Inside the Oxford Union Society debating chamber, William Hague puffs out his chest and wags his silver tongue, disarming any rash challengers with naked charm and vocal cords. The Union is the Victorian equivalent of mud wrestling, and the object of the game is to channel one's saliva so as to lubricate a path all the way to the prime minister's residence.

Suprisingly frequently, it works. For more than 150 years, this private debating society at Oxford University has produced prime ministers and politicians with assembly-line regularity. The roster of alumni is staggering.

Prime Ministers William Gladstone, Herbert Asquith and Edward Heath were presidents of the Union; Prime Ministers Harold Macmillan and Lord Salisbury held lower offices. Michael Foot, current leader of the Labor Party, and Tony Benn, Labor's enfant terrible, are former presidents. Roy Jenkins, leader of the new Social Democrats, was librarian, and Jeremy Thorpe, former head of the Liberal Party, was president. The list of famous alumni seems endless, encompassing politicians, journalists and businessmen.

The Union activists, known as hacks for their incessant campaigning, consider themselves the heirs of the prime minister's legacy. A different set of officers is elected each term, and competition is bitter. The technique is to bribe members by buying them drinks while stabbing opponents in the back so gracefully as not to bloody one's sleeve.

"I think people are quite aware I'm willing to manipulate, and hence am very dangerous," declared the Union librarian, Sally V. Littlejohn.

She, like almost everyone else, yearns to be president. "President of the Oxford Union" -- it has a Pavlovian ring to it that makes hacks salivate. Employers and national political leaders prick up their ears at the title. It opens doors. It arouses curiosity. It is the classiest obituary: "He was educated at Eton and Balliol College, Oxford, where he was president of the Union." It is magic.

A few hundred students troop to the debating chamber each Friday evening during the school year. Topics range from capital punishment to prostitution (several prostitutes were invited to speak). Two of the more famous topics were: This House does not believe in God, and This House will not fight for its King and country. The speakers -- every hair in place, every gesture practiced -- express their opinions passionately in the wood-paneled chamber modeled after the House of Commons.

Now and then a member rises from the audience to ask a stinging question. In a recent debate about the viability of a "middle way" in British politics, Jackie Newstead was speaking when Roland Rudd stalked to the speaker's box and inquired, his voice oozing sarcasm, "Aren't you being just a tiny bit simplistic?" He walked heavily back to his seat amid cheers, but she retorted, "Sir, if I were complicated, nobody would understand." More cheers.

Famous speakers come from London or farther to participate in debates or give speeches. Richard Nixon, Robert Kennedy and Queen Elizabeth have all been here. Sometimes a debate is televised nationally, and periodically the Fleet Street press denounces the young politicos for an immoderate stand.

The Union has attained an aura of power and prestige because in Britain the best and the brightest -- and the aristocrats -- flock to Oxford and Cambridge. There, the politicos gravitate toward the unions, of which the one at Oxford is by far the more famous. Its impact is rooted in a peculiarly class-conscious society, where the presidency of the Oxford Union is probably the highest status symbol a college student can achieve anywhere in the country.

The Union's current golden boy is William J. Hague, an amiable politics students from Yorkshire who was consecutively president of the Conservative Association and president of the Union. A brilliant orator, he first gained attention nationally as a 16-year-old addressing the Tory (Conservative Party) conference on national television. His rousing speech won a standing ovation, newspaper headlines, television interviews and the patronage of Tory leaders.

Incredible as it may sound, Hague is already seriously mentioned as a prospect for prime minister. One magazine article presented him as the prime minister in the year 2020; others put him in that office two decades earlier. Even his detractors think he will be a cabinet minister, but doubt he will go higher.

Hague will say only that a political career is "conceivable," but friends say he is strongly considering running for Parliament, with Tory blessing, in 1984. He graduated from Oxford in June, and now works for Shell Oil in London, in the public affairs division.

"I know William very well," said a conservative politico who is a close friend of Hague, "and he's an excellent political manipulator."

While lounging in the Union bar one afternoon, nursing a half-pint of bitter, Hague argued that tales of Union back-stabbing are exaggerated. But he admitted it happens: "People encourage one person to stand for an office and tell him they will support him. Then they oppose him in the hope it will get him out of the way."

Hague paused, sipped and smiled. "You can't rely on any advice you get here from anybody with a vested interest."

Others say the back-stabbing is endemic. "In my term as secretary, I was completely shocked," said Mary A. Morgan, who resigned this year from the Union standing committee after losing a race for president. "They cheat. They break every rule there is. I found hacking detestable."

One technique is to spread rumors about rivals. Morgan said false reports were deliberately spread that she had violated campaign rules. A woman is at a particular disadvantage, she said, because of her susceptibility to rumors that she is trying to sleep her way up.

One efficient medium for slandering other hacks is the gossip column of Cherwell, Oxford's tabloid student newspaper. The weekly gossip column focuses on Union hacks and shreds them. One recent issue named a student the "man of a thousand zits." He was termed a "polysexual politico" and accused of passing himself off as a tutor and marrying to improve his image.

Few students take the allegations seriously. Knowing a Cherwell editor is considered very important, and even Hague admits that probably half the malicious gossip is planted by hacks. It can be effective sometimes: Morgan's image suffered after she first was reported to be "lascivious" and later was described as the "ice queen."

Some of the most vicious gossip is planted by the "victims" themselves. "That's the best thing, when it picks on you," said Littlejohn. "Then your friends feel moral outrage. And it doesn't matter what is said -- it's just publicity."

One recent gossip column reported, groundlessly, "In the corner I see Charlotte (to rhyme with harlot) Cole doing her best to get intimate with the epicene Hague." A friend of Cole blushed: "Yeah, I put that in. But it's for her own good. It's getting her known."

Political considerations enter into every aspect of a hack's life, from rooming to sex. "Whom you sleep with counts a lot," said former president Kevin D. Brennan, who graduated in June. Hague, reddening slightly, conceded that he chose his college room for political reasons: It was on High Street above his college entrance so he could see who was going by and invite people up for drinks.

Romances are sometimes made to boost political image, but several hacks hasten to urge that it is best to remain single. That way one is more likely to attract the interest and votes of members of the opposite sex. Clothing can also be very important, in different ways. Christopher C.J.A.A. Wortley, the current president, is said to cultivate his scraggly image because it sets him apart and draws support from non-conformist voters. Wortley's election was also said to depend on the Catholic vote at the Union.

Littlejohn, a vivacious and excitable woman with flowing black hair, recalled, "I wanted the image of a hard woman, so I had my hair cut very blunt. I wore jeans a lot. But then this year I needed my image softened. I changed my hair and put ribbons in it. This term I thought people wanted a summer image, so I dress summery. Image is very important."

Friendships, too, are political, for it is dangerous to befriend people out of power. "The trick is to be on the bandwagon," Littlejohn said. "Last term I had Chris Wortley over for dinner -- he's a good friend and I knew he was running for president -- and he won. But if Hilali Noordeen his opponent had won, I'd be dead."

Subsequently, Noordeen was elected president to take office next winter.

Now Littlejohn says she is trying to build a political machine in her college, St. Hilda's. She recruited one woman whom she heard talking loudly at breakfast and whom she has since maneuvered onto the library committee. Now Littlejohn is taking a new tack: "Blonds are very important in politics. I've found a blond girl to run. She'll run for library committee. It's a very deliberate ploy."

No wonder that one member of Parliament declared that after three years in the Union, the House of Commons was like a rest home.

All this politicking can be very expensive, especially for a woman who must buy long dresses. Littlejohn calculated that she spends about $1,500 each year for political expenses: clothing, trips, parties and buying drinks. "People do remember who has bought them a drink," she said.

Compared with other university clubs, the Union also costs a bit more to join -- about $90 for a life membership, the only kind available. Partly as a result, it tends to be dominated by Oxford's conservative students. The Union functions not only as a debating society but also as a cozy club, offering films, cocktail parties, wine-tastings and an excellent library.

Partly because leftist groups urge students to boycott the Union, it has become increasingly right wing. The overlap between active members of the Union and members of the Oxford Conservative Association is enormous, and many Union officers previously were officers of the Conservative Association.

But for Union hacks hoping to get ahead by becoming active in the Tory groups, a complication interferes. The conservatives at Oxford are bitterly divided into two factions, both of which regularly field candidates in Union elections. The successful Union politician must cultivate one faction while trying to hold on to some votes in the other faction.

"The Union is stale," said John A. Bacquie, a Jamaican Rhodes Scholar who is active in the Union. "To be elected to an office nowadays means not only do you go to tea every day at the Union and see people, but you speak out at TRG Tory Reform Group meetings, and go to the Yacht Club or to Brown's Restaurant with the right crowd.

"People make the society their life," he added, shaking his head. "It's chronic. It's sick."

But Bacquie, who lost an election for treasurer last year, said he probably would run for office again -- "and I would think of it as a steppingstone to Jamaican national politics," he added.

It is part of the imprint of colonialism: An Oxford degree and an office in the Union carry enormous weight in politics in Jamaica, Sri Lanka and other British Commonwealth countries. If a Sri Lankan can return as a former president Hilali Noordeen will be the third , then his career is almost made.

Two careers that were not made at the Union, perhaps because women were not admitted until 1963, are those of Prime Minister Margaret Thatcher and Social Democrat Shirley Williams. Both were at Oxford, and Thatcher was president of the Conservative Association, but at the time they could not participate in the Union.

Many women are involved in the Union now, and half a dozen have become president, but several say it remains a sexist bastion. "They're very happy to have me as secretary," said Littlejohn (she was secretary last term). "I'm decorative, a hostess. I'm a token."

Some women try extra hard to be decorative, wearing short skirts or plunging necklines to catch male eyes and votes. One woman running a few years ago submitted a photo for the election bulletin board in which she was wearing a top cut so low it was almost superfluous.

Why do people go to such lengths to succeed in the Union?

"You're very conscious that life after Oxford is still Oxford," Littlejohn explained. "The real world is right here. It perpetuates itself. You go from one private club, the Union, to another -- the House of Commons. That's why it all matters."