This section is from the book "Hill's Manual Of Social And Business Forms: A Guide To Correct Writing", by Thos. E. Hill. Also available from Amazon: Hill's Manual Of Social And Business Forms: The How-To-Do-Everything Book Of Victorian America.
Acquaintances are usually entitled to the courtesy of a bow. It is poor policy to refuse recognition because of a trifling difference between parties.
The young lady should show similar deference to an elderly lady, or to one in superior position, that a gentleman does to a lady.
When bowing to ladies, it is etiquette for the gentleman to raise his hat from his head. If passing on the street, the hat should be raised and salute given with the hand farthest from the person addressed.
A bow or graceful inclination should be made by ladies when recognizing their acquaintances of the opposite sex. It is the privilege of the lady to bow first.
A gentleman on horseback should grasp whip and reins in his left hand, and raise his hat with his right, when saluting a lady. The lady salutes by bowing slightly.
To a casual acquaintance you may bow without speaking; but to those with whom you are well acquainted greater cordiality is due. A bow should always be returned; even to an enemy it is courtesy to return the recognition.
When a gentleman, accompanied by a friend, meets a lady upon the street, it is courtesy in the salutation for the gentleman's friend to bow slightly to the lady also, as a compliment to his companion, even though unacquainted with the lady.
On meeting a party, some of whom you are intimately acquainted with, and the others but little, the salutation should be made as nearly equal as possible. A slight recognition of some and great demonstration of pleasure toward others is a violation of etiquette.
A gentleman should return a bow made him on the street, even if the one making the same is not recognized. The person may possibly be a forgotten acquaintance; but, even if a mistake has been made, there will be less embarrassment if the bow is returned.
A gentleman should not bow from a window to a lady on the street, though he may bow slightly from the street upon being recognized by a lady in a window. Such recognition should, however, generally be avoided, as gossip is likely to attach undue importance to it when seen by others.
A warm cordiality of manner, and a general recognition of acquaintances, without undue familiarity, is a means of diffusing much happiness, as well as genial and friendly feeling. In thinly-settled localities the habit of bowing to every one yon meet is an excellent one, evincing, as it does, kindliness of feeling toward all.
When meeting a lady who is a stranger, in a hallway, upon a staircase, or in close proximity elsewhere, courtesy demands a bow from the gentleman. In passing up a stairway, the lady will pause at the foot and allow the gentleman to go first; and at the head of the stairway he should bow, pause, and allow her to precede him in the descent