A Rank is a line of military personnel, drawn up in line abreast (i.e. standing side by side).
Commonly, troops called to 'On the right, fall in!' do so by forming in line abreast, determining their initial position in relation to a marker. This may be a position on the ground or a single person placed previously to the movement. Often troops determine their spacing on the rank by extending their right arm to touch the left shoulder of the marker, or the person on that marked position, and, then starting from the right, align themselves visually to form a straight row. The alignment may then be checked by a non-commissioned officer making observations and calling orders from the end of the rank. (Rarely, the order may be given to fall in on the left).
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The original article can be found at Rank (formation) and the edit history here.