Gallons and Cubic Inches

Date: 09/04/2001 at 11:13:26
From: Darryl Nester
Subject: Volume conversion - history

I know that 1 gallon is 231 cubic inches, based on the old English 
"wine gallon" unit. But I have not been able to find out WHY the 
number 231 was used. Was it simply the case that at some point in the 
process of standardizing volume measurements, it was determined that a 
wine gallon was "pretty close to" 231 cubic inches, so someone decided 
to use that number from then on? Or was there some deeper reason for 
this choice?

Date: 09/04/2001 at 16:49:29
From: Doctor Rick
Subject: Re: Volume conversion - history

Hi, Darryl.

You can find some information on this page (under "Volume"), from the 
"How Many?" site by Russ Rowlett,  linked from our Dr. Math FAQ:

  http://www.unc.edu/~rowlett/units/custom.html   

It doesn't say exactly how the wine gallon was defined. The following 
page indicates the original definition of the wine gallon:

  Weights & Measures 1: An American Encyclopedia
  http://www.todd.demon.co.uk/encyc/measures1.htm   

I quote:

   "In 1824, the British abandoned both the Ale and the Wine gallons 
    in favour of the Imperial gallon, based on the volume of 10 pounds 
    of water (which works out at 277.41945 cu in). America, by this 
    time, had already standardised on the Wine Gallon of 231 cubic 
    inches (strictly speaking, this was defined as the volume of a 
    cylinder 6 inches long and 7 inches in diameter, or 230.9070 cubic 
    inches)."

Indeed, the volume of this cylinder is

  V = pi*r^2*h = 3.14159 * (7 inches/2)^2 * (6 inches)
               = 230.90706 cubic inches

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/