This section is from the book "Cassell's Cyclopaedia Of Mechanics", by Paul N. Hasluck. Also available from Amazon: Cassell's Cyclopaedia Of Mechanics.
The term balanced or dancing steps is applied to a geometrical staircase, where the nosings of the winders are so placed as not to converge on the same point, but each directed to a different point, so that the inner edge of tread is wider than it otherwise would be, and the steps are thus intermediate in shape between llyers and winders. This allows of a better curve being given to the inclination of the handrail. In the sketch, the first lour and the last three steps are ordinary parallel flyers, and the remainder are "balanced" or "dance," as described.

Balanced or Dancing Steps.
 
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