In 1879 C.T. De Witt published a book titled: Cartier and Baron's practical illustrated waltz instructor, ball room guide, and call book. Giving ample directions for dancing every kind of square and round dances, together with cotillons--including the newest and most popular figures of "the german."

This is what the book said about styling.

• The gentleman prior to engaging in the dance, places himself in front of his partner, a little to her right, encircles her waist with his right arm, supporting her firmly, yet gently, and holds her right hand with his left, extending it nearly to the height of his waist, slightly bent at the elbow.
• The lady's left hand should rest lightly upon her partner's left shoulder, while the right arm should be extended nearly straight with the palm of her hand turned downward. The gentleman then places the inner side of the fingers of his left hand against the inner side of the fingers of the lady's right hand.
• The gentleman being at all times responsible for the guidance of his partner he should, therefore, use the greatest precaution against colliding with other couples. He should regulate the proper distance to be maintained between himself and his partner, neither holding her so close as to impede her freedom of action, nor stand too far aloof, which would prevent his rendering her sufficient support. The lady should allow herself to be entirely guided by her partner, without in any case endeavoring to follow her own impulses.
• In all the round dances, the lady commences with the right foot and the gentleman with the left. Both dancers should turn their heads slightly to the left, overlooking one another's shoulders.

This is what the book said about etiquette:

• At a private party a gentleman may offer to dance with a lady without an introduction; at balls the rule is different, and a gentleman should be introduced either by the floor manager or the lady's escort. This introduction is for the mere purpose of dancing, and does not entitle you to claim her acquaintance afterwards. A lady who declines dancing with a gentleman should afford him some reason. Never wait until the signal is given to take a partner, for nothing is more impolite than to invite a lady hastily, and when the dancers are already in place, this can be allowed only when the sets are incomplete.
• Gentlemen should dance the first set with the ladies under their escort. Among persons not previously acquainted, the acquaintance ends with the dance; and if a gentleman desires to dance a second time with the same lady, he must be presented again; and unless the lady indicates otherwise, he has no claim to her recognition at any subsequent time or place.
• The proper head of the ball room is generally opposite or furthest from the main entrance. Many suppose it to be nearest the orchestra; this is an error, for the orchestra is sometimes on the side, or over the entrance of large ball rooms, but the head is never at either of these places. When the entrance is on a side of the room, custom determines which end, to the right or left of it, is the head. At private houses there is no established rule for determining the head. It may be near the front windows or at the opposite end, at the option of the master of ceremonies.
• Never attempt to stand up in a Cotillion without knowing something of the figure. Do not kick or caper about nor sway your body to and fro: lead your lady gently, only by the fingers, not to grasp her hand. It is a breach of etiquette, when dancing, to leave one set to join another, except when the change is occasioned by mistakes as to the pre-occupancy of place. Rather than dispute as to the pre-occupancy of place. it is better to withdraw from the set.
• During the dance, all should be exclusively devoted to their partners, and never allow themselves to keep up by conversation or the telegraph of the eye and face, a communication with others. Even those persons who are familiar with all the formalities of fashionable society, are often the worst offenders against the common decencies of life.
• It is very impolite and insulting in either lady or gentleman, while dancing in a quadrille, to mar the pleasure of others by galloping around or inside of the next set.
• A lady should never engage herself more than for the following set, unless by the consent of the gentleman who accompanies her.

Modern Round Dancing is certainly more complex in structure today. There are over 700 moves on the list of moves. However, the rules of engagement, etiquette wise, were certainly more complicated than today in the nineteenth century.

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