Ten years ago today the Six-Day War erupted in the Middle East. Two days later, Israeli troops stormed through St. Stephens Gate into the old walled city of Jerusalem and, after overcoming the resistance of Jordan's Arab Legion, reunited the city for the first time in nearly 20 years.

The barricades that had divided Jerusalem were torn down in a moment of hope and exhilaration that many Iraelis remember today as the high point of their own lives and of the nation's morale.

Today, the hopes that the 1967 victories would at last bring peace seem very faraway. Israel's security has been improved only in the narrow tactical sense by the adquisition of territory. Another war, far more cruel than the Six-Day War, has come and gone and the heroes of 10 years ago, Moshe Dayan and Yitzhak Ragin to name but two, have seen their reputations tarnished.

Today, the question of what to do with most of the captured territories has become the center of a national debate as Israel fumbles to form a new government.

But there is no debate in Israel about the future of Jerusalem, annexed outright following the Six-Day War. Israeli public opinion is over-whelmingly in support of keeping united Jerusalem as the capital of the Jewish state. The conquest of 10 years ago was viewed by israelis as the rightful return of Jewish sovereignty over all the Jerusalem - a sovereignty claimed when King David's general, Joab, captured the city from the Jebusities around 100 B,C. and ended when the Romans under Titus broke the back of the Jewish revolt in the first century AD. Titus destroyed Herod's temple and dispersed the Jews from their holy city.

Thus did the western wall of the ruined temple become for the Jews the symbol of their sorrow and the object of their devotion for 2000 years.Its capture 10 years ago, after Jordanians had denied them access to it since 1948, was a moment of national rejoicing, for Isaelis.

For the Arabs, the events of 10 years ago represented an unreconcilable loss of pride, power and prestige, as well as territory. The most important symbol of their defeat was the loss of their holy places. Jerusalem is the third most holy city in the Islamic world after Mecca and Medina.

Jerusalem's curse as well as its glory has been its importance as a focus of religious devotion for the three great monotheistic religions. The city has known bloodshed, repeated destruction and political controversy for most of its recorded history.

The Christian world, whose political and military struggle against Islam in the late Middle Ages has also symbolized by the desire to control the holy places of Jerusalem, is today no longer a contender. But the industrial countries of what used to be called Christendom fear that the age-old struggles in the Middle East might spread to destroy them as well.

So thorny is the problem of Jerusalem that Israeli leaders and officials of the Palestine Liberation Organization have both said that any peace formula must tackle the issue of Jerusalem last and only when all the other issues have been resolved.

Meanwhile, as united Jerusalem has prospered and grown by nearly a third in the last decade. The population today is about 370,000 - 268,000 are Jews and 102,000 are Arabs, with a smattering of armenians and others. This proportion is not dissimilar to what it was, 90 years ago under the Turkish administration, when there were 40,000 Jews in Jerusalem and 20,000 non-Jews.

Today, while some Jews and Arabs live side-by-side in the city there is an invisible border dividing Jerusalem. Arabs make up about 15 per cent of the work force in the Jewish section of the city and on any Saturday the Arab sections throng with Jewish shoppers. Except for a commercial relationship, however, Arabs and Jews remain separate and aloof.

Most Arabs in Jerusalem have chosen not to take up Israeli citizenship and would prefer not to be under Isaeli rule. One Arab acquaintance takes his children to see the plot of land the Israelis have confiscated from him - about a third of what was once East Jerusalem has been confiscated for housing projects - just to remind them of their loss. My plot of land is my Wailing Wall, he says, a reference to the western wall of Herold's temple and its meaning for Jews.

Mayor Teddy Kollek insists that relations between Arabs and Jews in Jerusalem are much better than before 1948.

He contends that Jerusalem's critics present an ideal that never was. Israeli policy has never been to seek complete integration. Arabs and Jews keep their own customs, schools, and traditions. They could not mingle freely during most of the British mandate period and there were frequent riots and disturbances in the 1920s, '30s and '40s.

Many travelers of the 19the century described Jerusalem under Turkish rule as a degrading place as the Rev. J. M. Wainwright wrote a hundred years ago, with the Jews cringing in their own city.

Today, freedom of worship is respected and Moslems are not denied access to their holy places as were the Jews in the days of Jordanian control. The Arab press is remarkably free to say what it wants - perhaps freer than in many Arab countries.

Although there are sometimes riots and demonstrations against the Israelis in the old town - usually triggered by some controversy surrounding the holy places - outside observers are often amazed that the Palestinians have never been able to organize a sustained resistance movement either in Jersusalem or on the occupied West Bank.

Still, the Arab population remains unhappy and in a position of inferiority.

One cause for optimism is that many Arab leaders, including Jordan's King Hussein, agree with the Israelis that Jerusalem should not become a divided city again, with a wall down the middle. There has been much thought given to various plans for sharing power in the city, but as a man who had studied most of these plans, Deputy Mayor Meron Bebvenisti says the essential willingness to compromise is still lacking.

Jerusalem's international status remains in a diplomatic limbo. No country has recognized reunited Jerusalem as Israel's capital. The Americans, French and British maintain their embassies in Tel Aviv.

So complicated is the matter that not even the Concise Oxford Dictionary knows how to define Jerusalem. Recently the respected lexicographers changed their definition from a city in Israel to a city west of the Jordan River.