The story is told of a psychiatrist who, after a long and arduous day of listening to patients' problems, goes to another psychiatrist, lies on the couch and begins: "Let me tell you about the difficult day I've had..." The second psychiatrist, who has worked a longer and even more difficult day, goes, in turn, to his psychiatrist, lies on the couch and begins: "Let me tell you about the difficult day I've had..."

The third psychiatrist who has had the most difficult day of all, goes to the city's most respected psychiatrist, Freud's daughter, lies on her couch and begins: "Let me tell you about the difficult day I've had..." When he leaves, she lies on her own couch, looks at the ceiling and begins: "God..."

Not all experts would go that far, but experts do call upon expert help. Psychiatrists see other psychiatrists and car mechanics have a mechanic of last resort, even as talented a pianist as Andre Watts gets help from another pianist. If Washington is a city of experts, it also has its experts' experts. WILLIAM GRANATIR Psychiatrist's psychiatrist

As a psychiatrist and psychoanalyst in Washington since 1964, Dr. Ralph Wittenberg has listened to the problems, fears and self-doubts of a lot of patients. But even he finds it comforting to have someone else to talk to -- both personally and professionally, he says.

Meet Dr. William Granatir, a psychiatrist's psychiatrist. Says Wittenberg: "It's very nice to have someone else to tell your problems to, especially when that person doesn't make you feel stupid or uncomfortable. The personal feelings of an analyst should be a part of the process without interfering with it, but everything tends to get entangled, your feelings and your patient's feelings, and it's helpful to have a more detached observer."

When another analyst consults him, Granatir says, his job may be to help that doctor decide what the patient's problem is -- it's not always what the patient says it is -- and what the best treatment would be. Or, he says, he may help the doctor clarify his own feelings, essential to responding to the feelings of a patient. STEVE STIENEKER A pilot's pilot

Talk about people looking over your shoulder: Robert Wallace is an airline pilot who checks up on other airline pilots. Steve Stieneker is a pilot who has checked up on Wallace checking up on pilots; call him a check pilot's check pilot.

Check pilots are employed by the airlines to monitor the performance of the company's pilots -- both on scheduled flights and in simulators, where they reproduce emergencies to see how the pilots respond. But to make sure the airlines' check pilots do their job well, the Federal Aviation Administration has inspectors, experienced pilots like Stieneker, who ride along periodically in the jump seat of the cockpit or observe their abilities in simulators.

"Essentially we're another set of eyes, like a doctor's second opinion," Stieneker says. "And our loyalty is different. It's the government, not the airlines, that signs my paycheck."

Much of the check pilot's work is done in simulators, models of the nose section of airplanes with large television screens showing what the pilot would see through the windows. Wallace, an Eastern Airlines captain based here, says that with the simulators, "We can put snow on the runway or stall the engines or limit visibility to 700 feet -- really put the pilot in a bind to see how he does."

Wallace and Stieneker both learned to fly in the service. Wallace joined the Navy when he was 17 -- "as soon as they would take me." He's been with Eastern 35 years. Stieneker spent 11 years as an Air Force pilot, was a civilian flight instructor and has been inspector since 1970. GERALD BROWN Mechanic's mechanic

He gets the "dogs," as they're called in service stations, the cars other mechanics have given up on. That's when they suggest trying Gerald Brown, the engineer who runs a mechanics' school in Falls Church.

"I don't think he ever gets an easy job," says Ira "Bud" Daniels, who runs Malcolm's Service Station in Arlington. "If Brown can't fix it, probably no one can."

Brown is an English-born design engineer turned mechanic and teacher who came to the United States in 1955 "for the adventure of it" and to work in the auto industry in Detroit. "But they were too specialized," he says. "I wanted to work on the whole car; they wanted me to work on the doorknob section."

Instead, Brown went to work for the Navy, building missiles. Returning in 1973 to "my first love," he started a school called Avocational Ltd. Automotive Academy. "It was to be for people outside the industry, to help them understand their cars," he says.

But the school "evolved," and he started teaching courses for mechanics. "If the big companies only spent a fraction on training of what they spend on advertising," Brown says, "there'd be a lot more qualified mechanics."

His approach to car repair is like that of a doctor. "Each car is different. You have to treat it like a doctor treats a patient -- try to find out as much as you can about it." His approach is "systematic, logical. You diagnose the problem, you develop a theory, then you analyze it piece by piece. You can't do that when it's rush, rush, rush, it's got to be finished by 5." DONALD GILMAN Weather forecaster's forecaster

It began with a hurricane he watched when he was in the first grade, and he has been fascinated by the weather ever since -- not just with today's weather or the chance of showers tomorrow. Donald Gilman picked a tougher job: He's head of the National Weather Service's long-range forecasting division.

Gilman has received calls from local weather stations and television weathermen, even construction foremen and ship routers. Tomorrow his office will release its outlook for December, January and February, a report that could influence construction schedules, fuel budgets or the amount of rock salt a highway department should have ready.

At best, Gilman admits, long-range forecasting is "more a technical art than a science." Short-range forecasts use computers and theoretical models but little of that is useful beyond five days. Long-range forecasters rely on statistics and patterns, looking for what Gilman calls "those slippery little clues."

"If there's high pressure over New England in November," he says, "what does that tell you about what follows -- does it bring more high pressure or low pressure or is there no tendency? Usually there's no tendency."

His business is one of probabilities. "We're like odds-makers and what we're doing is reducing the odds." He figures the National Weather Service has been right 65 percent of the time.

Gilman studied meteorology at Massachusetts Institute of Technology and did his doctorate work on long-range forecasting. LEON FLEISHER Pianist's pianist

'Andre Watts has that kind of personal magic that makes an Event of a concert. It cannot be taught, this mysterious transmission from stage to audience, and Mr. Watts has it in very large measure."

So wrote Harold Schonberg, The New York Times music critic, in 1970. Watts was 24 then, his career as virtuoso pianist well under way. But even if part of his talent couldn't be taught, he felt he still had a lot to learn.

For six years -- long after he attracted national attention -- Watts studied under Leon Fleisher at the Peabody Institute of Music in Baltimore. Watts thought of Fleisher, a one-time child prodigy himself, as "the ideal person to learn from." Fleisher, artistic director of Washington's Theatre Chamber Players, was the first American to win a major music competition abroad (in Brussels in 1952). His Beethoven recordings with the Cleveland Orchestra have never gone out of print in 20 years.

Fleisher was at the height of his career when in 1964 his right hand was disabled by a neurological disorder. He turned to conducting and teaching and restricted his repertoire to pieces for the left hand, including those commissioned by Paul Wittgenstein, a pianist who lost his right arm in World War I. More recently, after a successful operation on his hand, he has been practicing with hopes of performing again.

From Fleisher, Watts says, "I learned how to relax. I see old films of myself playing at 16 or 17 and my nose is right over the keys, symptomatic of a wild kind of tension. Leon would tell me: 'No, it shouldn't hurt. It should flow naturally.'... As Leon would say, 'It's not a matter of mistrusting your instincts but of controlling them.'"

Navy Capt. Grace M. Hopper, who will be 76 next month, is a "walking textbook," says Edward Morenoff, president of a computer firm, who met Hopper when he was studying for his doctorate in computer science at George Washington University.

In the computer world, Hopper is known as the creator of the fantastically successful COBOL (Common Business-Oriented Language). In the Navy she is known as the oldest officer on active duty; she was promoted to captain by act of Congress in 1973 when she was too old for normal promotion, and she says she's "having too much fun" to think about retiring.

Hopper taught mathematics at Vassar (her alma mater) and Harvard and was a staff scientist at Sperry Rand Corp. when she was called to active service in 1967, a year after she retired from the Naval Reserve. The Navy needed someone to standardize its COBOL program and "they knew I would come running if they called." FREDERICK J. ROSENTHAL Rose grower's rose grower

With a name like Rosenthal, perhaps it was destined. There's an eponymous quality to it: Rosenthal, which means rose valley, the rose expert's rose expert.

Frederick J. Rosenthal is a consulting rosarian, accredited by the American Rose Society to answer questions referred to him by nurseries and garden clubs and other rose-growing experts. Are the leaves yellowing? Troubled by black spots? Not sure when to prune? Call Rosenthal. The advice is free, a "labor of love" he calls it.

His horticultural passion began with three rose bushes; now he has 80. Rosenthal, vices at the Library of Congress, was, in his words, "a life-long apartment-dweller" until 1965. Then he bought a house in Bethesda that came with three Queen Elizabeth rose bushes about which he knew "next to nothing." So he started "asking questions and reading and observing, and one thing led to another."

Before long Rosenthal was president of the Potomac Rose Society, researching roses and writing for the American Rose Magazine.

Roses "give you more pleasure than any other flower I can think of," Rosenthal says. "The only thing you can't do is eat them -- though some people make confectionary candy out of rose petals. To me, that's going too far." HERBERT SPEVAK Spotter's spotter

He got into the business when he was 15. He's still in it 51 years later, and as Herbert Spevak puts it, "You learn a few things in all that time."

So when Besson's Cleansing Establishment -- a 14th Street dry cleaner -- has a garment with a stain that seems indelible, it calls on Spevak.

In the dry-cleaning business, a spotter is responsible for getting rid of the spots and stains. At Besson's (where men's shirts are cleaned for $5 each, collars and cuffs scrubbed by hand), spotter Benjamin Chung "can handle just about anything," says manager John Malerich. "But when he can't, we call in our consultant -- Herb Spevak."

Last month someone brought in a cushion cover made of Haitian cotton, which had discolored when it was accidentally washed. Since it was the oxidation as it dried that caused the fabric to discolor, Spevak washed the cover but dried it without exposing it to the air, using dry-cleaning agents to draw out the moisture. "A matter," he says, "of applying logic."

Spevak once had his own Capitol Hill dry-cleaning shop (razed when the Library of Congress expanded), taught the dry-cleaning trade to high school dropouts and set up the dry-cleaning departments for Lord & Taylor and Saks Fifth Avenue in New York.

"I've worked for people who started their business before the turn of the century," he says. "High fashion clothes are returning to the styles of the '20s and "30s -- lots of natural fabrics, which have to be cleaned more carefully. A lot of younger people in the business were brought up working on polyesters."