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Cat's idea is plausible; I've never seen a description of how it was done either, I wonder if a period photo exists that shows how the men nested the balls in the top rows?
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And it is just that, an idea based on atmospheric extraction. But then there might just be ...
Folks looked at hard difficult grunt-labor jobs differently back then - they just did it! It might have been handed to the latest nationality of imigrant of the time.
Cat, I don't think your idea was pulled out of the air, in fact, I think you may be right.
I think if the stackers were of the latest wave of immigrants, it'd be probable that they were in either a gray or a blue uniform. This would have been a great disciplinary duty.
You may be right, that the smaller shot was just muscled up to the top, but I think when we're talking about the larger stuff, that they would have had to have used some sort of apparatus.