Posted by George Pearsall on April 01, 2003
Many messages have addressed the implausibility of the nautical cannonball derivation of the otherwise
entertaining expression, "Cold enough to freeze the balls off a brass monkey." And the article in
"Meanings and origins of phrases and sayings" includes a scientific analysis to demonstrate the
unlikelihood that the expression could have come about this way. My minor contribution is to point
out that this quantitative analysis incorrectly concludes that a 200 degree Celcius drop in temperature
would cause a one-meter leg on the triangular "monkey" to shrink relative to the cast iron balls by
"a quarter of a millimetre" and is in error by an order of magnitude (factor of about 10). A leg would
shrink relative to a one-meter row of cannonballs by about 2 mm. This still is not enough to push the
cannonballs up and out of the frame constraining them, so the argument about the implausibility of this
supposed derivation still holds up. And a temperature change of 200 C is extremely unlikely on
shipboard, so the shrinkage will be even less than 2 mm (but not nearly as small as 1/4 of
a mm) over one m of original length.
For those interested in the calculation, the most reliable values I could find for the linear coefficients of
thermal expansion for brass and gray cast iron are 0.0000199/degree C and 0.0000105/degree C
respectively (from the ASM Metals Reference Book). So if a one-meter long leg of a brass triangle
"monkey" were cooled -200 degrees C, it would shrink unconstrained by 0.00398 m, or about 4 mm.
And a one-meter long row of cast iron cannonballs would shrink less, about 0.0021 m, or about 2 mm.
The difference between these two contractions is obviously about 2 mm (1.88 mm without rounding),
an order of magnitude larger than the "quarter of a millimetre" in the cited article. Not a big deal, and
not a large enough difference to invalidate the conclusion that the nautical cannonball explanation for
the expression cannot hold up, but when science is invoked, the calculations should at least be the right
order of magnitude.
In actuality, the outward force of the cannonballs pushing along the leg of the brass triangle would
prevent the brass from contracting the full 4 mm, and the inward force of the triangle along the row of
cannonballs adjacent to the brass leg would cause the cast iron balls to contract more than the
calculated 2 mm. The joint contraction for both the cannonballs and the triangle leg probably would be
about 2 to 3 mm. And a temperature change of -200 C is too extreme to be plausible. A temperature
of -100 C (equal to -180 F) probably is larger than any ship on the high seas would be expected to
experience, which would decrease the maximum expected shrinkage to about 1 to 1.5 mm, even less
likely than 2 to 3 mm to cause the cannonballs to fall off/out of the triangle (whether or not it was
called a "monkey") but still greater than 1/4 mm.