Cities stink, and their poor die young. The English social reformer Edwin Chadwick publishes a report on the living conditions of Britain’s working people, showing that those in crowded, filthy streets die far younger than those in clean ones. He and most doctors of the day blame miasma, bad air rising from rotting filth, sewage, and swamps, for cholera, typhus, and fevers. “All smell is, if it be intense, immediate acute disease,” Chadwick later tells a committee of Parliament. His cure is to clean up: drains, sewers, and fresh water. It saves many lives, though maybe not for the reason he thinks.

In Vienna’s General Hospital, mothers beg not to be taken to the First Clinic. There, where doctors and medical students deliver babies, childbed fever killed 459 of the 4,010 women who gave birth in 1846: one in nine. In the Second Clinic next door, run by midwives, it killed one in thirty-six.

The Hungarian physician Ignaz Semmelweis, an assistant in the First Clinic, rules out cause after cause, bad air among them: both clinics breathe the same air. Then, in March, a colleague, Jakob Kolletschka, cuts his finger during an autopsy and dies of an illness just like childbed fever. The doctors, Semmelweis realizes, come to the mothers straight from dissecting corpses, carrying something from them on their hands. In May he makes them wash their hands in chlorinated lime. Deaths in his clinic fall from 18 in 100 births in April to 2 in June. They had dropped that low before, only to climb again. This time, they stay low.

In October, the doctors examine a woman with a foul-smelling cancer of the womb first, wash only with soap, and go on to twelve women in labor. Eleven of them die. No corpse was involved, so Semmelweis widens his theory: any decaying matter can cause the fever, from the living too, and hands must be washed in chlorine between every examination.

Many of his colleagues remain unconvinced, and two years later he loses his post. Back in Hungary, as head of a maternity ward in Pest, he brings deaths down to under one in a hundred. But when his book finally appears in 1861, most doctors reject it, and he answers them with furious open letters, calling them murderers. In 1865, colleagues have him committed to an asylum in Vienna. Beaten by the guards, he dies two weeks later, at 47, of an infected wound, much like the infections he fought.

On the night of August 31, cholera explodes in Soho. Within ten days, more than 500 people living within 250 yards of one street corner are dead. The English physician John Snow, who has long argued that cholera spreads through water, marks where the dead lived. They cluster around the public pump on Broad Street. The exceptions fit too: a nearby workhouse with its own well loses only 5 of its 535 inmates, and none of the more than 70 men at the brewery, who drink beer, die.

On September 8, at Snow’s urging, the parish takes the handle off the pump. The outbreak is already waning by then, as Snow admits, with so many dead or fled. A local curate, Henry Whitehead, at first skeptical, later finds how the well was fouled: by a sick baby’s diapers, rinsed into a cesspool three feet from it.

Snow finds a test that no one could have planned. In South London, two water companies supply the same streets, their pipes running side by side, so that next-door neighbors often drink different water. The Southwark and Vauxhall Company takes its water from the Thames in London, below the sewers that empty into it. The Lambeth Company moved its intake upriver in 1852, above them. In the first seven weeks of the 1854 epidemic, houses on Southwark and Vauxhall water lose 315 people to cholera for every 10,000 houses, and those on Lambeth water 37. Snow publishes it all in the new edition of his book. The government’s General Board of Health isn’t persuaded: its committee still blames the air.

Microbes have been seen through microscopes since the 1670s, when the Dutch draper and lens maker Antonie van Leeuwenhoek first saw what he called animalcules. But where do they come from? Many naturalists believe they arise on their own, from the broth or the rotting matter they’re found in. The French naturalist Félix Pouchet defended this “spontaneous generation” in a book in 1859.

The French chemist Louis Pasteur boils broth in flasks whose necks he has drawn out into long, bent curves, like a swan’s. Air can get in, but the dust it carries, with whatever germs ride on it, settles in the low bend. The broth stays clear for as long as he cares to watch. Tip a flask so that the broth touches the bend, though, and in a few days it teems with life. The Academy of Sciences had offered a prize for experiments that would show whether life can arise on its own, and awards it to Pasteur. Life, it seems, comes only from life, even at its smallest.

Pasteur puts the finding to work. In 1865, he patents a way to keep wine from spoiling: heat it gently, enough to kill the microbes in it, without boiling it. The method, named pasteurization after him, is later applied to milk, once a common carrier of tuberculosis and typhoid, and makes it far safer. Today it’s used on milk, juices, and much else we eat and drink, saving uncountably many lives.

In the hospitals of the day, a broken bone that pierces the skin often means death: the wound festers, and gangrene sets in. Surgeons blame the bad air of their wards. The English surgeon Joseph Lister, working in Glasgow, reads Pasteur and draws a different conclusion: wounds go bad the way broth does, because germs get into them. He dresses wounds with carbolic acid, which kills germs, and washes his hands and instruments in it.

In 1867 he reports his first cases: open fractures that would once have meant amputation heal cleanly. Three years later he counts the deaths after amputations in his wards: 16 of 35 patients before he began, 6 of 40 since, in the same wards with the same air.

Twenty years earlier, in Vienna, Semmelweis saved mothers the same way, with chlorine on the doctors’ hands, and was ignored, though he blamed decaying matter, not living germs. Lister doesn’t know of him yet, but his germs answer Semmelweis’s decaying matter all the same.

For the first time, one particular germ is shown to cause one particular disease. Anthrax kills cattle and sheep across Europe, and rod-shaped bacteria had been seen in the blood of animals that died of it. The German physician Robert Koch, a district medical officer working in a makeshift laboratory in his home in Wollstein, grows these bacteria in drops of fluid from cattle’s eyes, outside any animal, passing them from drop to drop for eight generations. Injected into mice, the last generation still kills them with anthrax. He also finds that the bacteria form hardy spores, which survive in the soil for years, explaining why some pastures stay deadly. Bad air can’t be grown in a drop of fluid.

One of Germany’s most famous scientists drinks cholera to prove a point. Koch identified the cholera germ, a comma-shaped bacterium, in 1883 and 1884, though the Italian anatomist Filippo Pacini had described it in 1854. The German chemist and hygienist Max von Pettenkofer isn’t convinced: a germ alone, he holds, can’t cause cholera without the right conditions in the soil. That summer and fall, cholera kills about 8,600 people in Hamburg. On October 7, Pettenkofer, aged 73, drinks a culture of the germ in front of witnesses, with baking soda to neutralize his stomach acid. He gets nothing worse than diarrhea.

Koch, sent to Hamburg, finds that Altona, the next town over, on the same soil and under the same sky, is largely spared. The difference is the water: Hamburg drinks it unfiltered from the river Elbe, while Altona, which draws its water from the river below Hamburg, sewage and all, filters it.

Can a germ float from one person to the next? Since the 1930s, the American sanitary engineer William Wells had argued that tuberculosis spreads on droplets coughed or breathed out, so small that they stay in the air. With the American physician Richard Riley, he pipes the air from a tuberculosis ward at a veterans’ hospital in Baltimore into a room of guinea pigs. Over the years, dozens of them catch the disease. In a second room, guinea pigs breathe the same air, but with ultraviolet lamps killing the germs in it first, and none fall ill.

So the air was never bad in itself, as the miasma theory had it. What makes it dangerous is the germs riding in it, as they rode on the dust in Pasteur’s flasks.

Today, germs are known to cause most infectious diseases: bacteria like the ones Koch grew, viruses too small for an ordinary microscope, and fungi and parasites too. The viruses of measles and the flu, among other germs, spread through the air.

Semmelweis never found out what caused childbed fever: he blamed decaying matter, not germs. But he took an idea seriously, tested it, acted on it, and stood by it when almost no one else would. Rejected in his lifetime, he is remembered today as the savior of mothers, and Budapest’s medical university bears his name.