Some careless hostesses neglect to complete introductions. This causes embarrassment for both, or all, people concerned, and reflects discreditably on the hostess.
Who has not heard the otherwise charming hostess greet a friend cordially in this manner: "Oh, how-do-you-do, my dear! Let me introduce Mrs. Allen, Mrs. Baker and Mr. Carter." The young person who has just arrived can hardly avoid feeling a bit confused, and perhaps a bit slighted. And the people to whom this introduction was made will certainly feel embarrassed when they meet the stranger again and must ask his or her name.
Another type of incomplete introduction is to draw two strangers into conversation by saying casually: "Mrs. Roberts, Mrs. Jones was at the opera last night and heard the same pianist you heard two weeks ago." This is hardly sufficient. The remark should have been either preceded or followed by a _bona fide_ introduction, though the smile and bow of the hostess as she speaks may be so cordial as to remove whatever feeling of constraint there might have been.
The incomplete introduction is careless and unkind. The hostess is unfair to her guests if she does not make each introduction definite and formal, if she does not pronounce clearly the names of both people to be presented to each other.
The indirect introduction is entirely different from the incomplete introduction. The former is often necessary and purposely resorted to; the latter is invariably a mistake or the result of carelessness.
When it is desirable to draw another into conversation, then the hostess may make an indirect introduction to avoid stiffness and constraint. Thus, while conversing with one guest, she may turn to another and say: "Mrs. Blank, Mrs. Smith was just telling us about the famous picture that was brought recently to America. Have you seen it?" The purpose of the hostess will be achieved, for the guest addressed will join the conversation, although there has been no formal introduction.
When two people are brought together in this manner, the question of whether or not they continue their acquaintanceship depends entirely upon themselves. In taking leave of each other, women who have been only semi-introduced may nod or shake hands as they please. It is not necessary to seek out a woman to whom one has been indirectly introduced in order to take leave of her. If the semi-introduction is between a man and woman, the woman must either nod first, or offer her hand first, in leave-taking. It is the sign of her willingness to be formally introduced.