The man in the gold-painted hard hat with the statue of the Virgin Mary perched on top is trying very hard to explain what Notre Dame means to him, which isn't all that easy in the middle of a pep rally.

It is the Friday night before Notre Dame plays Arizona, and onstage the bouncing cheerleaders and the brass band and the solemn faces of the starting lineup are glowing, bright beacons in the black midwestern night.

"This is God's country," said Jim Murphy, a municipal court judge from Akron, Ohio, who has come for this home game as he comes to them all. "It's America at it's best, the true melting pot. God, country and Notre Dame in that order, that's what it's always been about for me."

Not that there haven't been changes since Murphy graduated in 1953, changes that bring a dark cloud to his face, a stern gathering of the Murphy brow that must give pause to Akron's pickpockets, malingerers and drunk and disorderlies.

The way Murphy sees it, take away the 8 a.m. compulsory mass, bring in the women students (as they did in 1972) and what you have is a grave tendency toward liberalism.

And then there was last year's 5-6 record, the first losing football season in 19 years, and Murphy "died a thousand deaths." Still, there he is, cheering loudly as the band breaks into the victory march. "There's just a mystique here," he says. "There's no place like it on earth."

Murphy has brought his son-in-law, Tom Dye of the Akron police department, and Fred Shaheen, a member of the university's celebrated subway alumni. "My father's greatest joy was listening to the Notre Dame games every Saturday afternoon on the radio," said Shaheen, an accountant. "He couldn't afford college, but his greatest dream was to come here."

Shaheen is wearing a similarly painted hard hat, and the sweat is beginning to glisten under the gold. "Mary's getting awfully heavy," he said. "But like my Mom said, Our Lady's carried me all these years, I guess I can carry her for an hour."

The last light of an autumn afternoon seems to leave the Notre Dame campus reluctantly, turning the golden dome of the campus administration building into a temporary sun of its own. The shadows gather by the French Gothic buildings and curl around the stern stone statues, and it seems as if Notre Dame survives in a time of its own choosing, a myth that survives its own marketing.

It is an American postcard, an incubator of legends, a symbol of diehard dreams since the days of Knute Rockne, George Gipp, Johnny Lujack and the Four Horsemen. They were heroes when America was full of heroes, and here they remain so in a time that could use a few, in a country traditionally hard on heroes, given to watching them self-destruct with a horrified fascination.

Here the heroes live on. Rockne smiles his crumpled smile and cocks his head and peers out of his funny-sad eyes from every corner of the campus, from the bas relief on Alumni Hall (where a student has obligingly filled his hand with an empty beer can) to the bust in the Athletic and Convocation Center near the trophy cases that contain a deflated football bearing his faded autograph.

"Rockne," said former Coach Ara Parseghian, "why, he's more alive than some people I know."

For years, Notre Dame was a lighthouse to the immigrant dream, not just for the working-class Irish who adopted it as their own, but for all of the poor Catholics with the vast ambitions and the alien names who saw in it not only a standard-bearer for their pride, but a symbol of their destiny.

In the early decades of the century, when it took all of their battling and scrapping just to make a living and fight the prejudice and prove a newly acquired patriotism, there was Notre Dame fighting and winning on the battlefield of that most American of causes, football.

And so the nuns in their cloistered convents said their rosaries for the Fighting Irish team and the leather-lunged workers in the dark little coal-mining towns hoisted a glass and counted up each victory as vindication.

It hasn't changed all that much really, although most of the students who come here now tend to be the sons and daughters of a prosperous middle class, polite young men and women whose ruddy optimism fits them as comfortably as their blue and gold sweatshirts.

It also remains a world apart.

"It's an elite, there's no secret about it," said Mike Hughes, Class of '67 as he sits in the senior bar the evening after the Arizona game. "Practically the first thing they did in orientation was show us, "The Knute Rockne Story . . ,"

"It was a fantasy," said David Huffman, a Minnesota Viking lineman and a 1979 graduate who came back for the weekend. "I never felt closer to teammates, never felt more joy in winning. It's a good place for an education; not just the academics but those parts of it that include in your freshman year. Things like seeing how many times you can throw up in a week. You can't hurt yourself here, like you might in a big city doing something like that."

But the very safety and security of Notre Dame can also be a drawback, Huffman said. "It's small, you're not dealing with the real world, you're isolated. It's a very middle class, very white campus. There's 1,500 kids and most of them are Biffy and Skip from Shaker Heights."

Huffman was not a Catholic when he came to Notre Dame, although he converted when he married. Religion, he said, never greatly occupied anybody's mind, either on the campus, despite the mandatory theology credits, or on the football field. "If God was on the field, He was there as a spectator," he said with a laugh. "God never helped anybody catch a football."

Still, said Gerry Faust, the head coach, "There isn't a day that goes by that I don't say a prayer at the Golden Dome and at the Grotto." He is sitting in his office, radiating a warmth and an enthusiasm that melts the most carefully chilled skepticism.

Last year, when the Irish went 5-6 in his first season, Faust said he "prayed a lot, not just to the Blessed Mother, but to St. Jude, the patron saint of lost causes, because I'm sort of a lost cause myself."

Last year, it certainly looked that way to some of Notre Dame's more vehement alumni. "Send the Holy Roller back to Moeller," was the way some of the more vocal members of the minority put it, referring to Faust's previous position as head coach at Cincinnati's Moeller High School.

Looking back, Faust said he sees where he made his mistakes, spending too much time on the field instead of guiding the overall operation, not spending enough time working on the defense, tring to handle his players differently than he had handled his players at Moeller and deciding too late that he hadn't been tough enough with them. "I was humbled a lot last year," he said.

"It keeps you up at nights. You put pressure on yourself. You know what it means to so many people, Notre Dame. This place is so unique. This place more than any other place really cares about people, about helping to guide young people, about . . . "

But it doesn't take much more to realize that this frantic, friendly man with the perpetually hoarse voice is desperately and rapturously in love with this university, and that this is a dangerous emotion with which to live while sitting in a seat that has been described as the third-toughest job in America.

"I would do anything to relieve these men of the pressure on them, but I don't know how to do that," said the Rev. Edmund Joyce, vice president of the university and chairman of the athletic board, the man who who has anointed Notre Dame football coaches since 1952.

He is a tall, handsome man, a high school football player, an elegant figure in his black cassock. "We try to make it clear to them that they are not under any pressure to win," he said, the blue eyes gazing steadily ahead. "All we demand is an honest man."

And if this sounds a trifle opposed to the legendary desire of the Notre Dame fans for a victory, that of course is not Father Joyce's fault. "We don't want to build it up into something bigger than the school," he said. "We just get more publicity for football than we do for our chemistry department, but the chemistry department is still more important." Still, he will say with a small smile that winning "does keep us all happy on a Saturday."

It is 11 o'clock on a football Saturday morning, and Touchdown Jesus, as they call the 42-foot-high mosaic on the library wall facing the stadium, is looking down on a scene of barely controlled hysteria.

Already the traffic is thickening around the campus, the bookstore is swollen with memorabilia-minded fans and the band is out and ready to roll.

From all corners of the campus, the fans are beginning to congregate for the tailgate parties that precede the kickoff and, at this point, it becomes necessary to make a few distinctions.

At Notre Dame, there are two kinds of alumni, those who graduated from the university and those who merely deeded Notre Dame their hearts and minds at approximately the moment they were born, but never set foot inside a classroom. Subway alumni, they're called, after the hordes of New York Irishmen who trudged out to Yankee Stadium when the team came to town to play Army in some of the more legendary of football battles. You don't need a diploma to tell the difference between the two.

One group congregates in the parking spaces nearest the stadium and these are the old grads. The old grads' pink faces beam out over natty green blazers and green pullovers and green plaid trousers, and sometimes the year of their graduation is emblazoned on their lapels.

Old grads drive station wagons, drink scotch whiskey and greet each other heartily over mountains of tinfoil-wrapped chicken and roast beef. Old grads call from Ireland to see who won the Michigan game, as John Shelley of New Rochelle, N.Y., did. Old grads say, as Phil Russo of Virginia Beach, Va., did that, "Once you live under the shadow of the Golden Dome, you never get it out of your system."

And they tell you things like how its the blend of different forms of excellence that they love about Notre Dame, and that it is the closeness, the spirit of belonging that brings them back and keeps the place bright in their memories.

And when it is all over and Arizona has done the sort of thing that Notre Dame is supposed to do -- kick a 48-yard field goal into the wind to win the game as time runs out -- the old grads look stern, and one of them says, "If that coach spent more time playing football instead of praying then we'd have a better team."

The subway alumni park their RVs farther back in the parking lot, and hand around the Budweisers. Subway alumni tend to be burly men with roughened hands and gruff faces, and they wear blue jeans and windbreakers and hats with visors and adjustable plastic bands in the back.

The subway alumni come from places like Wilkes Barre, Pa., riding all night on a bus. Such as Ed McGeehan, an employee of the Pennsylvania Turnpike, who said, "When we were growing up, Notre Dame was it; that's what you listened to on the radio, that's all you cared about."

Or you drive 11 hours from Rochester, N.Y., for every home game in a green RV with "Fightin' Irish" painted all over it in white script, like an electrician by the name of Cahal Magee does. And win or lose you go to the pep rally and the smoker at the Knights of Columbus hall, and afterward you hit Nicky's and Corby's and Bridget's, until, "Finally, you just cave in wherever you happen to fall."

And when someone asks you why you love this team so much, you look very young and sheepish for a moment, like Frank Sheriden, who is down from Detroit for the game.

"All your life when you're a little kid you wished you had a little more upstairs and could afford to come here," he said. "But it just wasn't possible and so it gets real special. It's got class, it's got standards. You look around and it's just different, that's all."

And when the team loses, you say you're broken-hearted, and you go off by yourself for a while, or you say very seriously, as someone did, "If Gerry Faust was so holy as he thinks he is, then God would have won the ballgame for him."

"Well, that team's got a long way to go," said Nordy Hoffman with a sigh in the welcome warmth of the Morris Inn after the Arizona game.

An all-America and Hall of Famer, he had never played football before that day when he was walking across the campus with a friend and suddenly found himself face to face with Knute Rockne. "It was like God stopping to talk to you," he remembered. "We shook hands, and I had pretty big hands though I wasn't so big as I am now, and he said, 'Young man, how come you're not playing football?"

"We were the '29-'30 team. This is the only team he coached that's still alive," he said. Every other year they come back for the Southern Cal game, and next year will be the 53rd year since they played together. Hoffman comes back more often than that. He's on the university's alumni board, and every time he returns, he lights 40 candles at the grotto, "for all the guys who are dead; for all the players and the coaches."

It never changes, he said. It never will. "The spirit of the place is the same as when I went here, and it was that way long before I got here. There's nothing I could do to give back to Notre Dame what I got out of it."

He has been the legislative director of the steelworkers' union, he ran the Democratic senatorial campaign committee and for five years until the Republicans came in he was the Senate's sergeant-at-arms.

"I've done a lot of things and I've met a lot of people," said Nordy Hoffman. "But the greatest years I ever spent, I spent here."