Another definition I've heard of the "square load" concept: the shot charge is equal in weight to a solid lead ball that will fit the barrel of the particular gauge gun in question. That's the definition of "gauge" in the case of shotguns. We call a 12 a 12 because a solid lead ball weighing 1/12 of a pound will fit in the bore. 16ga fans are about the only ones that really like this particular "square load" definition, because it happens to work perfectly for their gauge: 1/16 of a pound = 1 oz. Hence, a shot charge weighing 1 oz is a "square load" for the 16. Unfortunately, things don't work out so well when you try the same formula with the other gauges.
Besides which, "square load" is a contradiction in terms. The barrel of a shotgun is round. How do you fit a square load into a round hole??