Maybe I'm reading into Ch 38 a little too optimistically but can there be the beginnings of some romantic feelings between Emma and Mr. Knightley? From Ch 38:

"...... Emma had no opportunity of speaking to Mr. Knightley till after supper; but, when they were all in the ball-room again, her eyes invited him irresistibly to come to her and be thanked....."

Mr. Knightley, having known Emma his entire life, I think, has never gotten that "look" from Emma Before. Mr. Knightley and Mrs. Weston had high praise for Emma's eyes and I'll bet she used them on Knightley to her expressive best! I've been at the receiving end of "that look" from a woman when her eyes say "I find you attractive and want you to come closer to me."

Then, further down in Ch 38:

"......"Whom are you going to dance with?" asked Mr. Knightley.

She hesitated a moment, and then replied, "With you, if you will ask me."

"Will you?" said he, offering his hand.

"Indeed I will. You have shown that you can dance, and you know we are not really so much brother and sister as to make it at all improper."

"Brother and sister! no, indeed."

What does that signify? That Mr. Knightley is indeed more than just mere family? Indeed Emma reflects upon that exchange with great pleasure the next morning after the ball in Ch 39.

I think this little exchange between Emma and Mr. Knightley was felt more on his side and I'll button up now so as to not get into spoiler territory.