NEW YORK -- As he sits behind his empty desk measuredly discussing his first fitful year in office, which has coincided with a cataclysmic decline in the fortunes of his city, one is struck by David Dinkins's refined detachment, his precise diction, his immaculate grooming, even his distinguished gray scalp -- the one they are braying for outside in the street.

Outside in the street, there is bedlam.

The city's unions call him a turncoat, a disgrace, a coward. The bankers suggest he is inept. Even the homeless have turned against him.

The city is rotting, the mayor is being blamed, and you can read about it every day in the tabloids, the public id of the world's most bellicose city.

"THE FEAR IS REAL," gnashes one headline.

"WE'RE CAPTIVES IN OUR OWN HOMES," howls another.

Finally, inevitably:

"DAVE, DO SOMETHING."

Even the New York Review of Books, a publication with absolutely no tabloid in its soul, portrays the tennis-playing mayor on its cover, dragging a violin bow across an oversized tennis racket. In the background, highlighting a story titled "A New York Collapse?," gentle flames lick the page.

None of this would occasion much surprise -- this is, after all, New York, where politicians are to the people what fireplugs are to stray dogs -- were it not for one more voice out there, rising nasally above the others, a yowl, a caterwaul. This dissonance belongs to the last mayor of New York, the defeated mayor, Ed Koch. He's out there too, weighing in weekly with a cranky column in the New York Post and appearing on TV more often than Ed McMahon, lobbing stink bombs at his successor, stridently questioning David Dinkins's motives, his talent, his guts.

Nobody can quite remember another time in the history of this city when a mayor -- especially one with a legacy as grim as the one that Koch bequeathed to Dinkins -- has had to face such a barrage of public criticism from the man who preceded him. Wagner, Beame, Lindsay -- they all faded discreetly from view. But not this guy.

"That gently into the night thing?" says Koch, guf-fawing. "That's ridicccculllouuuss."

In New York, opposites repel. You're either Uptown or Downtown. Black or white. Tenant or landlord. David Dinkins or Ed Koch.

Galling as it may seem to both men, in many ways the current story of this city can be reduced to a tale of two mayors.

First there was the epoch of Koch, the egregiously outgoing "Mayatollah," who insisted for more than a decade that he was "mayor of all the people" but for whom New York increasingly became the fairy tale of Manhattan, the city's glittering enclave of wealth and privilege, and aspiration. Ed Koch was about as soft-spoken as the pneumatic drills that, during his 12 years in office, help to erect enough new real estate to fill Dallas. He was belligerent, confrontational, rude. He bragged about making his employees cry. His relentless aggression stood for New York in the '80s, a town of fast deals for many but fading ideals for more.

Now there's Dinkins, the son of a barber and a maid, up from a world Koch so often seemed to ignore, or failed to understand. For many hopeful voters the Me Decade ended the blustery New Year's Day David Dinkins strolled into Gracie Mansion, the soft-spoken great black hope of a city tired of racial tension, tired of a former mayor who often seemed to take pleasure in pouring gasoline on fire, and tired of a sense that the city of ultimate possibilities was running short of its historic magic.

"Have you ever gone into the theater and sat next to a woman who has poured what smells like an entire bottle of perfume over her head?" asks Norman Adler, a longtime New York political consultant. "That's Ed Koch. David is the one with a couple of drops applied daintily behind each ear. "

That is precisely why New Yorkers elected the 63-year-old former Manhattan borough president after 12 years under the manic Koch, whose famous motto "How'm I doin'?" began to sound disagreeably messianic. People wanted someone calm, a person who wouldn't rush in without thinking. They were looking for an urban Abe Lincoln, a man who could knit together a city demoralized in every way.

But Dinkins hasn't had much time for healing. He finds himself presiding -- tentatively at best -- over a city besieged by the worst run of economic bad news since it almost collapsed in 1975. People cannot sell their apartments. Since July, 31 children have been shot by mistake or for fun; crime has become so random and brutal that recently, when a teenager was killed by accident in the Bronx -- gunned down in a fusillade -- it failed to make any local newspaper.

It's been a great year for Ed Koch. At 65, he is having the time of his life.

"The people threw me out and they elected him," says Koch, in his midtown law office, surrounded by photos of himself with political luminaries, "but I am entitled as a longtime resident of this city to be both critical and positive." A portentous pause. "And I intend to continue."

Labor Woes One need not be a major cynic to view Koch's carping as the meddling of a scorned lover who cannot bear to see his city's new relationship succeed, or as an effort to absolve himself of blame for his city's wretched plight. If that has been his goal, he has failed. Recent polls show that most New Yorkers hold Koch more responsible than Dinkins for the current state of the city, or hold no one responsible at all. There are those who say the city today, terrors and deficiencies snaking throughout it with the fury of Hydra, can no longer be governed.

Still, day after day into the Dinkins administration, the news gets worse, and the mayor's popularity continues to plummet.

Many of the social service activists and labor union leaders who saw in him their ticket to harmony and promise have turned away. The mayor, who issued a press release on the eve of his inauguration describing the special seating area reserved for homeless men and women, can hardly communicate with their leaders anymore.

Two weeks ago labor officials, who once strongly supported Dinkins, angrily suspended negotiations over new contracts with the city; the mayor had outraged them when -- committing a puzzling breach of labor-relations etiquette -- he announced the possibility of massive layoffs without first notifying them. And the conservative business executives who help determine what kind of credit the city gets in the financial markets have finally begun to wonder, aloud and in print, if Dinkins is tough enough for the job he sought.

"David is not a weak man, he is a deliberate man," responds Felix G. Rohatyn. "The fate of the city requires a very firm hand on the tiller. David knows he needs to move, but it may be very painful for him to do that. Some of the people he feels closest to will be badly disappointed." Rohatyn has been predicting increasingly gloomy futures for the past decade. Last month, he announced his intention to step down as chairman of the city's Municipal Assistance Corp., which rescued New York from bankruptcy in the 1970s.

CITY THE PITS, HE QUITS, was the headline in Newsday.

City Hall estimates a budget deficit of $1.6 billion in the coming year. The city comptroller says it could be twice that. Layoffs are certain; it is now only a question of whether they will be bad, or worse. Whatever numbers turn out to be correct, David Dinkins has become the most prominent elected black politician in America at a time when he will have no choice but to pare back school construction, reduce medical help to the indigent, limit sanitation collections, close firehouses and trim nearly every other service that cities like New York were invented to provide.

"People are scared," says Manhattan Borough President Ruth Messinger, one of Dinkins's solid supporters. "The economic situation is terrible. The federal government couldn't help us if they wanted to. Crime, the homeless, peddlers, garbage, they are all problems. People want God as mayor."

The Tennis Factor There is about David Dinkins's Gracie Mansion office, as there is about David Dinkins, an air of gentility. The furniture is prim Victorian, the antique wooden desk shiny of surface and nearly bare. Tastefulness prevails, without a hint of idiosyncrasy, except, perhaps, for the placement of photographs. On a shelf across the room are snapshots of the mayor's handsome family and of his hero, Nelson Mandela. But more prominently displayed, out on the desk, are photographs of the mayor with tennis stars Steffi Graf and Zina Garrison.

His Honor is a big tennis fan. It has wounded him, in the press.

"Sooner or later folks will arrive at the conclusion that the fact that I play tennis is fine," he says, lobbing a smile. "I'm 63 years old, and I get up at 5:30 in the morning to play an hour or an hour and a half of tennis. How in the hell can that be not good?"

The mayor is asked about all the bad news.

"Does it get me down?" Dinkins asks. "No, I just keep coming. I am one tough Marine. I don't just fold because of adverse publicity."

Dinkins says he is addressing problems systematically, that he will eventually be seen as an effective and courageous leader who took necessary steps, at peril to his political image.

"It doesn't mean I can't make mistakes because God's not finished with me yet."

About Koch's broadsides, the mayor has this to say:

"Ed Koch is a journalist. It happens that he was my predecessor."

That's it?

"I don't have any comment to make about him."

It's hard to know whether Dinkins is being courtly, or simply politically astute. Surely, he has little to gain and much to lose by trading blows with Koch. But Dinkins's reticence makes it nearly impossible for him to get the attention Koch receives nearly every time he opens his mouth.

Koch, as they say in the newspaper business, gives good quote.

In October, when Dinkins granted the city's 65,000 teachers a 5.8 percent pay raise -- considered too generous by many -- Koch told a TV talk show that the city had been "taken to the cleaners." Then he elaborated, calling Eric Schmertz, the city's chief labor negotiator, "incompetent" and suggesting that a new verb be added to the English language: "to schmertz."

"It means unwarranted gift," he said. "When you get an unexpected gift from the city of New York, you say, 'Thank you for the schmertz.' When you've been hustled on the street, you tell your friends you've been schmertzed."

Good quote. Say what you will and think even worse, but the man gives good quote.

A Difference of Style "The personal differences between Ed Koch and David Dinkins are so overwhelming," says one former city official who knows both men. "Briefing Koch was something. He would yawn and puff his cheeks while you talked, and he would often take the work you had done and throw it away while you were talking.

"There would be these episodes," he says, "where you weren't done and he would have to haul Page 3 out of the garbage can. Dinkins would take your jacket and hang it up himself. He gets you coffee. He asks personal questions about your health."

Dinkins is always well dressed and well spoken. He doesn't shout. Nobody is a "wacko," or a "punk" or "a nut case," words that were indispensable to his predecessor.

Koch dresses like a seltzer salesman. He sends his suits to the rumpler.

Dinkins, in bold silk ties and subtly woven double-breasted suits, looks like an ad from Gentleman's Quarterly. He has occasionally been portrayed in the local papers and on television as a stylish, courtly functionary obsessed with tennis and grooming, a description that many people here think is grossly unfair and subtly racist.

"Is it a bad thing for our city that the guy has nice clothes and a sense of style?" asks Ethan Geto, a public relations executive who has worked as a fund-raiser for Dinkins. "Can there be a better role model for minority youths?"

Dithering? Koch says the criticism of his criticism is small-minded, that he is just doing his job as a public-spirited civilian.

"When {Dinkins} failed to move against illegally striking corrections officers I denounced it. When he failed to arrest them it was terrible. His first deputy had to fly there by helicopter. Ludicrous. When he enters into a contract with the city teachers that is so damaging to New York, horrible. When there has been damage to this city I must speak out."

One of Dinkins's greatest perceived errors -- one Koch has gleefully exploited -- stemmed from an incident in January when blacks began a boycott of a Korean-owned grocery store in Brooklyn, charging that the store's owners had abused a black customer. Dinkins did not enter the fray for months.

"Ed was always the first person to act," says one friend of both men, a former city official. "That is part of his problem. He would have been the first to buy groceries from the Koreans. He may have caused a race riot and he may have settled the thing. But he wouldn't have dithered."

Dinkins, critics say, dithered.

He finally did visit the store six weeks ago, purchasing a few vegetables. But he went only after he was jeered off a stage by thousands of angry Koreans during a speech the previous week. By that time he had angered Asian and blacks and had done nothing to solve the crisis.

Dinkins defends his action, or lack of it: "To have gone there would have been to have chosen sides at a time when we were trying to mediate it, and all along the way there was the belief that we were going to achieve a resolution. I might add that many of the people who argue that I should have gone out earlier have not been {there} yet. You should also know there was such a conflict during the time of my predecessor. He ... did not himself go during his time and settle it."

The Big Chance No one could honestly say that David Dinkins has fiddled with tennis while New York burns. His neatly typed daily schedule is almost always packed from morning deep into the night. He is always late, often having to cancel appearances and meetings because he is overbooked.

Dinkins has a natural advantage as mayor of New York. Every time Koch tried to close a hospital or a clinic he was accused by minorities of racism. Nixon was able to go to China because he was an anticommunist; Dinkins may be able to turn his background to similar advantage, taking tough measures in parts of the city others would rather avoid. But he will have to move fast, before his chance at leadership slips silently away.

"Voters have short memories and it's three years until the next election," says Jay Severin, a Republican political consultant. "He has had no honeymoon, no grace period and no margin of error. If he can turn it around at all this will seem like an initial rough spot. He will look back and chuckle.

"But if he doesn't he is going to become a permanent lightning rod for the disaffection and anger that New Yorkers feel about their lives, not because of who he is but because he is where the buck stops. If that happens he will certainly be through and this city might go with him."

Missing Ed Koch Once, in a speech in Harlem, while he was still mayor, Edward Koch said, "While I know that it was the people who elected me, it was God who selected me."

Could be. In New York, anything's possible. But unquestionably, it was the people who fired him last year, emphatically, like a Saturday night special. Koch is unquestionably nursing a wound, and -- dare we suggest it? -- a plan.

Koch for Mayatollah in 1993?

Naaah, he says. Never again. A flat-out denial.

Then he says this:

"You know what happens when I walk down the street today? Its very telling." A sly smile spreads slowly across his face. "Five, 10, no, 20 times a day, people come up to me and say, 'I miss you.' Exactly the same in every case. 'I ... MISS ... YOU.' And I say, 'But you threw me out!' And they say, 'Not me.' Then I say, 'If not you, who,' and then we laugh. I don't meet people who voted against me. I'm sure many of them lie, but nevertheless they clearrrrly do miss me now."

So, how does he think he would do if the mayoral primary were this month, instead of last year? Edward Koch spreads his long arms out on a couch high above the city.

"It really does interest me," he says, "that nobody has taken such a poll."