Degrees of introduction are utterly unknown to best society. It makes not the slightest difference so far as any one's acceptance or rejection of another is concerned how an introduction is worded or, on occasions, whether an introduction takes place at all.
Fashionable people in very large cities take introductions lightly; they are veritable ships that pass in the night. They show their red or green signals--which are merely polite sentences and pleasant manners--and they pass on again.
When you are introduced to some one for the second time and the first occasion was without interest and long ago, there is no reason why you should speak of the former meeting.
If some one presents you to Mrs. Smith for the second time on the same occasion, you smile and say "I have already met Mrs. Smith," but you say nothing if you met Mrs. Smith long ago and she showed no interest in you at that time.
Most rules are elastic and contract and expand according to circumstances. You do not remind Mrs. Smith of having met her before, but on meeting again any one who was brought to your own house, or one who showed you an especial courtesy you instinctively say, "I am so glad to see you again."
=INCLUDING SOMEONE IN CONVERSATION WITHOUT AN INTRODUCTION=
On occasions it happens that in talking to one person you want to include another in your conversation without making an introduction. For instance: suppose you are talking to a seedsman and a friend joins you in your garden. You greet your friend, and then include her by saying, "Mr. Smith is suggesting that I dig up these cannas and put in delphiniums." Whether your friend gives an opinion as to the change in color of your flower bed or not, she has been made part of your conversation.
This same maneuver of evading an introduction is also resorted to when you are not sure that an acquaintance will be agreeable to one or both of those whom an accidental circumstance has brought together.
You must never introduce people to each other in public places unless you are certain beyond a doubt that the introduction will be agreeable to both. You cannot commit a greater social blunder than to introduce, to a person of position, some one she does not care to know, especially on shipboard, in hotels, or in other very small, rather public, communities where people are so closely thrown together that it is correspondingly difficult to avoid undesirable acquaintances who have been given the wedge of an introduction.