The exhibit describes how the president’s fluctuating medical condition became a national obsession in the summer of 1881. His doctors issued daily medical briefings, which were rapidly disseminated by telegraph and published in newspapers across the country. In response, the White House received letters by the bushel basket.

Image Two bullets hit President Garfield. One grazed his arm; the second pierced his first lumbar vertebra, above. Credit... National Museum of Health and Medicine, Armed Forces Institute of Pathology

“One man suggested that they turn the president upside down and see if the bullet would just fall out,” Dr. Barbian said.

The exhibit also includes an image of the metal detector designed by Alexander Graham Bell to search for the bullet. It was composed of a battery and several metal coils positioned on a wooden platform and was connected to an earpiece.

Jeffrey S. Reznick, senior curator at the museum, said the device was designed to create an electromagnetic field, which would be disrupted in the presence of a metal object. The disruption would cause the device to emit a clicking sound through the earpiece.

“Electricity and magnetism were just being appreciated as ways to explore the body’s interior,” Dr. Reznick said.

Bell’s invention failed on two occasions to pinpoint the bullet’s location. Historians say this may have been because the device picked up metal coils in the president’s mattress, or because Bell searched only on the right side of Garfield’s body, where the lead physician, Dr. Doctor Willard Bliss — Doctor was his given name — had come to believe the bullet was lodged.

In early September, the president was moved from the White House to a cottage in Elberon, N.J., on the shore.