Beirut was deserted by its Syrian protectors today as Israeli warships appeared offshore and Israeli tanks approached its southern outskirts.

For residents of the Lebanese capital, it was the opening of the next chapter in a long history of suffering and violence.

Even in a capital all but anesthesized with pain, Beirutis were well aware that tomorrow could bring the most destructive battle yet in Lebanon's seven-year history of violence, which has claimed more than 80,000 lives.

Stuck in their apartments in the largely blacked-out city--the Israelis had captured and cut off the city's major power plant in the south--the capital's inhabitants calmed their nerves by talking about the various options before them.

As if to exorcise their fear the discussions about their fate were conducted with a dispassion that has often shocked foreigners initially upset by the surface calm readily displayed before adversity.

Random conversations with Lebanese friends reflected a cold detachment as they weighed the pros and cons of a major fight between their uninvited guests, the Palestinians and Israelis, in the full knowledge that they themselves risked becoming the principal victims.

"The Palestinians may have 3,000 tough troops, and their backs to the wall, they are determined to go down fighting," a middle-aged man argued, "but the Israelis will make short shrift of them and the Lebanese leftist allies will run for it, a short, nasty fight and it will all be over."

"If the Israelis are smart they'll bottle Yasser Arafat up in West Beirut and let him twist in the wind," his wife argued, "while they go through the areas they now control killing every Palestinian guerrilla they can find much as you Americans did in your search-and-destroy operation in Vietnam. The Israelis don't like to take casualties, and Beirut is a city of 1 million people.

"Yet another reason for the Israelis not to enter Beirut is that it would require a large number of troops to police once they eventually gained control," she said.

"Arafat could recoup prestige and his losses so far by shooting it out," reasoned a third Beiruti. "He would not fight in the Palestinian camps, he'd take the war to all of West Beirut, the fancy neighborhoods, and there could be another 20,000 even 30,000 casualties on top of all we have suffered so far. Street fighting is the Palestinians' kind of war and the shooting could go on for two weeks."

"The Israelis would never dare destroy West Beirut," a fourth Beiruti said. "Remember that the foreign embassies and the world's press is in that sector watching everything they do. This is not Tyre, Sidon, Nabatiyah where nobody even now knows what really happened."

Indeed what is known of the fighting in the provinces indicated that the violence had taken an extremely heavy toll of both lives and property.

A delegate of the International Committee of the Red Cross reported "heavy damage" in both Tyre and Sidon and that "1,200 Sidon residents" required "urgent serious medical attention."

In the hills overlooking Beirut, the remnant of once proud sovereignty, the Lebanese government, met in emergency session to argue apparently ineffectually over the proposals for sending the Lebanese Army into West Beirut, a once taboo thought vetoed by the Palestinians and their leftist Lebanese allies alike.

It was more an act of national wish fulfillment than a practical idea.

Amid the rumor and reflection amplified in the city with a half-dozen radio stations all given to broadcasting fiction as fact, the little verifiable information provided but poor comfort.

The Syrian troops, who six years ago entered Beirut triumphantly to the relief of Lebanese exhausted by a 19-month civil war, overnight had largely retreated down the road to Damascus for fear of being trapped by the Israeli offensive.

So much for the Syrians' controversial Arab Deterrent Force that has come to be hated not just on the Christian side of the city, whose militiamen fought the Syrians in 1978 and again in 1981, but also among Moslems fed up with their occupation army behavior.

Here and there, Syrian troops remain, in front of the central bank for instance, or at the now closed international airport only a mile or so from advancing Israeli armor helicoptered ashore from ships in late afternoon.

For many in West Beirut, the decision to stay put--rather than follow the Syrians out of town while the going was still good--was dictated by the new wave of squatters provoked by the Israeli invasion.

"This time the refugees came in twos, like incoming artillery following outgoing artillery," a Beiruti joked, as the Syrians left for Damascus and Lebanese arrived from the war zone in the south.

As in 1976 and again in 1978 before a smaller Israeli invasion, armed guards at buildings fired in the air to prevent refugees from entering.

"All night long the refugees kept banging on my door," said one terrified young woman. "They must have shot off the heavy locks on the main outside door. God only knows what would have happened if I had opened. What animals have we become? Everyone, but everyone, in this country is armed, except me."

In one neighborhood two rival gangs of the kind that have proliferated over the years fought each other. One group wanted some refugees to enter a newly finished apartment building. The others were opposed.

Determined to maintain a semblance of law and order--in addition to worrying about the Israelis--were the Palestine guerrillas' military police, spread out throughout West Beirut, and the Syrian-officered Palestine Liberation Army. They were still manning their side of the green line dividing the city's Moslem and Christian sectors.

The Palestinians are a serious force, quite unlike the teen-age militiamen of various Lebanese leftist groups who range up and down largely deserted streets, perched on their truck-mounted anti-aircraft guns, posturing their defiance.

Each group has its turf, the Druze guarding the seaside American Embassy sector and the beach of the American University nearby, for example, and the group loyal to the memory of Egypt's late President Gamal Abdel Nasser in charge of the nightclub and bordello area.

Long ago cut off by their once generous Libyan and Iraqi paymasters, they were in near total disarray even before the Israeli invasion.

A potentially hopeful sign for the future was the disappearance of dozens of once stringent Syrian checkpoints on the Damascus Road. In fact the only really effective check was carried out by the Lebanese Army near their Defense Ministry in the hills overlooking Beirut. For some that was an encouraging sign.