Brad Naylor wrote:
In the heyday of sailing ships, all war ships and many freighters
carried iron cannons. Those cannons fired round iron cannon balls. It
was necessary to keep a good supply near the cannon. However, how to
prevent them from rolling about the deck? The best storage method
devised was 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 or rolling from under the others. The solution was a
metal plate called a "Monkey" with 16 round indentations. However, if this
plate were made of iron, the iron balls would
quickly rust to it. The solution to the rusting problem was to make
"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 cannonballs would come right off the monkey. Thus,
it was quite literally, "Cold enough to freeze the balls off a brass
monkey."

http://www.history.navy.mil/faqs/faq107.htm

It has often been claimed that the "brass monkey" was a holder or storage
rack in which cannon balls (or shot) were stacked on a ship. Supposedly when
the "monkey" with its stack of cannon ball became cold, the contraction of
iron cannon balls led to the balls falling through or off of the "monkey."
This explanation appears to be a legend of the sea without historical
justification. In actuality, ready service shot was kept on the gun or spar
decks in shot racks (also known as shot garlands in the Royal Navy) which
consisted of longitudinal wooden planks with holes bored into them, into
which round shot (cannon balls) were inserted for ready use by the gun crew.
These shot racks or garlands are discussed in: Longridge, C. Nepean. The
Anatomy of Nelson's Ships. (Annapolis MD: Naval Institute Press, 1981): 64.
A top view of shot garlands on the upper deck of a ship-of-the-line is
depicted in The Visual Dictionary of Ships and Sailing. New York: Dorling
Kindersley, 1991): 17.

http://www.askoxford.com/asktheexper...onkeys?view=uk

What is the origin of the term 'brass monkey'?

The story goes that cannonballs used to be stored aboard ship in piles, on a
brass frame or tray called a 'monkey'. In very cold weather the brass would
contract, spilling the cannonballs: hence very cold weather is 'cold enough
to freeze the balls off a brass monkey'. There are several problems with
this story. The first is that the term 'monkey' is not otherwise recorded as
the name for such an object. The second is that the rate of contraction of
brass in cold temperatures is unlikely to be sufficient to cause the reputed
effect. The third is that the phrase is actually first recorded as 'freeze
the tail off a brass monkey', which removes any essential connection with
balls. It therefore seems most likely that the phrase is simply a ribald
allusion to the fact that metal figures will become very cold to the touch
in cold weather (and some materials will become brittle).