"With the passing of the ridiculous half-finger handshake, with the arm extended upward and the wrist bent awkwardly, introductions have become more cordial and sincere.
Which is as entirely as it should be.
Too many people go through the ceremony of an introduction merely as a matter of duty, without realizing its portent in the matter of friendship and future acquaintance.
We have all met the man or woman who nods stiffly in acknowledgement of an introduction and offers some stereotyped expression of welcome. And we have all met the man or woman who smiles warmly, offers a sincere hand-clasp and acknowledges the introduction so cordially that one feels entirely at ease. In the latter case, a brief acquaintance usually ripens into friendship, while in the former instance, one is inclined to forget promptly the one to whom the introduction has been made.
The next time your are introduced to a stranger, smile sincerely, make your hand-clasp warm and firm, put cordiality into your welcome and see how your new acquaintance responds!
The correct introduction alone is not the cornerstone of friendship; but the correct introduction that is also cordial opens the door to friendships that perhaps are sealed to every other effort.
Whether you are making an introduction or acknowledging one, be sure that it is both correct and cordial."
Lillian Eichler -Book of Etiquette VI (1921)