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 storage method devised was to stack them as a square based
pyramid, with one ball on top, resting 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 -- how to prevent the bottom layer
from sliding/rolling from under the others.
The solution was a metal plate with 16 round indentations, called, for reasons
unknown, a Monkey. But if this plate were made of iron, the iron balls would
quickly rust to it. The solution to the rusting problem was to make them 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, folks thought that was just a vulgar expression?