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In the history of the world, it was necessary to keep a good supply of cannon balls near the cannon on old war ships. But how to prevent them from rolling about the deck was the problem. The best storage method devised was to stack them as a square based pyramid with one ball on top restig on four resting on nine which rested on sixteen. Thus a supply of 30 cannon balls could be stacked in a small area right next to the cannon.
There was only one problem now - that was how to prevent the bottom layer from sliding/rolling from under the others. The solution was a metal plate called a "monkey" which had 16 round indentations. However, if this plate were made of iron (the common strong metal of the day back then) the iron balls would quickly rust to it. The solution to the rusting problem was to make it out of brass; hence, "Brass Monkeys".
Few landlubbers realize that brass contracts much more and much faster than iron when chilled. Consequently when the temperature dropped too far the brass indentations would shrink so much that the iron cannon balls would come right off the monkey. Thus it was quite literally cold enough to "freeze the balls off a brass monkey".
And all this time you probably thought that was a vulgar expression. Nahhh, it's history - really.
Hee, hee, I actually did know that, I researched it once because the term made no sense to me and I wanted to know why it was used. Good job Excon, educate the world!