Vice President Joe Biden speaks at the 18th annual Tragedy Assistance Program for Survivors (TAPS) Seminar May 25 in Arlington, Va. (Win McNamee/Getty Images)

Vice President Biden, speaking Friday to families and friends of military personnel killed in action, gave a powerful retelling of the death of his wife and daughter 40 years ago — saying he’d realized then how grief might push a person to suicide.

“For the first time in my life, I understood how someone could consciously decide to commit suicide,” Biden told a meeting of the Tragedy Assistance Program for Survivors at a hotel in Crystal City. The group offers counseling to relatives and friends of military personnel who have died. It was holding its 18th annual military survivor seminar.

“Not because they were deranged, not because they were nuts,” Biden continued, according to a transcript. “Because they’d been to the top of the mountain, and they just knew in their heart they’d never get there again, that it was never going to get — never going to be that way ever again. That’s how an awful lot of you feel.”

In 1972, just after the Delaware Democrat was first elected to the Senate, his wife, Neilia, and his 13-month-old daughter, Naomi, were killed in a car crash. Biden’s two sons — Beau, then 3, and Hunter, 2 — were grievously injured but survived.

On Friday, Biden told the military families how low the crash had brought him. “I probably shouldn't say this with the press here, but — no, it’s more important — you’re more important,” he said.

Biden had actually told the story before, on page 80 of his 2007 memoir, “Promises to Keep.”

“I began to understand how despair led people to just cash it in,” Biden wrote.

On Friday, that story was a powerful section of a speech that illustrated Biden’s particular style of rhetoric: frequently meandering, slightly pompous but movingly personal.

Biden often veered from the topic at hand — once, to tell the story of how he proposed to his current wife, Jill, five times before she said yes. He referred to himself, oddly, as “one of those folks they called the chairman of the Foreign Relations Committee.”

And, in a manner as unpolished as a living-room conversation, Biden told of climbing back out of grief.

“I have to tell you, I used to resent — I knew people meant well. They’d come up to me and say, ‘Joe, I know how you feel,’ ” Biden said. The audience laughed.

“Right?” They clapped.

“You knew they meant well. You knew they were genuine. But you knew they didn’t have any damn idea how you felt,” Biden said to laughter. “Right? Isn’t that true?”

Biden talked about his internal conflicts, as he tried to start another relationship after his wife’s death. “You’re going to go through periods when, after a while, you’ll see somebody you may have an interest in, and you’re going to feel guilty as hell. You’re going to feel this awful, awful, awful feeling of guilt,” he said.

Biden did not look like a vice president giving a speech: He hunched over, he looked down at his hands, he spoke at times haltingly and at times through clenched teeth.

And he told the story of his slow recovery — relying on family members and calling other people who’d been through the same kind of loss.

Biden said another elected official who had suddenly lost his wife advised him to start keeping a daily journal.

Write a “1” for the day, he advised Biden, if it feels as bad as the first day of your grief. For other days, write down a number that corresponds to your feelings — all the way up to 10.

“He said, ‘You won’t have 10s for a long time, but measure it, just mark it down.’ And he said, ‘After two months, take out that calendar and put it on a graph, and you’ll — you’ll find that your down days are just as bad as the first day,’ ” Biden said. “But here’s what happens . . . they get further and further apart. He said, ‘That’s when you know you’re going to make it.’ ”

Biden said he meant to offer these family members the same kind of hope.

“There will come a day, I promise you and your parents, as well, when the thought of your son or daughter or your husband or wife brings a smile to your lips before it brings a tear to your eye. It will happen,” Biden said.

“My prayer for you is that day will come sooner or later,” he continued. “But the only thing I have more experience than you in is this: I’m telling you it will come.”