This is structural racism: the system is not self-correcting. Government has to intervene to break the cycle, and that is something that government has found it hard to do, even when the political winds were blowing in a direction favorable to civil rights.

Systemic racism is the subject of Michelle Adams’s “The Containment: Detroit, the Supreme Court, and the Battle for Racial Justice in the North” (Farrar, Straus & Giroux). The book, some five hundred pages long, is the story of a single Supreme Court case, Milliken v. Bradley, decided in 1974. That case concerned efforts to desegregate public schools in Detroit. It attracted a lot of attention at the time, and it remains a landmark case in civil-rights law. There are at least two previous books specifically about Milliken.

Adams, a Detroit native who teaches law at the University of Michigan, does not propose a new understanding of the facts or the law, but her book is passionate and well researched. It can also get a little in the weeds. The trial alone lasted forty-one days, and there is a sizable cast of characters. We get a full appreciation for the complexities of the campaign for racial justice from the book.

The Bradley in Milliken v. Bradley was a six-year-old named Ronald. Ronald was a student at Clinton Elementary School, in northwest Detroit. His mother, Verda, served as a lunchroom aide there, and she could see that the school was suffering from underfunding and neglect. Classes, which might have as many as fifty students, sometimes had to be held in trailers, owing to a shortage of space. When it snowed, the city didn’t bother to plow the schoolyard. It just threw some cinders on it.

Verda Bradley didn’t think that the reason for the neglect was mysterious. Ninety-seven per cent of the students at Clinton were Black. She believed that, if it were fully integrated, services would improve, and so would the quality of Ronald’s education. She was from Tennessee, a Jim Crow state. She had come to Detroit in 1942, as part of the Second Great Migration. When she arrived, the city was about nine per cent Black. By 1970, the year of the lawsuit, it was 43.7 per cent Black. Whites were moving to the suburbs, a trend that started after the war but was accelerated by urban unrest in the summer of 1967, during which at least forty-three people died and more than seven thousand were arrested.

Like many Black parents in the post-Brown v. Board of Education era, Verda was not interested in integration for its own sake. She simply believed that a school with a lot of white kids was going to get more resources than a school in which almost all the kids were Black. So she approached the local chapter of the N.A.A.C.P., which, in 1970, filed a class-action lawsuit in federal court. The defendant, William Milliken, was the Republican governor of Michigan.

The history of school desegregation—the history of Brown after Brown—is well known. After the decision came down, in 1954, Thurgood Marshall, who had argued the case before the Court, predicted that public schools would be integrated in five years and all of American society would be integrated in nine.

Things didn’t quite work out that way. In 1955, in a case known as Brown II, the Court ordered school systems to desegregate “with all deliberate speed,” a phrase that Marshall said would be interpreted as “S-L-O-W.” Slow turned out to be an understatement. Southern states resisted desegregating their public schools for years. In 1963, the year John F. Kennedy proposed a civil-rights bill, only two per cent of Southern Black children were attending schools with whites.

That started to change when the Justice Department and the Department of Health, Education, and Welfare began putting pressure on school districts to desegregate. Finally, in 1968, the Supreme Court put its foot down. In Green v. County School Board of New Kent County, it charged school boards that once operated a dual system with “the affirmative duty to take whatever steps might be necessary to convert to a unitary system in which racial discrimination would be eliminated root and branch.” A year later, in Alexander v. Holmes County Board of Education, the Court said that school desegregation must happen “at once.” The era of all deliberate speed was over.

“Root and branch” is a reference to systemic racism. The Court was saying that it was not enough to have mixed-race classrooms. Sending small numbers of Black children into schools with overwhelmingly white student bodies and virtually no Black adults in the building had been a disaster. The lesson was that, for integration to work in the way the Court had imagined with Brown, the whole system needed to be desegregated. The Court’s order in Green therefore extended to “every facet of school operations—faculty, staff, transportation, extracurricular activities and facilities.”

In 1968, then, the federal government finally seemed ready to make good on the vision of Brown: integrated schools as a step toward a post-racial society. The plaintiffs in the Milliken case had reason to believe that they might prevail.

They had two problems, neither insurmountable. The first one was shared by all Northern school-desegregation cases. Brown had established that it was unconstitutional for a state to have a law mandating segregated schools, and Michigan had no such law. Since 1869, segregation in Detroit public schools had been outlawed by the state’s Supreme Court. There was nothing to strike down. But, in a 1961 case, a federal court in New York had ruled that gerrymandering school-district lines could count as state-ordered segregation, so there was a legal lifeline.

The other problem was that, because of the racial imbalance in the city, no integration plan could be effective unless it included the suburbs, where the residents and the schools were virtually all white. What was needed, therefore, was an interdistrict, or “metropolitan,” remedy. In order to get a court to endorse this solution, the plaintiffs had to show that what looked like de-facto segregation, just the pattern resulting from personal housing choices, was a result of state action.

The N.A.A.C.P. amassed an impressive amount of evidence, which it used to convince the district-court judge Stephen Roth, who initially seemed unsympathetic, that school segregation was the result of government and not just real-estate-industry policies. The evidence showed that the Detroit school board had made decisions about districting, sites of new school construction, feeder schools, and school transportation with a view to maintaining a racially segregated system.

Housing patterns, too, were the result of discriminatory actions whose effects had compounded over decades. Government decisions about the location of public-housing and urban-renewal projects had been guided by racial considerations. Redlining practices used by the Federal Housing Administration and the federally funded Home Owners’ Loan Corporation had made it almost impossible for Black people to get mortgages. By mid-century, more than eighty per cent of the properties outside central Detroit had racial covenants—which were generally clauses in deeds signed by white homeowners pledging not to sell or rent to Black people.

In addition, the National Association of Real Estate Boards’ “Code of Ethics,” adopted in 1924, specified that “a Realtor should never be instrumental in introducing into a neighborhood a character of property or occupancy, members of any race, or nationality or any individuals whose presence will clearly be detrimental to property values in that neighborhood.” (The explicit reference to race was eliminated from the code in the fifties.) Black real-estate agents in Detroit did not have access to white agents’ listings of homes. Presiding over all this was the state government, whose constitutional duty it was to provide for the equal protection of its citizens.

There was a ton of evidence, but it was agreed that the most powerful witness for the plaintiffs was a ten-by-twenty-foot map of the city that showed the evolution of residential segregation. The map was placed, for the duration of the trial, in the judge’s line of vision, a constant reminder of racial separation. At one point, Roth allowed a question about whether a map wouldn’t show similar concentrations of Poles, an ethnic group with a reputation for insularity. He was informed that Poles in Detroit were less than half as segregated as Blacks. This seemed to surprise him.

In June, 1972, Roth issued the metropolitan remedy that the N.A.A.C.P. wanted. He brought fifty-three school districts in surrounding suburbs and small cities into the plan and required the authorities to distribute students among districts to achieve integration throughout the system. The ruling affected nearly eight hundred thousand students, and distributing them meant busing, or, as opponents called it, “forced busing.”