And eugenics was of particularly keen interest to doctors, including Albert Priddy, the superintendent of Ms. Buck’s institution. “He saw it as the best way to rid the world of the sort of patients he spent all of his days ministering to,” Mr. Cohen explains. His patients, in his view, were miserable — and a future burden on the state, sure to lead to an uncontainable problem of “pauperism and criminality.”

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Of all the tools to stem the tide of feeblemindedness, sterilization was by far the most efficient. During the Progressive Era, a number of states had enacted compulsory sterilization laws, including California and Connecticut. So bullish was Dr. Priddy to do the same for Virginia that he worked in concert with a methodical, meticulous local lawmaker, Aubrey Strode, to design a statute that would withstand the test of the highest court of the land. Ms. Buck was the test case.

“There was only one problem,” Mr. Cohen writes. “Carrie had no idea what was going on.”

An unsuspecting innocent, an ambitious country doctor, a nation briefly infatuated with a despicable ideology — these would all seem to be the elements of a captivating narrative. Yet “Imbeciles” is often a boggy read, and a disorganized one at that. Mr. Cohen, now a senior writer at Time magazine, repeats himself early and often, which suggests that the basic outline of a propulsive story eluded him. (Strange, given that he’s written brisk, readable narratives before, including “Nothing to Fear” and “The Perfect Store.”) He takes the reader down a couple of biographical sinkholes, giving us pages of back stories when a simple paragraph would have done the trick.

Most crucially, he writes as if he’s retrying Buck v. Bell. But we already know the decision was an egregious miscarriage of justice — it was the unenlightened product of an unenlightened time. And the case itself was unsuspenseful. The fix was in from the start.

We learn early on that Ms. Buck’s lawyer, Irving Whitehead, had close personal and professional ties to the Virginia Colony for Epileptics and Feeble-Minded — the superintendent paid his legal fees — which meant he made no efforts to mount a serious defense for his client. He never called on Ms. Buck’s teachers to confirm that she’d acquitted herself well in school; more fundamentally, he never asked Ms. Buck to testify on her own behalf. His petitions for appeals were always brief and incomplete, making insufficient use of precedent.

“He was an impostor,” Mr. Cohen writes.

What this means, from the reader’s point of view, is that although the courtroom scenes involving Mr. Whitehead are tragic, they are utterly devoid of drama.

By the time the case made its way to the desk of Justice Holmes, himself an eager eugenicist, readers are hardly surprised by his chilling opinion. Nor are they surprised that his Supreme Court colleagues, many of them enthusiastic race purists, overwhelmingly sided with him.