If there is a difference of station or age, then it is necessary only to ask the older or more prominent person whether the introduction would be acceptable. This should be done quietly, and quite out of hearing or knowledge of the other person concerned.
A gentleman should ask a mutual friend for an introduction to a lady whom he wishes to meet. Unless there is no possible objection, the mutual friend should not introduce the gentleman until he has made sure that the lady is willing.
It is not well to introduce gentlemen to one another indiscriminately, nor should ladies be so introduced. One wishes to keep the boundaries of one's acquaintance within certain definite limits, and choice is easier made before acquaintance than after. So, one shows great care in offering introductions to others, and exercises the same care for one's self.
If a hostess and her guest are out walking together, the hostess would introduce to her guest every friend who happened to stop and speak with her, and the guest, should she meet acquaintances of her own, would introduce each of them to her hostess. This is practically the only case where indiscriminate introducing is good form, and here the obligations of hospitality safeguard it.
A lady usually offers her hand to a gentleman who has been introduced to her, but a bow, a smile, and a repetition of the name are all that is necessary where several introductions are being made, as at a large reception or dancing party.
A gentleman always offers his hand to another gentleman on being introduced.
An elderly lady may offer her hand in all introductions with perfect propriety.
If, while walking out with a friend, you meet another, do not introduce the two. A transient meeting is of no particular moment to them, and their friendship or acquaintance with you is not necessarily of strong enough interest to make them desire acquaintance. If, however, you meet at some public place, and are detained there together for several minutes, then the introduction should be given.
When meeting at the house of a mutual acquaintance, friends may introduce friends, but it is preferable to leave the introductions to the hostess.
It is no longer necessary to introduce each guest to everybody else at a party. Introductions are made as opportunity or necessity may dictate. This abolishing of promiscuous and wholesale introductions relieves two very embarrassing situations,—that of being introduced by announcement to a whole roomful of people, and that of being taken around and introduced to them singly.