Kili could not believe that this was the same uncle who so vehemently hated  elves; he hadn't expected this, and it was apparent that no one else had expected this public apology, either. Not only had Thorin apologized, he'd shown her gratitude, and both occurrences were very rare indeed.

Thorin nodded once to show his respect, and in passing he clasped a hand to Kili's shoulder to show that all was well. The mountain was off in view, a silhouette in the distance. 

"Is that what I think it is?" Bilbo neared the edge so that he might see, and at the same time, a thrush chirped and flew by.

Thorin had noticed too, and a light smile crossed his face as he looked to their home. “We’ll take that as a sign. A good omen.” 

Bilbo returned the smile. Things had turned out far better than he'd anticipated. Thorin now accepted him and Saeril. Their journey was close to over. "I do believe the worst is behind us."

Kili smiled warmly to Saeril in order to see her reaction to Thorin's change of heart. For the first time since they'd left Bilbo's home, no one was at odds. They'd all learned to prove themselves and they had all worked together in order to survive. "I believe Bilbo is right...the worst is behind us," he told her happily, and then Thorin waved for them to follow. They still had a deadline to keep, but they were making good time.