The supreme arbiter of mass for humankind is a polished cylinder of platinum alloy just smaller than a golf ball. It was cast in London in 1879, unveiled a decade later in a ceremony in France, and now resides beneath three nested bell jars in a vault outside Paris, somewhere in a manor overlooking the Seine. (Its handlers prefer not to disclose its precise location.) Every scale on earth is calibrated to this artifact. Every dumbbell, every microdose of medicine, and every sack of cement weighs what it weighs, in effect, because the lump of metal weighs what it weighs. The lump is called the International Prototype Kilogram, or I.P.K. As its name suggests, it weighs, precisely and always, by definition, one kilogram.

By international consensus, the kilogram is the world’s universal base unit of mass, the ur-unit from which all others are derived. This rule applies even in the United States, where the government has been quietly using metric units since 1893. Insofar as the notion of the American avoirdupois pound has any official meaning, it is by relation to the kilogram, of which, by law, it is 0.45359237. This is not to suggest that the kilogram possesses some inherent authority. Like all units of measure, it is a tool entirely of man’s making. It exists in nature no more than a pound does, or a unicorn. It is an invented abstraction defined by an invented object. The object is the I.P.K.

Every forty years or so, the I.P.K. is taken out for comparison with the various copies that have been dispatched across the earth to “disseminate” the kilogram. These calibrations insure that the kilogram as the Argentines know it, for instance, matches the kilogram in use in Kenya, and that all kilograms everywhere match the unit defined by the I.P.K. This is a perfectly sensible system, but it depends entirely upon our trust in the I.P.K., and that trust is more tenuous than you might think. On Friday, however, at the general conference of the International Bureau of Weights and Measures, scientists intend to fix the kilogram for posterity.

For a sense of what they will, exactly, be fixing, consider the case of K20—so named because it is copy No. 20 of the I.P.K.—which serves as the primary American mass standard. In 2010, when it was sent to France for calibration at the International Bureau of Weights and Measures, it was discovered to be about thirty-five micrograms heavier than anticipated. This is no more than the mass of two or three thumbprints. But the discrepancy implied that all American mass measurements were slightly off, and metrologists are a fastidious bunch. “This is, for this crowd, very, very high-stakes stuff,” Jon Pratt, a metrologist at the National Institute of Standards and Technology (NIST), in Maryland, told me. NIST, which is responsible for K20, could find no explanation for the increase. Pratt’s boss called the International Bureau of Weights and Measures. “They were a little snarky with her,” Pratt said. “They said, ‘No, no, you’ve got a problem over there at NIST. You’ve got some contamination in your system.’ ” NIST was obliged to issue a correction to the U.S. mass scale, and to recalibrate all high-precision kilogram weights in the country. The process took years.

It turns out the thirty-five micrograms never existed. When K20 was calibrated, in France, it had been compared not directly with the I.P.K. but with the so-called working standards of the International Bureau of Weights and Measures. (The bureau typically goes by its French acronym, B.I.P.M.) In 2014, the B.I.P.M. checked the working standards against the I.P.K. “They do this,” Pratt told me, “and, sacré bleu—thirty-five micrograms! Whoops.” It was not K20 that had gained mass, it seemed, but the working standards that had lost it. The B.I.P.M. concluded that the standards had been worn down, ever so slightly, from being repeatedly placed in balance pans.

That physical objects change and fluctuate is a problem for a mass system that depends upon them, not least because this inconstancy extends to the I.P.K. itself. At the B.I.P.M., the I.P.K. is stored alongside six “witness” kilograms. Over the course of the twentieth century, the I.P.K. and the witnesses diverged steadily in mass. No one knows why. The I.P.K. could be losing mass, or the witnesses could be gaining it, or they could all be changing at once. It’s extremely unlikely, though, that the I.P.K. has the same mass as it did at the outset, and it’s impossible to know how much it has changed.

On its face, the solution seems easy enough. I asked Terry Quinn, a former director of the B.I.P.M., why one could not simply weigh the I.P.K.

“When you say ‘weigh it,’ ” Quinn said, “what do you mean?”

“As opposed to comparing its mass with the others,” I said. “You know, placing it on a scale that reads out to a high degree of—”

“Well, there’s no such thing,” he said. “Today, every balance in the world that gives a number when you put something on it, that number is ultimately linked to the I.P.K.”

“So if that balance tells you that the I.P.K. is not a kilogram, it’s the balance that’s wrong, and not the I.P.K.,” I said.

“Well,” Quinn replied, “it can never tell you that the I.P.K. is not a kilogram.”

In a mass system derived from a physical artifact, the unit accommodates the artifact, and not the other way around; which is to say the unit is constantly subject to change. It is a relief to mass metrologists, then, that the unit is about to be revised. On Friday, the kilogram will receive a new definition.

The kilogram, and the metric system to which it belongs, are products of the utopian rationalism of the French Revolution. Ancien régime France, like most nations of the time, contained a mess of competing systems of measurement, with standards varying by region, town, and trade. At the revolution, the country’s philosopher-scientists proposed a unified system, the units of which would be derived from an eternal feature of the natural world; they would be intelligible across all times, it was hoped, and by all peoples.

As the system’s basis, the Academy of Sciences settled on the quarter-meridian, the distance from the equator to the North Pole. The new, “natural” unit of length, to be called the mètre, would be defined as one-ten-millionth of this distance. The new unit of mass would be derived from the metre, and would be natural by extension; it would be equal to the mass of a cube of pure liquid water, one-tenth of a metre high, deep, and wide, and would come to be known as the kilogramme. Both units would be scaled in tens, and would together compose the système métrique décimal. “Never has anything grander and simpler and more coherent in all its parts come from the hands of men,” Antoine Lavoisier, the celebrated chemist, declared in 1793.

The meridian had to be measured precisely before the new units could be fixed, though, and it was another six years before the surveyors returned to Paris with a number. It has since been determined that their measurement was slightly short, but from it the metre was calculated, and then the kilogram, and a platinum prototype of each was presented to the French legislature on June 22, 1799. (The date was recorded as 4 messidor, year VII, the metric system being just one of the revolution’s many social innovations. Another, the guillotine, had claimed Lavoisier a few years earlier.) The president of the upper chamber hailed the Academy’s “immortal service” to the French Republic and the “kindness it has done for mankind.” The metric system, he said, ought to “breach the borders that separate the peoples of the world.”