SADDLE IT with something dreary like a cost-benefit analysis, and you'll never uncover a rational basis for steeplechasing. But that's not the point.

The point, as any fan will tell you (often, but not always, in the cadence of high patrician), is that steeplechasing, after all, is practically the only sport left in America that's still conducted for the sake of sport alone.

The fall steeplechase season comes to Virginia this Saturday with the Fairfax Race Association's annual "hunt meeting" in Leesburg. The occasion will allow workaday Washingtonians to mingle with some of the best-heeled steeplechase aficionados and fox-hunting enthusiasts this side of the Atlantic. (Fox-hunting and steeplechasing, like bridle and bit, are both of a piece.) They can also commune with nature.

What's more, the masses of the great unwashed, namely most of us who don't know a national fence from a timber jump, can watch thoroughbreds and riders take flying leaps over immovable objects at breakneck speeds in the countryside. But best bring a pair of binoculars and look closely. Even the race announcer, ensconced atop the officials' tower, is apt to cry, "And there they go behind the trees!"

The chase, more or less,is the domain of the very rich -- people for whom it's less a sport than a way of life; for some, less a way of life than an obsession. Only a handful of jockeys and trainers can make a living at it.

But if playing the game usually involves large amounts of money, not to worry. Most of these folks, to paraphrase the bard, are different from you and me.

Like Randy Waterman, all of 31, who stables 13 jumping horses, five of them pricy Chilean thoroughbreds, on his 800-acre spread in Upperville. A financier of substantial means, Waterman took up steeplechasing as a "gentleman rider" eight years ago ("It was a long time before I had even the vaguest notion of what I was doing"), and now, despite his amateur status, is rated fourth best jockey in the nation.

"I don't worry too much about the financial end of it," says Waterman, who puts himself through a tortuous regimen of dieting and jogging to stay 20 pounds below his normal weight during the chasing season. "I just like to compete fairly with other people. For me, the appealing thing about steeplechasing is not just the thrill of the moment, but the total satisfaction of accomplishment. I'm like a painter who starts with the first brushstrokes on canvas, and then, when the painting's finished, can sit back and be satisfied with what he's done. Not so much because it's brilliant, but because it's nothing to be ashamed of."

Of Randy Rouse, the developer who built the Seven Corners shopping center in Arlington. At 63, Rouse would nicely fill the bill of grand old man of American steeplechasing, except that he still rides competitively. I've always liked horses," says Rouse, who owns 15. "I've been at it a long time [here he cracks a boyish grin] so I guess you could say I've won a couple hundred races or so."

The two Randys fit neatly into the notion of steeplechasing as a plaything for the wealthy, but there are some exceptions.

"Sure," says Peter Winants, editor of The Chronicle of the Horse in Middleburg, "if you're going to be a bigtime owner, you have to have some money in back of you. But they're still a lot of slobs like myself, who love it in their own way." Winants, who keeps two horses, doesn't ride in the fall meetings, but sometimes takes part in informal chases, known as point-to-points, held in the spring.

His wife, Rose, however, has no use for horses, as a matter of fact is afraid of them, and takes a dim view of the horsey set. "The stereotype is absolutely true," she says ruefully. "Most of them are rich snobs."

At worst, the spectacle of the chase can have the air of a demolition derby; at best, a celebration of equine beauty in the most natural setting possible.

There were elements of both the other day at Ligonier, Pennsylvania, down a grassy hillside from the old and estimable Rolling Rock Country Club.

It was the 43rd meeting of the Rolling Rock Hunt Racing Association, the first of two race days, and the manicured course swarmed with DuPonts, Mellons and Phippses, to say nothing of Biddles, Grisnolds, Valentines and other fine species of millionaire.

Tweeds and skinny ties were as numerous in the paddock as fox-face lapel pins, which were plentiful indeed, and here and there was an accent of khakis and blazers. Diamond chokers and othe r such baubles did right by hundreds of imported suntans. A young woman whose velvet sash identified her as "Miss Ligonier 1980" wandered daintily through the throng, ladies-in-waiting trailing. And Mrs. John Hopewell of Middleburg, owner of the noted steeplechase winner Running Comment and two excitable terriers, showed up in a frock covered with brown horses bounding over bright green fences.

"I'll be all a-twitter in a minute," she predicted.

Shined to nines, Rolls-Royces and antique Packards, along with an errant Mercedes ("See how the door's rusted? That's why I didn't buy one," a Rolls man confessed), glutted prime space along the rail. The motorvessels' owners took no notice of scores of common gawkers, including a television crew from Pittsburgh. They busied themselves instead with champagne magnums, Chivas, canapes, goose-liver pate and, in one party, an outsized silver chalice brimming with jumbo shrimp.

"Ligonier is about the poshest you can get," said Connie Coopersmith, editor of Spur Magazine. "You go to parts of Maryland and Virginia, and a lot of people are starting to show up at the races in cutoff shorts, drinking beer straight from the can and not even paying attention to the horses. Some of the regulars resent it."

Across the race course, the Ligonier High School Band struck up a fanfare, and at length, post time arrived.

The first race, the Malcolm McGiffin Cup, was a telling example of what Dr. Joseph M. Rogers of Hamilton, Virginia calls "the terrible facination" of the steelechase. A gentleman farmer and horseman, the doctor should know.

Rogers' five-year-old mare, Baby Doe ("Red, White Cross Sashes, Red Sleeves, White cap," read the program), took a bad jump over a brush fence, horse and rider toppling to the cement hard ground, the horse rolling over several times over the young jockey, Ricky Hendricks, before struggling to its feet.

Their stripped ties fluttering at their backs, the officials raced an ambulance through the brush to the back stretch, down a knoll and beyond a clump of trees. Rogers white-faced, hopped aboard the starter's pickup and sat wordlessly in the truck bed.There was no talk, as there was later, after Rogers determined that boy and horse were all right, of "the vigor and high, adrenaline excitement" of steeplechasing.

"Let's all go now and get collectively nervous," Rogers said gamely when the shock wore off.

Half an hour later, in the next race, the A.M. Byers III Cup, the unspeakable happened. Corning Day, an eight-year-old gelding ridden by jockey Bobby Sloan, snapped a leg negotiating a timber jump in the last stretch of a three-mile gallop. The horse crashed to earth. Sloan was tossed on his back and trampled by another horse. It took a day, so it seemed, to get a doctor. Pittsburgh aluminum magnate Alfred M. Hunt, co-chairman of the race committee, scurried to and fro from steed to rider, looking stricken. "My God," he gasped.

Ominously motionless, Sloan finally was lifted into the late-arriving ambulance. And after several attempts to coax the horse into a van, the race vetinarian destroyed the animal, which then was hoisted ignominiously into a flatbed truck.

"Just rotten luck," owner Robert H. Crompton III of Lancaster County, Pennsylvania, ventured with a pained smile. "The horse was doing what it was bred and trained to do. What else can I say?"

The third race, the Edith Flinn Patterson Cup, was a happier event, especially for Raymond H. Norton Jr., a longtime horse trainer lately from Middleburg. (Actually, he was reared at National Airport, before it was an airport, when it was the Norton family farm.)

Norton, who's had his trainer's license 31 years, may have witnessed races enough for a measure of professional detachment, but as he cheered on his trainee Sharpian ("Green, White Ball, White Sleeves and Cap"), he got a little carried away.

A man of considerable girth, Norton barreled through a mob of captains of industry, who scattered before him like sparrows, and waved his bulky arms, to impressive effect.

"Hot damn! Lookit that sonofabitch jump!" he commented at the top of his sandpaper voice. "Hot damn!"

Sharpian, a four-year-old chestnut gelding, finished fifth in a field of five. Norton was delighted.

"There's a social aspect, and a little gambling sometimes, but those aren't too important to me," he said after he'd calmed down. "With a race like this, you're just very pleased any time your horse gets around the track."

The sixth race, this one on the flat track, brought even better results, as Norton's Bangka, an eight-year-old gelding, came in first. For the jockey, Hilary Thompson, it was a maiden race, which made victory all the sweeter. Norton said of Bangka: "He started out on the flat, broke a splint bone, bowed a tendon, and then the girl that owned him committed suicide and willed him to me."

A century after the pastime started in Ireland, the first American steeplechase was held in the wilds of Paterson, New Jersey, on June 7, 1865, when Nannie Craddock beat Maid of Ottowa over three miles and 27 fences. The tradition since has been passed down from generation to generation, like baronial estates and stock portfolios, essentially unchanged. And despite the perennial warnings of experts that the thing is on its hind legs and heading for a tumble ("The same people who are in steeplechasing now are the ones who were in it 25 or 30 years ago," jockey Jerry Fishback said on retiring last year, "that's one reason the sport is dying"), the chase is alive and well.

Charles Colgan, executive secretary of the sport's governing body in the United States, the National Steeplechase and Hunt Association, says interest seems to be picking up after a steady decline over the last three decades. "The crowds at all the hunt meetings have grown dramatically in the last five years," Colgan says, adding that this year's fall and spring purses, for the first time in history, will exceed a million dollars.

This is not to say that there's a lot of money to be made by bettors and participants on any given race day. The purses usually are paltry, the odds, when a bookie can be rustled out of the bushes, lousy.

Four American racetracks currently feature steeplechasing, but more as curiosity than as staple. "I just don't think the betting public will support it," says John Schapiro, chairman of Laurel Race Course, not among the tracks that have the chase.

So the sport survives largely at the pleasure of horse owners and race-meeting sponsors, including steeplechase "angels" like Marion DuPont Scott, who puts up the $100,000 purse for the fall Montpelier races, and Mariann de Tejada, who built and operates the Foxfield course in Charlottsville.

"It's the most important thing in the world to me." Mrs. Tejada says. "I can't explain why."

"The lady is a fairy godmother," Foxfield director Raymie Woolfe says of his employer. But, Woolfe says, the future of steeplechasing rests with corporate sponsors, who could use the sport as an "upscale" advertising medium. "We've got to go out and hustle people, on a whole different level, because steeplechasing here just isn't that universally popular."

But for loyal fans, the chase seems to hold a primal, even tribal, appeal, provoking a kind of glandular response from what used to be, in less egalitarian times, the ruling class.

"I rode the things myself for close to 15 years," Woolfe says. "I've got a pretty impressive orthopedic catalogue. I've broken both shoulders a couple of times, one collar bone six times and the other one four times, I lost count of the concussions, and ribs I don't even count, I break so many goddamn ribs. I broke my back once and ripped all the ligaments in my spine another time, and I broke both wrists and all my fingers. Oddly enough, I've never broken anything below the hip. It took skiing to do that."

"It may be agony," concedes Mrs. A.C. Randolph, a septuagenarian horsewoman who, since the late 1960s, has presided over the Virginia Fall Race Meeting at Middleburg's Glenwood Park Course. "But it's a pleasant agony, wouldn't you say?"