I would say that the tone of this passage from <em>Tristam Shandy</em> is serious and intimate.
Explanation:
Although the words that the speaker uses are formal, the intention and the tone is clearly intimate. The reader can easily understand that the speaker is willing to tell everything about himself to the other person. He already feels comfortable telling him about his life and his opinions. As he himself says at the end of the passage, the acquaintance that begins between them will grow into familiarity and that will terminate in friendship. By reading this sentence, we can realize how the speaker feels about the other person. He already feels their relationship is close and intimate, even now that they technically don’t know each other.
