From "Etiquette," Emily Post, Funk & Wagnall's Company, 1922 and 1927, and purloined from the CavHooah.com site.

WHEN A GENTLEMAN TAKES OFF HIS HAT

A gentleman takes off his Hat and holds it in his hand when a lady enters the elevator in which he is a passenger, but he puts it back on again in the corridor. A public corridor is like the street, but an elevator is suggestive of a room, and a gentleman does not keep his Hat on in the presence of ladies in a house.

This is the rule in elevators in hotels, clubs and apartments. In office buildings and stores the elevator is considered as public a place as the corridor. What is more, the elevators in such business structures are usually so crowded that the only room for a man's Hat is on his head.

When a gentleman stops to speak to a lady of his acquaintance in the street, he takes his Hat off with his left hand, leaving his right free to shake hands, or he takes it off with his right and transfers it to his left. If he has a stick, he puts his stick in his left hand, and gives her his right. If they walk ahead together, he puts his Hat on; but while he is standing in the street talking to her, he should remain Hatless. There is no rudeness greater than for him to stand talking to a lady with his Hat on, and a cigar or cigarette in his mouth.

WHEN A GENTLEMAN LIFTS HIS HAT

Lifting the Hat is a conventional gesture of politeness shown to strangers only, not to be confused with bowing, which is a gesture used to acquaintances and friends. In lifting his Hat, a gentleman merely lifts it slightly off his forehead and replaces it; he does not smile or bow, nor does he even look at the object of his courtesy. No gentleman ever subjects a lady to his scrutiny or his apparent observation.

If a lady drops her glove, a gentleman should pick it up, hurry ahead of her offer the glove to her and say: I think you dropped this! The lady replies:Thank you. The gentleman should then lift his Hat and turn away.

If he passes a lady in a narrow space, so that he blocks her way or in any manner obtrudes upon her, he lifts his Hat as he passes.

If he is on a street car which is very crowded, when he wishes to leave it and a lady is directly in his way, he asks: May I get through, please? As she makes room for him to pass, he lifts his Hat and says: Thank you!

If he is in the company of a lady anywhere in public, he lifts his Hat to a man who offers her a seat, or who picks up something she has dropped or shows her any other civility.

He lifts his Hat if he asks a woman or an old gentleman a question, and always, if, when walking on the street with either a lady or another man, his companion bows to another person.

In other words, a gentleman lifts his Hat whenever he says or speaks to or is spoken to by a lady, or by an older gentleman. And no gentleman ever keeps a pipe, cigar or cigarette in his mouth when he lifts his Hat, takes it off, or bows.

THE INFORMAL BOW

In bowing on the street, a gentleman should never takes his Hat off with a flourish, nor should he sweep it down to his knee; nor is it graceful to bow by pulling the Hat over the face as though examining the lining. The correct bow, when wearing a high Hat, or derby, is to lift it by holding the brim directly in front, take it off merely high enough to escape the head easily, bring it a few inches forward, the back somewhat up, the front down, and put in on again. To a very old lady or gentleman, to show adequate respect, a sweeping bow is sometimes made by a somewhat exaggerated circular motion downward to perhaps the level of the waist, so that the Hat's position is upside down. If a man is wearing a soft Hat he takes it by the crown instead of the brim, lifts it slightly off his head and puts in on again.

AT THE OPERA, THE THEATER AND OTHER PUBLIC GATHERINGS

In walking about in the foyer of the opera house, a gentleman leaves his coat in the box but he always wears his high Hat. The Hat is for use in the seats rather than in the boxes, but it can be worn perfectly well by a guest in the latter if he hasn't one.