In the heyday of the sailing ship, every ship had to have cannons for protection. Cannons of the times required round iron cannon balls.
Of course, they needed to store the cannon balls in such a way that they could be of instant use when needed, yet not roll around on 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, and the next had 16, and so on. Four levels would provide a stack of 30 cannonballs.

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 plate (called a "monkey"), with one rounded indentation for each cannonball in the bottom layer.

When iron was used to make the 'monkey' plate, the cannonballs would rust to the plate. As a result, these plates were made of brass to solve the problem. Thus, "the brass monkey."

When temperatures falls or drop, 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 would pop out of the indentations, spilling the entire pyramid all over the deck.

Thus it was, quite literally,