VATICAN CITY – Three rounds of ballots had been cast with no winner, but it was becoming clear which way this conclave was headed.

When the cardinals broke for lunch, Sean P. O’Malley of Boston sat down next to his Argentine friend Jorge Mario Bergoglio.

“He seemed very weighed down by what was happening,” O’Malley said.

Hours later, the Buenos Aires archbishop would step before the frenzied masses packed into St. Peter’s Square as Francis, the first pope from the Americas.

Cardinals take an oath of secrecy when they enter a conclave, promising never to reveal what goes on inside. But as is customary, the cardinals involved share memories of their experience.

It began Tuesday afternoon with a procession.

Reciting a hypnotic Gregorian chant, the 115 princes of the church, dressed in red robes over white lace tunics, filed two by two into the frescoed masterpiece that is the Sistine Chapel and took their seats at four rows of tables. One used a wheelchair and was helped to his place by his colleagues.

Then each man moved to the front and took an oath not to reveal what was about to occur: “We promise and swear not to break this secret in any way, either during or after the election of the new pontiff.”

With a cry of “extra omnes” – “all out” – the massive double doors swung shut, the key was turned and the conclave was under way.

No matter how beautiful the Sistine Chapel may be, Chicago Cardinal Francis E. George said, the acoustics aren’t great. The presiding cardinal, Giovanni Battista Re of Italy, had to explain each step in the voting ritual twice, once to each side of the room. Other than that, there was only silence.

“The conclave is a very prayerful experience,” O’Malley said. “It’s like a retreat.”

Each man wrote a few words in Latin on a piece of paper: “I elect as supreme pontiff …” followed by a name.

One by one, they held the paper aloft, placed it on a gold-and-silver saucer at the front of the room, and tipped it into an urn. And then the tallying began, with three cardinals – known as scrutineers – reading out the name on each slip.

When they finished counting, it was clear the field remained wide open, said Cardinal Sean B. Brady, leader of the church in Ireland.

“There were a number of candidates,” he said.

A cardinal threaded the ballots together and put them in a stove.

Outside, in St. Peter’s Square, as black smoke billowed from the chimney, the cheering crowd fell silent and began to thin.

Wednesday morning, the cardinals filed in again and repeated the ritual of voting. Each man filled out his ballot and walked to the front of the room.

“When you walk up with the ballot in your hand and stand before the image of the Last Judgment, that is a great responsibility,” O’Malley said.

There were two votes before lunch, and the field was narrowing. But the smoke was black again, and the crowd was again disappointed. This time, however, they didn’t leave the square.

And this time, after the inconclusive balloting, Bergoglio’s stock was rising, and support seemed to be gravitating his way.

Longtime Vatican reporter John Thavis, author of “The Vatican Diaries,” said his sources had told him that Bergoglio “spoke up clearly and forcefully during general congregations” the week before “and got the cardinals’ attention.” Thavis reported that Monday, the day before the conclave convened, on his blog.

In retrospect, Bergoglio fit the profile the cardinals were looking for, analysts said. “It was the cardinals recognizing that the church’s universal center needed a new style of papacy, one that was simpler and more focused on standing with the poor,” Thavis said.

“They also wanted someone to restore order in the Roman Curia and make it less of a barrier between bishops and the pope,” he said.

At lunch, as sentiment seemed to be coalescing around Bergogilo, O’Malley sat down beside the Argentine cardinal. “He is very approachable, very friendly,” O’Malley said. “He has a good sense of humor, he is very quick, and a joy to be with.”

But with the vote going his way, Bergoglio was uncharacteristically somber. In the first afternoon ballot, the cardinals were getting close to a decision. But not quite. They started over, and the scrutineers read out the names.

And it began to dawn on the men that their work was done.

“It was very moving as the names were sounding out,” Brady said. “Bergoglio, Bergoglio, and suddenly the magic number of 77 was reached.”

The cardinals applauded at 77, and again once the tally was complete.

“I don’t think there was a dry eye in the house,” said Cardinal Timothy M. Dolan of New York.

A cardinal asked Bergoglio whether he accepted the papacy. “I am a sinner, but as this office has been given to me, I accept,” he said, according to three French cardinals.

Bergoglio announced the name he would assume – Francis – and went to change into the papal robes in the Room of the Tears, so named because many have wept at the enormity of the task they face. When Francis returned to the chapel, “his first action was to go to a cardinal in a wheelchair and go to the back of the chapel to greet him,” Brady said.

Aides brought in a platform with a white chair for Francis to sit on as the cardinals came one by one to pay their respects. The pope declined, Dolan said.

“He met with us on our own level,” Dolan said.

Dolan said he felt a strange emotion as he kissed the pope’s ring. “It’s very difficult to explain,” Dolan said. “You obviously get to know your brother cardinal. But all of a sudden, the identity is different.”

It was time to face the public. More than 100,000 people had jammed into the square, and Francis prepared to greet them from the balcony. Vatican workers lined up to shake his hand, but Francis was worried about a delay, Dolan said. There were too many people outside waiting in the rain, and he didn’t want to keep them.

As Francis stepped out on the balcony, cardinals rushed to the windows to look out over the crowd.

After the new pope spoke his first words to the faithful, a car came to take him to dinner, and buses arrived for the rest of the cardinals. But the car returned empty.

“As the last bus pulls up, guess who walked out?” Dolan said. Francis had dinner with the others. By the time the night was over, cardinals said, the new pope seemed comfortable in his new robes.

“Last night, I think there was a peace in his heart,” O’Malley said, “that God’s will had been accomplished in his life.”

Newsday contributed to this report.