After the controversy of recent weeks with bashed bridges, furlongs and novel signs, we turn to something deadly dull – the definitions of length, mass (or weight) and capacity (or volume) and their relationships.
The earliest civilisations, the Sumerians, the Egyptians, the Greeks and Romans, all developed metrological systems, and central to those systems were standards of mass and length, traditionally a metal block or cylinder and a metal rod from which copies could be made as and when required. But what about the standard for capacity, which could be based on either length or mass?
It might seem that length is the obvious choice, and indeed the US gallon is derived from the English gallon of 1707, defined as a cylinder seven inches in diameter and six inches high, giving a volume of exactly 231 cubic inches (pi was assumed to be 22/7).
Ah, ha! Not so fast. When the Secretary of the Royal Society, John Wilkins, made proposals in 1668 for a measurement system based on a universal measure of length he suggested that the standard of mass be “this cubical content of distilled rainwater”. This “cubical content” was his proposed standard of capacity, which came from his proposed universal measure of length cubed. This idea, linking mass to volume, would appeal, but in different ways, to the founders of both the metric and Imperial systems, bringing benefits and problems to both.
The fathers of metric system set out in 1793 to define the grave, as the kilogram was then known, as a cubic decimetre of rainwater weighed in a vacuum at the melting point of ice. But for the standard, they reverted to a traditional metal cylinder. The original prototype kilogram, manufactured in 1799, had a mass equal to that of 1.000 025 litres of water at 4°C.
Britain too was beginning to realise that its chaotic collection of measures was no longer fit for purpose. In 1819, a Royal Commission was appointed to consider the issue. The Commission included polymath Thomas Young, who favoured rationalising existing measures rather than adopting the decimal metric system, and this view prevailed. However, in its first report, the Commission made this recommendation:
“… on account of the great convenience which would be derived from the facility of determining a gallon and its parts, by the operation of weighing a certain quantity of water, amounting to an entire number of pounds and ounces without fractions, we venture strongly to recommend, that the Standard Ale and Corn Gallon should contain exactly ten pounds Avoirdupois of distilled water, at 62° of Fahrenheit, …”
The recommendations of the Commission led to the Imperial system of measures, but also to the divergence of UK and US measures of capacity.
This Imperial gallon, not to be confused with its US counterpart, would also cause a headache for metrologists, as the definition that applied up to 1976 indicates:
“a gallon is the space occupied by 10 pounds of distilled water of density 0.998 859 g/mL weighed in air of density 0.001 217 g/mL against weights of 8.136 g/mL.”
Meanwhile, the Bureau International des Poids et Mesures (BIPM), the international body set up in 1875 to ‘maintain’ the metric system, was trying to ensure a precise 1:1 relationship between capacity and mass. From 1901 to 1964, the litre was defined as the volume of one kilogram of pure water at maximum density and standard pressure, which gave a volume of 1.000 028 dm³. It is now defined as one cubic decimetre.
Eventually, in 1976, the Imperial gallon was redefined as exactly 4.546 09 dm³. Twenty years later, it ceased to be legally authorised in the UK, although it remains in use for specifying fuel consumption, confusingly for any cars that also sell in the USA.
And what about the Imperial standards for mass and length?
In 1959, Australia, Canada, New Zealand, South Africa, the UK and the USA agreed on these definitions:
the avoirdupois pound is exactly 0.453 592 37 kg;
the yard is exactly 0.914 4 m.
In the UK, they were implemented in the Weights and Measures Act 1963. The traditional metal standards for the yard and the pound, dating back to the middle of the nineteenth century and in semi-retirement since 1898, were finally pensioned off.
And the standard metre and kilogram?
In 1960 the metre was redefined in terms of the wavelength of light, and the International Prototype Metre forged by Johnson Matthey in London in 1879 became a museum piece. Then, in 1983, this new definition was replaced by one based on the speed of light.
However, for mass, the International Prototype Kilogram, also manufactured in 1879 by Johnson Matthey, still reigns supreme from its home at Sevres near Paris. It remains the worldwide standard for mass. However, even that may be changing, as explained in this recent article:
So, John Wilkins, where does that leave us? Well, for a start there are some easy-to-remember relationships:
1 L of water has a mass of about 1 kg;
1 m³ of water has a mass of about 1 tonne; and, for example,
1 L of cooking oil of specific gravity 0.92 has a mass of 920 g;
the kids’ paddling pool, 1.5 x 1.0 m with water 120 mm deep, requires 180 L to fill it.
Other readers may be able to suggest areas where the switch from Imperial to metric measures of capacity has made life easier or safer for them.
The latest article from the Metric Maven in the US discusses some of these issues, but adopts a totally different approach: http://themetricmaven.com/?p=6191