In the book, Legolas overhears a different conversation,
between Eowyn and Aragorn.
When the light of day was come into the sky but the sun was
not yet risen above the high ridges of the East, Aragorn made
ready to depart. His company was all mounted, and he was about
to leap into the saddle, when the Lady Eowyn came to bid them
farewell. She was clad as a Rider and girt with a sword. In her
hand she bore a cup and she set it to her lips and drank a little,
wishing them good speed; and then she gave the cup to Aragorn,
and he drank, and he said: 'Farewell, Lady of Rohan! I drink to
the fortunes of your House, and of you, and of all your people.
Say to your brother: beyond the shadows we may meet again!'
Then it seemed to Gimli and Legolas who were nearby that she
wept, and in one so stern and proud that seemed the more grievous.
But she said: 'Aragorn, wilt thou go?'
'I will,' he said.
'Then wilt thou not let me ride with this company, as I have
'I will not, lady,' he said. 'For that I could not grant without
leave of the king and of your brother; and they will not return
until tomorrow. But I count now every hour, indeed every minute.
Then she fell on her knees, saying: 'I beg thee!'
'Nay, lady,' he said, and taking her by the hand he raised
her. Then he kissed her hand, and sprang into the saddle, and
rode away, and did not look back; and only those who knew him
well and were near to him saw the pain that he bore. Chapter
II The Passing of the Grey Company, The Return of the King.