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But Casey calls "marching by the flank" a formation with 4 abreast. To me, that is no longer a line of battle. It's a doubled-up line of battle.
Your file would be the guys in line with you by 2 or 4. Say you are marching down a street in 4s and the road makes a right turn the order would be by files right each line of 4 makes a right turn at the turn in the road. Firing by file goes down the battle line with the first front and rear man on the right firing then so on down the line. You're right a column of 4s is not a battle line. Technically by the book any movement in any formation to the side is marching by the flank. We just tried to show how you would move by 2s or 4s. I know it's confusing, the manuals are not easy reading.A related question is...what does it mean when a unit moves "by file?"