Éomer and Aragorn's New Mood (TT 3.ii.433)

Gimli and Legolas looked their companion in amazement, for they had not seen him in this mood before. He seemed to have grown in stature while Éomer had shrunk; and in his living face they caught a brief vision of the power and majesty of the kings of stone. For a moment it seemed to the eyes of Legolas that a white flame flickered on the brows of Aragorn like a shining crown.

Éomer stepped back and a look of awe was in his face. He cast down his proud eyes. 'These are indeed strange days,' he muttered. 'Dreams and legends spring to life out of the grass.

'Tell me, lord,' he said, 'what brings you here?'

In rejecting the logic of either going after the Ringbearer or continuing on to Minas Tirith, and instead choosing to pursue the orcs who have abducted Merry and Pippin, Aragorn does the right thing because it is the right thing, regardless of its seeming hopelessness. In doing so he passes the test and proves himself worthy to become king, though that, too, seems a hopeless cause. Is it any wonder that he seems so different so immediately? His unhesitating, bold declaration of his identity and purpose to Éomer stuns his comrades, 'for they had not seen him in this mood before' (one of the funniest lines in the book), but it also finds confirmation in Éomer’s response. He takes a step back, lowers his eyes, accepts what he has seen and heard, and addresses Aragorn as 'lord'. He is the first to do this.