Their ship was going down. That much was clear as four U.S. Army chaplains helped hustle fellow soldiers onto lifeboats after a German torpedo struck the USS Dorchester during World War II.

Then, the life jackets ran out, and the chaplains made a brave choice: They handed over their own vests and stayed aboard the sinking ship.

Rabbi Alexander Goode, 32, of the District was among the chaplains who gave up their lives that day. On Monday, he and 13 other rabbis who have died while serving in the U.S. military got their due in a monument in Arlington National Cemetery.

The monument honoring Jewish chaplains corrects an oversight on Chaplains Hill, where the first monument honoring clergy members was erected in 1926. A separate monument for 134 Protestant chaplains was built in 1981, and another one, to honor 83 Catholics, eight years later.

“I think it was purely an oversight, but once they realized it, the House and the Senate moved quickly,” said Jerry Silverman, president and chief executive of the Jewish Federation of North America.

The two-hour service in the cemetery’s amphitheater brought together Jewish veterans from across the country, as well as family members of the rabbis, members of Congress and military officials.

“It only took 20 minutes for the ship to go down,” Army Staff Sgt. Ernie Heaton, one of the few remaining survivors, said of the panic after the USS Dorchester was struck.

The ship was sailing off the coast of Greenland. Soldiers grabbed all of the life jackets available, but there were not enough. Heaton said he never forgot the image of the four chaplains locking arms, singing a hymn as the ship sank.

“Men were screaming, and I saw the chaplains. They were together, and they didn’t have their life preservers on,” said Heaton, who spent nine hours in the water before he was rescued.

The four chaplains who died aboard the USS Dorchester, known as the Immortal Chaplains, were Goode, a graduate of Eastern High School who never got the chance to return to the Washington Hebrew Congregation; George Fox, who was Methodist; Clark V. Poling, of the Reformed Church in America; and John P. Washington, a Catholic.

Maj. Gen. Cecil Richardson said those who serve as military chaplains are much more than clergy in military uniforms. “They lived the life of warriors,” he said.

Jewish leaders who spoke fought back tears. Members of the West Point Jewish cadet choir sang in Hebrew and English. “This was a very special day for the country and my family,” said Paul Fried, Goode’s son-in-law.

The 13 other rabbis who have died in uniform are: Nachman S. Arnoff, in an Army truck accident in 1946 at Camp Kilmer, N.J.; Meir Engel, of heart disease in 1964 in a Saigon hospital; Frank Goldberg, in a Jeep accident in 1946 in Austria; Henry Goody, after being hit by a streetcar at 14th and Upshur streets NW in 1943; Joseph I. Hoenig, of cerebral hemorrhage in 1966; Samuel Hurwitz, in 1943 in a military hospital in Temple, Tex.; Herman L. Rosen, who drowned just before reporting to chaplain school; Samuel Rosen, in a plane crash in 1955; Solomon Rosen, in 1948 after his plane exploded over Oklahoma; Morton Singer, in a plane crash in 1968; David Sobel, in an accident in Thailand in 1974; Irving Tepper, in action in France in 1945; and Louis Werfel, in 1943 after his plane crashed in the North Algerian mountains.