While the original link Ray posted was information supplied from the Steton web links, it is fairly common and shared information.
According to the Webster Dictonary
There are two degrees of politeness:
1.With your hat-lifting or tipping it, which you do for strangers.
2.Taking it off, which you do for friends.
Tipping your hat is done by barely lifting it off your head:
By the crown of a soft hat, or the brim of a stiff one.
Your cigarette, pipe or cigar should always be taken out of your mouth before removing or tipping your hat.
a. A man takes off his hat outdoors:
(1) when he is being introduced, or saying good-by;
(2) as a greeting when passing someone he knows on the street;
(3) when talking, particularly with a woman, an older man, or a clergyman;
(4) when the National Anthem is being played, or the flag is passing;
(5) at a burial, or (except in large cities) in the presence of a funeral procession.
b. A man tips his hat:
(1) when walking with a friend who passes a woman only the friend knows;
(2) any time a lady who is a stranger thanks you for some service;
(3) any time you excuse yourself to a woman stranger, as in a crowded bus when you jostle her, or when you have to ask to crowd past;
(4) any time a stranger shows courtesy to a woman you are with, as when. a man or woman picks up something she has dropped, or a man gives her his seat;
(5) when you ask a woman (or elderly man) for directions.
c. Indoors, a man always takes off his hat, except:
(1) in public buildings, such as railroad stations or post offices;
(2) in entrance halls and corridors of office buildings or hotels;
(3) in elevators of public or office buildings. (You have to use your judgment about this, though. In a department store elevator full of women you might take it off. Also, if a woman you know gets into an office building elevator, you would probably take it off, and you certainly would do so if you started talking to her.)
Can you tell me what is the difference in the number of X's in a hat and do all hat companies use a standard system to rate the number of X's they put on a hat? The X's on a hat stands for the quality. In otherwords, the higher the X's the better the quality. No, all companies do not use the same standards for X rating. What this means to you is, one company's 10X may be equal to another company's 30X. The best thing to do is feel the hat. Check it for softness and stiffness, the better the quality the softer and less stiff the hat will be. What makes the hat softer and less stiff is the amount of beaver fur used in the hat body (the more beaver fur used the higher the X's).
Hope this helps.