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In the days of sail every sailing ship had to have one or more cannons for
protection.  Cannon of the times required round iron cannonballs.  The
master wanted to store the cannonballs such that they could be of instant
use when needed, yet not roll around the gun deck. The solution was to stack
them up in a square-based pyramid next to the cannon. The top level of the
stack had one ball, the next level down had four, the next had nine, the
next had sixteen, and so on. Four levels would provide a stack of 30

The only real problem was how to keep the bottom level from sliding out from
under the weight of the higher levels.  To do this, they devised a small
brass plate ("brass monkey") with one rounded indentation for each
cannonball in the bottom layer.  Brass was used because the cannonballs
wouldn't rust to the "brass monkey," but would rust to an iron one.  When
temperature falls, brass contracts in size faster than iron.  As it got cold
on the gun decks, the indentations in the brass monkey would get smaller
than the iron cannonballs they were holding.  If the temperature got cold
enough, the bottom layer of cannonballs would pop out of the indentations
spilling the entire pyramid out over the deck.  Thus it was, quite
literally, "cold enough to freeze the balls off a brass monkey."

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