The Kilogram That Lost Weight: How Le Grand K Was Replaced by a Constant of Nature

In a basement vault on the edge of Paris, behind a door that took three separately held keys to open, sat a small cylinder of polished metal about the size of a golf ball. It rested under nested glass bell jars, and almost nobody was allowed to touch it. For 130 years this one object was, by international law, the kilogram. Not a good example of a kilogram, not the best copy of one. It was the definition. Every bag of flour, every pharmaceutical dose, every truck on a highway scale and every grain of gold on a jeweler’s balance traced its mass, through a long chain of comparisons, back to that cylinder.

Metrologists called it the International Prototype of the Kilogram, or IPK. Everyone else came to know it by its nickname, Le Grand K. And by the late 20th century it had developed an embarrassing problem. Compared with its official copies, it appeared to be getting lighter, by something like 50 micrograms over a century. The BBC once put the gap at less than the weight of a single eyelash. Yet because Le Grand K was the kilogram by definition, it could not technically lose anything. If it shed atoms, the whole universe, in a bookkeeping sense, got slightly heavier.

This is the story of how the world fixed that absurdity: how scientists spent four decades learning to weigh things with electricity and to count the atoms in a nearly perfect ball of silicon, and how, on a November day in 2018, delegates from around the world voted to retire the last physical object that defined a unit of measurement.

A kilogram made of water

The kilogram began as a revolutionary idea in the literal sense. In the early 1790s, French scientists set out to replace the country’s tangle of local weights and measures with units drawn from nature, “for all times, for all peoples,” as the motto later put it. Length would come from the size of the Earth: the metre was to be one ten-millionth of the distance from the North Pole to the equator, measured along the meridian through Paris. Mass would come from water. In 1793 the new unit, briefly called the grave, was defined as the mass of a cubic decimetre of water at the temperature of melting ice. The chemist Antoine Lavoisier and the mineralogist René Just Haüy weighed it at 18,841 grains in the old French units.

Water, though, is a terrible thing to keep in a drawer. In 1795 the grave was renamed the kilogram, and once the surveyors Jean-Baptiste Delambre and Pierre Méchain had finished measuring the meridian from Dunkirk to Barcelona, the units were fixed for good. Louis Lefèvre-Gineau and Giovanni Fabbroni carefully determined the mass of a cubic decimetre of water at about 4°C, where water is densest, and a platinum cylinder was made to match it. In June 1799 the republic adopted that cylinder as the standard, and in December it was formally ratified. Because it was stored in the national archives, it became the Kilogramme des Archives. From that moment the kilogram was no longer really about water. It was about a lump of metal.

Forty cylinders from London

By the 1870s the metric system had spread across Europe and Latin America, and scientists wanted a standard that was not the property of one country. On May 20, 1875, 17 nations, the United States among them, signed the Metre Convention. It created the International Bureau of Weights and Measures, known by its French initials BIPM, and gave it a home at the Pavillon de Breteuil, a 17th-century pavilion, inaugurated by Louis XIV, in a park in Saint-Cloud, just southwest of Paris.

The new standards needed a better material than pure platinum, which is soft and scratches easily. The London firm Johnson Matthey cast an alloy of 90 percent platinum and 10 percent iridium, hard, dense, almost immune to corrosion and only weakly magnetic, and in 1879 it produced the cylinder that would become Le Grand K: 39 millimetres tall and 39 millimetres across, a shape chosen to give the smallest possible surface for its volume. In 1883 it was found to be indistinguishable in mass from the old Kilogramme des Archives, and in 1889 the first General Conference on Weights and Measures made it the international kilogram. Forty copies, made of the same alloy and given numbers, were handed out to member countries.

The United States received two of them, K4 and K20. On January 2, 1890, their packing boxes were opened at the White House in the presence of President Benjamin Harrison, the Secretaries of State and the Treasury and a small crowd of guests, and Harrison signed a certificate accepting them as authentic. Three years later, in 1893, a short notice from the U.S. Coast and Geodetic Survey known as the Mendenhall Order made a quietly radical decision: American pounds and yards would from then on be defined in terms of the metric standards. The old customary standards had proven unstable, and the metric copies were simply better made. The final step came in 1959, when English-speaking countries agreed that a pound is exactly 0.45359237 kilogram. Every pound in the United States has been, legally, a fraction of a kilogram ever since, a fact worth remembering whenever someone treats the two systems as rivals. Mixing them carelessly can still be very expensive, as the engineers behind the Mars Climate Orbiter found out in 1999.

The care and feeding of a kilogram

Keeping a definition in a vault turned out to be fussy work. Le Grand K and its six official “sister” copies lived together under bell jars at the BIPM, while ten working copies did the day-to-day weighing in the calibration lab. The prototypes were stored in air, and air is dirty: hydrocarbons and other contaminants settle on a polished metal surface and slowly add mass. Between 1939 and 1946 the BIPM worked out an official cleaning ritual. A prototype is rubbed with a chamois leather soaked in equal parts ether and ethanol, steam-cleaned with doubly distilled water and then left to settle for a week or more. A cleaning removes between 5 and 60 micrograms of grime, and the moment it ends the cylinder starts collecting more, about a microgram a month at first and roughly a microgram a year after that.

National copies came back to Paris for checkups called periodic verifications, and there were only three of them, in 1889, 1948 and 1988 to 1992. Getting a kilogram to France was its own small drama. In 1984 the American prototypes K4 and K20 were hand-carried in the passenger cabins of separate commercial flights, so that a single accident could not take out both. K20, the U.S. primary standard, was officially 39 micrograms lighter than Le Grand K in 1889, 19 micrograms lighter in 1948 and back to 39 micrograms lighter in 1989. K4, the American check standard, which was handled far more often, lost 41 micrograms relative to the international prototype over 110 years, most likely to ordinary wear.

The drift nobody could explain

The third verification revealed something more troubling than wear. Taken as a group, the copies made from the same alloy at the same time had been slowly drifting apart from Le Grand K, almost all of them in the same direction. Compared with the international prototype, the original batch of copies seemed to have gained around 25 micrograms on average over a century, and the overall divergence between the master and its siblings was about 50 micrograms.

The maddening part was that nobody could say which side was moving. Perhaps the copies were gaining mass. Perhaps Le Grand K was losing it. Perhaps everything was drifting together, which no comparison among the cylinders could ever detect, because the only thing they could be weighed against was each other. Researchers proposed explanations. Hydrogen absorbed by the platinum surface was one. In 2013, Peter Cumpson’s group at Newcastle University reported that old platinum weights carried mercury on their surfaces, possibly picked up from the mercury thermometers and barometers that once sat near them in labs, and Le Grand K had long been kept within centimetres of a mercury thermometer. None of these ideas settled the question.

The problem then surfaced from a different angle. In 2014, ahead of the planned redefinition, the BIPM brought Le Grand K out of its vault for an extraordinary round of calibrations, the first direct comparison with its working copies in more than 20 years. The master and its six sisters agreed well. But the working copies used to calibrate everyone else’s standards had each lost between 18 and 88 micrograms since the early 1990s, probably from wear, and the bureau’s own kilogram, the one it actually passed on to the world, had shifted by 35 micrograms. The BIPM ended up correcting the calibration certificates it had issued for one-kilogram standards between 2003 and 2013.

Why a few micrograms matter

Thirty-five micrograms is 35 parts per billion of a kilogram. Your kitchen scale will never notice. But the kilogram did not stand alone. Before 2019 the newton was defined as the force that accelerates one kilogram by one metre per second every second, so the joule and the watt rested on the kilogram too. The ampere was defined through the force between two wires carrying a current, and the mole and the candela leaned on the gram and the watt. A wobble in the cylinder in Paris was, in principle, a wobble in much of physics.

There was also a practical problem of scale. A one-kilogram standard can be compared with another to a few parts in a billion, but getting from a kilogram down to a milligram takes a long chain of comparisons, each adding error. By the time you reach a milligram, the uncertainty is a few parts in ten thousand, a real limitation for drug makers, chip fabs and chemists working with ever smaller samples.

And the kilogram had become an outlier. Time had once been defined by the spin of the Earth, the same steady rotation John Harrison’s sea clocks were built to keep pace with, but since 1967 the second has been defined by the vibration of caesium atoms. The metre had once been a platinum-iridium bar kept at the same bureau. In 1960 it was redefined in terms of light from krypton atoms, and in 1983 it was tied to the speed of light, fixed at exactly 299,792,458 metres per second. After 1960, the kilogram was the last base unit still defined by an object you could drop on the floor.

Weighing with electricity

The way out began with a British physicist named Bryan Kibble. In 1975, working at the National Physical Laboratory in Teddington, he came up with an improved kind of current balance, a device that weighs an object by balancing it against the push of an electromagnet. NPL built the first one, the Mark I, in 1978 with Ian Robinson and Ray Smith, and a better vacuum version, the Mark II, in 1990. It was called a watt balance, because it compares mechanical power with electrical power.

The idea works in two steps. In weighing mode, a test mass sits on a pan attached to a coil of wire hanging in a strong magnetic field, and a current through the coil is adjusted until its upward force exactly balances the mass’s weight. The trouble is that the force also depends on the strength of the magnet and the length of the wire, which are hard to measure precisely. So in moving mode, the mass is taken off and the same coil is driven up through the same field at a carefully measured speed, which generates a voltage. Combine the two runs and the awkward magnet-and-wire factor cancels out, leaving a simple relation: current times voltage equals mass times gravity times velocity.

What makes this more than a clever scale is how the current and voltage are measured. Two Nobel Prize-winning quantum effects, the Josephson effect and the quantum Hall effect, let labs pin voltage and resistance to the Planck constant, the tiny number at the heart of quantum mechanics. Add a laser interferometer to track the coil, an atomic clock for timing and a gravimeter to measure local gravity, which varies from place to place and even with the tides, and a Kibble balance links a mass on its pan to the Planck constant.

Before the switch, that link ran the other way. As long as the kilogram was defined by Le Grand K, a Kibble balance weighing a copy of it was really measuring the Planck constant. The plan was to measure the constant so precisely, in several labs, that it could be frozen at a fixed value, and then turn the instrument around to measure mass. The best results came from NPL’s original balance, which was shipped to the National Research Council of Canada in 2009, and from the NIST-4 balance in Gaithersburg, Maryland. In 2017, after more than 10,000 weighings, the NIST team reported the Planck constant with an uncertainty of 13 parts per billion. Kibble did not live to see the vote. He died in April 2016, and two months later metrologists renamed his invention the Kibble balance. NIST has even published plans for a tabletop version built from LEGO bricks that can weigh a few grams to about 1 percent.

Counting atoms in the roundest ball

A second, completely independent route went through chemistry. If you could count exactly how many atoms are in a known lump of matter, you could tie mass to the Avogadro constant, the number of particles in a mole, and through it to the Planck constant. An international collaboration called the International Avogadro Coordination set out to do exactly that, starting in the early 1990s.

Its counting device was a sphere of silicon, a material the chip industry already knew how to grow as flawless single crystals. Ordinary silicon is a mix of three isotopes, which makes the average atom’s mass uncertain, so the project used silicon enriched in Russia to nearly pure silicon-28. The crystal was grown at the Leibniz Institute for Crystal Growth in Berlin and cut into one-kilogram blanks. Then the blanks went to Australia, where master optician Achim Leistner and his team at CSIRO ground and polished them by hand, using methods New Scientist compared to the way Isaac Newton ground his lenses.

The resulting spheres, 93.75 millimetres across, were among the roundest objects humans had ever made. Leistner told New Scientist that if one were blown up to the size of the Earth, its highest hill would rise only about 3 to 5 metres. Germany’s national metrology institute, PTB, later repolished two of them after finding a thin film of metal contamination left by the polishing, and got the diameter of one to vary by less than 40 nanometres. With X-ray measurements of the crystal’s atomic spacing, laser measurements of the sphere’s volume and careful work on its oxide skin, the team could count the atoms. A one-kilogram sphere holds about 21.5 trillion trillion silicon-28 atoms.

The two methods were rivals in friendly competition, and that was the point. If electrical weighing and atom counting landed on the same answer, nobody could argue the result was an artifact of one technique. For a while they did not quite agree, and the vote was pushed back from 2014. By 2017 they did, comfortably within the strict accuracy targets the metrology committees had set.

The vote in Versailles

On November 16, 2018, at the 26th General Conference on Weights and Measures, held in Versailles, delegates from 60 countries voted on the new definitions. The roll was called nation by nation, and the vote was unanimous. “It was very emotional,” NIST physicist Stephan Schlamminger told The Guardian. “They did a roll call of each country. One got a sense of how big metrology is.”

The kilogram is now defined by fixing the Planck constant at exactly 6.62607015 × 10^-34 joule-seconds. Because that unit is built from kilograms, metres and seconds, and the metre and second were already fixed by the speed of light and the caesium atom, the value pins down the kilogram with no object involved. The same vote redefined the ampere, the kelvin and the mole by fixing the charge of an electron, the Boltzmann constant and the Avogadro constant, which is now exactly 6.02214076 × 10²³ per mole. The new definitions took effect on May 20, 2019, World Metrology Day, 144 years to the day after the Metre Convention was signed.

What happened to Le Grand K

Nothing dramatic. Nobody melted it down or put it in a museum. It is still in its vault under its bell jars, and still weighs, as far as anyone can tell, one kilogram, though now that statement comes with an uncertainty of about 10 micrograms, because the cylinder must be measured against the Planck constant like everything else. The roles have flipped. Before 2019, if Le Grand K and a Kibble balance disagreed, the balance was wrong. Now the cylinder is the one that can be wrong.

For shoppers nothing changed; the redefinition was designed so that a kilogram of apples weighs exactly what it did before. The change is in who can make a kilogram. Any well-equipped laboratory with a Kibble balance or a silicon sphere can now realize the unit from first principles, at any scale, without a trip to Paris and without a chain of comparisons back to a single cylinder. The metric system’s founders wanted units that belonged to nature rather than to any one country or object. It took 220 years and quantum physics, but the kilogram finally got there.

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