior confrontation.

In this scene, Brutus is being fair to Cassius by not being defensive.  He acknowledges how Cassius probably feels about the situation, suggesting that he should be angry with him.  In addition, notice that Brutus never suggests that it is anything Cassius has done that prompted his outburst.  Brutus accepts full responsibility for what transpired.  No accusations fly between them.  Brutus grants Cassius his perspective of the event.