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For decades, the Society of Jesus has faced the same struggles to find priests that have plagued the wider Roman Catholic Church. The Rev. Chuck Frederico, one of the priests who evaluate Jesuit applicants, says he usually heard from five a week, or fewer.

Then, last month, the former Cardinal Jorge Bergoglio stepped out on the balcony of St. Peter's Basilica — the first Jesuit to be elected pope.

The number of queries jumped to four or five each day.

"Some guys who made contact in the past weeks are serious candidates," said Frederico, vocations director for the region from Maine to Georgia. "This election of the Holy Father has given them reason to examine this more fully."

Jesuits have only started absorbing the novelty of one of their own leading the church. Most were so shocked, they Googled to confirm the connection before they dared to celebrate. Robert Wassmann, an instructor at Washington Jesuit Academy, a middle school, told the Archdiocese of Washington newspaper he ran down the hall shouting: "He's a Jesuit! He's a Jesuit!"

But members of the order have also started thinking ahead, to the potential impact of this pontificate on their many ministries, colleges and overall future. Pope Francis could inspire new recruits and wider regard for the society. But he could also feel compelled to intervene in the inner workings of the order, which has had sometimes tense relations with the Vatican over the centuries.

"In the context of young men and women considering a religious vocation and calling, it has to have an impact," said the Rev. Thomas Gaunt, a Jesuit and analyst at Georgetown University's Center for Applied Research in the Apostolate. "And that impact will be at least a blip on the screen and could be more."

Bergoglio was more than a rank-and-file member of the Society of Jesus. He held the order's most trusted positions in Argentina.

Soon after he was ordained, he was appointed novice master, in charge of training the newest recruits. He went on to become provincial, or national leader, before joining the church hierarchy as a bishop in Buenos Aires. Francis has chosen a papal coat of arms featuring the Jesuit seal: a sunburst containing a red cross and the "HIS" abbreviation for Jesus Christ.

In pure marketing terms, it's the ultimate branding opportunity.

Many Jesuit-run colleges, such as Georgetown, are already prominent and a top draw for applicants, although most of the order's 3,700-plus schools worldwide are smaller and many are struggling.

The Rev. Tom Smolich, president of the Jesuit Conference USA, said some are half-jokingly wondering about a papal version of the "Flutie effect," a reference to Doug Flutie, quarterback for Jesuit-run Boston College whose last-second "Hail Mary" pass won a 1984 game against Miami. In the aftermath, BC's applications increased.

Mostly, though, the society is hoping for what the Rev. Matt Malone, editor of the Jesuit magazine America, called "a moment of reconciliation." Previous popes have disciplined Jesuit theologians over liberal teachings. In 2008, Benedict XVI sent a letter asking the order's worldwide members to pledge "total adhesion" to Catholic doctrine, including on divorce and homosexuality.

"That the cardinals would even consider choosing a Jesuit now, I thought, marked a new beginning in that relationship," Malone wrote.

Recognized by the church in 1540, the order was founded by Basque soldier Inigo de Loyola. Jesuits swear an oath of obedience to the papacy and have been dubbed "God's Soldiers" for their readiness to evangelize anywhere the pontiff sent them. Jesuits brought Christianity to 16th-century Japan. A 19th-century Belgian Jesuit was a peace negotiator between the U.S. government and Sioux Indians.

But depending on the era, the society could be viewed with as much suspicion as respect.

Their growing influence sometimes generated resentment. Anti-clerical European monarchs pressured Pope Clement XIV to abolish the society in 1773 — a suppression that wasn't lifted until 1814. Still, Jesuits remained a target for anti-Catholic conspiracy theorists who believed the priests were scheming to overthrow foreign governments.

The order has become known more recently for academic rigor seen in the universities they built in the U.S. and around the world. Jesuit scientists have made so many advances in astronomy, physics and math that 35 moon craters have been named in their honor. But partly because of these intellectual achievements, claims of elitism often surround the society.

The Rev. Joseph McShane, president of the Jesuit Fordham University, opened a recent event with a quip playing on the order's reputation and Francis' no-frills papacy. The pope has kept the simple, iron-plated pectoral cross he used as bishop and living in the Vatican guesthouse rather than the grand papal apartment.

"A humble Jesuit? An oxymoron. A Jesuit pope? An impossibility. A humble Jesuit pope? A miracle," McShane said.

In the 1970s, when the church was debating how it should relate to the modern world, the order's General Congregation, or legislative body, decreed that "the service of faith" and "the promotion of justice" would be the focus of every Jesuit ministry. This coincided with a period of high-profile — detractors would say notorious — activist Jesuits, including the Rev. Daniel Berrigan, a founder of the anti-nuclear Plowshares Movement.

In Latin America, the Jesuit emphasis on helping the poorest peoples often drew the society into political upheaval, including the cause of liberation theology, a Latin American-inspired view that Jesus' teachings imbue followers with a duty to fight for social and economic justice. U.S. Jesuit James Carney was killed in 1983 serving as chaplain to a rebel column from Honduras.

Pope John Paul II, hoping to re-direct the religious order, took the extraordinary step in 1981 of replacing the Jesuit's chosen leader with his own representative. The society encompasses a range of outlooks, including tradition-minded men. Still, conservative Catholics often view Jesuits as a band of disloyal liberals. The day after Francis was elected, George Weigel, a John Paul biographer, wrote in the conservative National Review magazine that the pope "just might take in hand the reform of the Jesuits" that Weigel argued was never finished. (Smolich rejects any suggestion that the order isn't faithful to the church or its teachings.)

It's too early to say how these past conflicts could influence Francis and his relationships with the society. He had disavowed liberation theology as a misguided strain of Catholic tenets, while still maintaining a focus on the economic failings of Western-style capitalism and the need to close the divide between rich and poor.

Jesuits also worry that the religious order could suffer in the spotlight. Maybe the new pope will keep his distance from the society, for fear of giving an appearance of favoritism. Or, he could use his new authority to become — from their perspective — too involved in the society, like John Paul. And they wonder if Jesuits would somehow be blamed for any of Francis' decisions that prove unpopular.

Jesuits were already at a crossroads when Francis was elected. Although the order remains the largest in the church for men, membership has dropped by more than half since peaking in 1965, Gaunt said.

The decline came mostly in the West. But In South Asia and India, Christianity, and Catholicism specifically, have been growing, and so too have the numbers of Jesuits in those areas. Gaunt calls it "the changing Jesuit geography." India now has the largest national group of Jesuits with just over 3,900 members, followed by the U.S., with just under 2,500. About one-third of the world's 17,287 Jesuits came from developing countries, a figure that is expected to rise in coming years.

For U.S. Jesuits, this has meant a long season of wondering where they go from here. The order is restructuring in the U.S., merging their 10 smaller provinces into four larger ones.

Lay people now staff most Jesuit schools and ministries, so the order has started Jesuit spirituality retreats and instruction for lay faculty and staff to help maintain the religious identity of what they've built. Among the newer Jesuit initiatives are high schools or middle schools in poor communities, and programs that bring online college-level classes to refugees in Africa and elsewhere.

Whatever is ahead, Jesuits are aware this is a signal moment.

Francis has visited with and exchanged letters and visited with the Jesuit superior general, the Rev. Adolfo Nicolas, with both pledging to work together as brothers. A photo of the two embracing is circulating around the Jesuit world.

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Follow Rachel Zoll at www.twitter.com/rzollAP