In both of the books she has written about American presidents, Candice Millard has zeroed in on events that other historians largely overlook. Her first book, “The River of Doubt,” followed Theodore Roosevelt’s strenuous efforts to regain his confidence after his failed 1912 third-party bid for re-election and described his near-disastrous journey down the Amazon tributary of the title. The details of this trip were hardly unknown, but they were easily overshadowed by other aspects of Roosevelt’s hugely eventful life. Ms. Millard turned a relative footnote into a newly mesmerizing story.

Now she has chosen an even more neglected and fascinating subject: the 1881 assassination attempt on President James A. Garfield and the dreadfully misguided medical efforts to save his life. Had it not been for this botched treatment, Ms. Millard contends, Garfield would have been one more Civil War veteran walking around with a bullet lodged inside him. Had he survived to serve more than 200 days in office, he might have been much more familiar than he is to many students of White House history.

“Destiny of the Republic,” which takes its title from a fateful speech given by Garfield at the 1880 Republican National Convention, has a much bigger scope than the events surrounding Garfield’s slow, lingering death. It is the haunting tale of how a man who never meant to seek the presidency found himself swept into the White House. It rediscovers Garfield’s more surprising accomplishments. He was, among other things, a teenage worker on the Erie and Ohio canals, a brigadier general and a scholar who devised an original proof of the Pythagorean theorem at some point during the 17 years he spent in Congress.

Garfield’s transformative effect on the contentious 1880 Republican convention put an end to all that. (Kenneth D. Ackerman’s “Dark Horse” gives a full account of the convention.) At an exhausting point when more than 30 ballots had been cast, Garfield rose to speak out against the chaotic “human ocean in tempest” he was witnessing. He injected a voice of reason. “I have seen the sea lashed into fury and tossed into spray, and its grandeur moves the soul of the dullest man,” he said. “But I remember that it is not the billows, but the calm level of the sea, from which all heights and depths are measured.”

Delegates began unexpectedly throwing their votes to Garfield. He had not been a presidential candidate; now suddenly he was the Republican nominee. When he and his family were swept into the White House, Garfield wrote: “My God! What is there in this place that a man should ever want to get into it?”

Garfield particularly bristled at the calling hours a president then traditionally kept. During this time he met members of the public, many of them office seekers. He quickly noticed a particularly obnoxious visitor: Charles Guiteau, whose pestering was so extreme that Garfield cited him as an “illustration of unparalleled audacity and impudence.” The grandiose and frankly creepy Guiteau wrote so many letters that he became enough of a nuisance to be noticed by other members of the Garfield administration and family. A former lawyer and theologist who earned himself the nickname “Charles Gitout,” he met Garfield on numerous occasions before deciding to shoot him.

Guiteau, whose story has also been much overlooked, made no secret of his plotting. In a letter explaining his plans to the American people, he reasoned: “It will be no worse for Mrs. Garfield, to part with her husband this way, than by natural death. He is liable to go at any time any way.” He scouted jails, deciding where he wanted to be incarcerated. He left instructions (“please order out your troops”) for Gen. William Tecumseh Sherman, who would be marshalling troops for Guiteau. They protected the assassin from being killed by a mob before he could go to trial.

“Destiny of the Republic” pursues many threads at first, including the political spoils system exploited by Senator Roscoe Conkling (who forced Chester A. Arthur on Garfield as a vice president); Alexander Graham Bell’s experiments with induction balance; and Joseph Lister’s much-mocked claims that antisepsis was crucial in warding off infection. And then midway through the book these elements converge in Ms. Millard’s gripping account of Guiteau’s attack. After Garfield was shot at the Baltimore and Potomac train station on July 2, 1881, doctors egregiously probed Garfield with hands and instruments, none sterilized. The president’s fever, vomiting and signs of infection were taken as evidence that his body was trying to heal.

The medics explored the wrong side of Garfield’s torso — and under the orders of the senior presiding doctor, D. Willard Bliss, only the wrong side — in efforts to find and remove the foreign body. In one of the many stunning moments that Ms. Millard describes, Bell was allowed to use his method of metal detection only on the bullet-free side of the president and was baffled by the faint, inconclusive noises that his test produced. It would be discovered, too late, that the sounds had come from metal bedsprings in the mattress beneath Garfield.

“His ultimate place in history will be far less exalted than that which he now holds in popular estimation,” The New York Times wrote after Garfield died. This book rebuts that claim. It restores Garfield’s eloquent voice, his great bravery and his strong-willed if not particularly presidential nature. Ms. Millard shows the Garfield legacy to be much more important than most of her readers knew it to be.