The story of the fifteenth element began in Hamburg, in 1669. The unsuccessful glassblower and alchemist Hennig Brandt was trying to find the philosopher’s stone, a mythical substance that could turn base metals into gold. Instead, he distilled something new. It was foamy and, depending on the preparation, yellow or black. He called it “cold fire,” because it glowed in the dark. Interested parties took a look; some felt that they were in the presence of a miracle. “If anyone had rubbed himself all over with it,” one observer noted, “his whole figure would have shone, as once did that of Moses when he came down from Mt. Sinai.” Robert Boyle, the father of modern chemistry, put some on his hand and noted how “mild and innocent” it seemed. Another scientist saw particles in it twinkling “like little stars.”

At first, no one could figure out what the Prometheus of Hamburg had stolen. After one of Brandt’s confidants provided a hint—the main ingredient was “somewhat that belong’d to the Body of Man”—Boyle deduced that he and his peers had been smearing themselves with processed urine. As the Cambridge chemist Peter Wothers explains in his new history of the elements, “Antimony, Gold, and Jupiter’s Wolf” (Oxford), Brandt’s recipe called for a ton of urine. It was left out in buckets long enough to attract maggots, then distilled in hot furnaces, creating a hundred and twenty grams of “cold fire.” Brandt believed that, if he could collect enough of this substance, he might be able to create the philosopher’s stone. In 1678, the Duke of Saxony asked him to collect a hundred tons of urine from a garrison of soldiers and render it into what Boyle and others soon started to call phosphorus—Latin for “light-bearer.”

The soapy phosphorus that Brandt cooked up was a curiosity. But, in England, Boyle began producing it in a purer, more solid form, which turned out to be highly flammable. Another scientist toying with Boyle’s phosphorus found that, “if the Privy Parts be therewith rubb’d, they will be inflamed and burning for a good while after.” Boyle, for his part, wondered whether it could be harnessed as a starter for gunpowder. (His assistant, the apothecary Ambrose Godfrey, set his head on fire and burned “two or three great holes in his breeches” while investigating the substance.) The phosphorus industry grew throughout the eighteenth century, in part because physicians wrongly believed that it had medicinal value. In the eighteen-hundreds, match producers found that wood splints tipped with phosphorus were less dangerous than their sulfur-coated predecessors; not long afterward, the discovery that electric furnaces could extract phosphorus from ore at a large scale led to the development of explosives. In the Second World War, in what Wothers calls “a tragic twist of fate,” Hamburg, Brandt’s home town, was destroyed by Allied bombers dropping phosphorus munitions.

Wothers finds many such twists in the stories hidden behind the squares of the periodic table. Antimony (element No. 51) is a lustrous mineral; four thousand years ago, people carved vases out of it, and it appears in cosmetic regimes described in the Old Testament. According to an account given by the seventeenth-century apothecary and alchemist Pierre Pomet (offered up by Wothers as possibly apocryphal), antimony got its name from the story of a German monk who fed it to his fellow-brethren. The monk had given some to a few pigs, who vomited at first but then grew healthy and fat. Unfortunately, every monk who ingested it died. “This therefore was the reason of this Mineral being call’d Antimony,” Pomet wrote, “as being destructive of the Monks.” (In a less fatal episode, a nineteenth-century doctor and his friends consumed fifteen milligrams of tellurium each: they had garlic breath for eight months.)

The names of the elements have long been a source of contention and incomprehension. Hydrogen, Wothers points out, is Greek for “water-former,” while oxygen is Greek for “acid-former”; in fact, it’s hydrogen that bonds together with other elements to make acids and oxygen that bonds hydrogen to make water. “Aluminium,” Charles Dickens wrote, in 1856, is “a fossilized part of Latin speech, about as suited to the mouths of the populace as an ichthyosauros cutlet or a dinornis marrow-bone.” (It has its root in the Latin for “bitter salt,” after the clay from which the once-precious metal was derived; Dickens’s suggestions—“loam-silver” and “glebe-gold”—weren’t much better.) The French chemist Marguerite Perey, a protégée of Marie Curie, discovered an element of her own, in 1939. She wanted to call it “catium,” to honor the particle’s strong attraction to cathodes, devices used to send electricity through a chemical substance; Curie’s daughter, Irène Joliot-Curie, worried that English speakers would associate the element with house cats. Perey, being French, decided to call it francium instead.

Many historians date the invention of the periodic table to the publication, a hundred and fifty years ago, of a textbook by the Russian chemist Dmitri I. Mendeleev. But Eric Scerri, the author of “The Periodic Table: Its Story and Its Significance” (Oxford) and a philosopher of chemistry at U.C.L.A.—he studies the history of questions such as “What is an element, really?”—bristles at the notion that Mendeleev revolutionized science when he brought chemical periodicity into clear relief. Periodicity—the idea that larger atoms chime with smaller atoms in a regular way, like notes on a keyboard—didn’t emerge as a bolt from the blue, Scerri argues. It came into focus through the work of a host of scientists; as it did so, ideas that by then were long disdained, such as alchemy, turned out to be right in some respects, and essentially wrong ideas, such as the irreducibility of the elements, turned out to be productive ways of thinking, anyway. Some of the eighteenth- and nineteenth-century chemists who began to notice patterns among certain elements were actually retracing the paths of ancient Greek atomists such as Democritus and Leucippus, who, in the fifth century B.C., had argued that invisible and indivisible particles made up everything we could see and touch. The atomists believed that those particles were myriad in shape and size, and that their perceptible properties came from the structures they formed when they hooked together.

By the Middle Ages, atomistic ideas had been mostly eclipsed by Aristotle’s theory that four principal elements—fire, earth, water, and air—combined to form the various objects in the universe. But atomism never went away completely. Renaissance scholars believed in a wide variety of elemental schemes. Wothers’s book reprints some of the diagrams that mixed these ideas in advance of the periodic table: a seventeenth-century engraving of the “seven metals” shows seven Roman gods brandishing ancient chemical symbols (the deities reminded viewers that iron was from Mars and copper from Venus); another shows the seven metals and Aristotle’s four elements in a triangular arrangement. Ringing the whole diagram is a Latin motto: “Although I am invisible, I am nonetheless the father and mother of all visible earthly bodies.”

You didn’t have to be a scholar, of course, to believe in a world made up of more than four elements. Seventeenth-century miners, Wothers writes, distinguished between different kinds of air: they called the lighter air that swirled at the top of caves “fire-damp,” because it easily burst into flames, and the heavy clouds that hung near the ground “choke-damp,” because they made it hard to breathe. In the eighteenth century, locals dubbed a cave near Naples the Grotta del Cane: dogs who wandered into the cave, unable to raise their heads above the gas seeping out of the Earth, soon began to choke to death; once returned to the open air, the animals would revive.