Although the formation and context differ from the Asker's source text, here is an example of rolling volleys in the 17th and 18th centuries:
"Another British tactic was platoon fire. At the time a platoon was a half-company. The right-hand files of a company would form the first platoon and the left-hand files of that same company would form the second platoon. The platoon fire would begin at one of the flank platoons of the battalion or regiment, and one or two seconds after the platoon beside them fired, the next platoon would fire. The effect would be platoon volley after platoon volley rolling down the face of the battalion or regiment, and the result of such disciplined fire was a constant hail of bullets on the enemy formation."

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Note added at 3 hrs (2015-04-21 11:56:56 GMT)
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More about the infantry square (albeit mostly static rather than advancing) here: https://www.tumblr.com/search/infantry square