A photo caption in Sunday's Outlook section reversed the identifications of Crown Prince Fahd and King Khalid of Saudi Arabia.

It was 236 years ago here in this storybook mud- and-brick village that two men, one an outcast Islamic religious reformer and the other a besieged tribal chief, entered into an historic alliance that gave rise to today's powerful House of Saud and still provides the cornerstone of its political legitimacy.

Under the impact of vast oil wealth and telescoped economic development, the physical landscape of the old Saud kingdom has changed beyond recognition in just the past decade, with skyscrapers and elevated highways leading into Riyadh, the new capital, visible from the rooftop of one restored mud palace here in the old capital.

In place of the tough Bedouin camel-riding ikwan (brothers) who helped the Sauds impose order and unity on the squabbling tribes of Arabia, a whole new generation of American-educated Saudis, holders of master's degrees and doctorates, has come to the fore to manage an increasingly computer-directed Saudi society.

But the Saud family, with its 4,000 princes and princesses, still rules over this mostly desert kingdom of scarcely 5 million people much as its founder, Mohammed Ibn Saud, and his religious ally, Mohammed Ibn Wahhab, did over Diriyah nearly two and a half centuries ago.

"The Saud family has the longest practiced rule not only in Arabia but in the whole of the Middle East," remarked Abdallah Masry, the director of Saudi antiquities and museums. A social anthropologist educated at Berkeley and the University of Chicago, Masry talks in awe of the incredible staying power of the ruling family. "It has not changed an iota, the way of making allegiances and keeping them. The Bedouins and other Saudis as well are moved by the continuity of the House of Saud and how they handle their complaints," he added, referring to the majlis, the daily open-door sessions where princes meet their subjects and adjudicate their petitions.

A late 20th century visitor to the kingdom is more than likely to regard the Saudi system of royal rule as highly colorful, even quaint, but altogether ready for the museum of history. Yet many Saudis, even those educated in the best American universities, argue with intensity that it is the very persistence of traditional Saudi rule that has provided the main rudder of stability in the storm of changes sweeping this ancient land.

"That form of stabilizing institution," says Masry of the majlis, "has played a giant role as society changes and dislocations set in."

Another such institution, according to Masry, has been the Wahhabi religious establishment -- the 10,000 or more ulama, or holy men, of ultraconservative Islamic faith led by the influential Sheikh family. It is they who enforce prayer five times daily with baton-wielding muttawwiun, or policemen, keep a tight ban on all liquor, movies and public entertainment other than sports, and see to it that the sharia, or Islamic law, is applied to the letter -- including public beheadings with a sword.

"Religion is stabilizing here while it was destabilizing in Iran," Masry said. "There, there was a fundamental antagonism. Here, the political power is continually appeasing the religious constituency."

Masry's comments about royal Saudi rule and religion go to the heart of what is undoubtedly the biggest political mystery of all Saudi Arbia -- the one outside analysts, from the Central Intelligence Agency and western embassies to resident company managers and curious visitors, are constantly trying to probe: the degree of stability, or instability, of the family ruling over more than a quarter of the world's proven oil reserves.

Few Third World polities have been so closely scrutinized, dissected and picked apart for potential strains and crises as has that of this strategic kingdom. In the aftermath of the shah's ignominious ouster from Iran, there were countless false predictions of doom about the Saud family. Among those predicting serious trouble ahead, after an in- depth study, was the CIA.

Then, last fall, the debate in Congress over the sale of sophisticated AWACS planes to Saudi Arabia, punctuated by the shocking assassination of Egyptian President Anwar Sadat on Oct. 6, raised anew a host of nagging doubts about whether the House of Saud was really built on stone or sand.

It is not an easy question to answer. After spending six weeks in the kingdom on two visits last year, I am struck by how little really is known by outsiders about some of the key sectors of Saudi society, let alone the inner workings of the royal family. "We don't know as much about this place as we would like to know or should know," confessed one diplomat, who compared Saudi Arabia with its mysteries to China wrapped in its inscrutable ways. "It's impolite to discuss politics here," another diplomat explained. "Saudis think there is something wrong with you if you do. They are too busy making money to talk politics."

Nor are there any public forums of discussion to take soundings of Saudi opinion, other than an occasional appearance by a minister, usually before a student audience. There is no national assembly or even consultative council, and the government-controlled press eschews politics as it does controversy.

When Saudis discuss their feelings, sometimes with amazing frankness even with a foreigner, it is mostly within the sanctity of their homes, which are widely held as inviolable to the police or security as are mosques. "They are a very private and family-oriented people," one longtime resident said.

Despite the veil drawn over politics, Western diplomats, long-time foreign residents and most Saudis themselves all assert confidently that an Islamic revolution such as swept away the shah of Iran, or an open assault on the House of Saud such as Moslem fanatics just carried out on Sadat's Egypt, is unlikely to occur here. They easily reel off a dozen or more fundamental differences between Saudi Arabia and Iran.

These include the deep reservoir of historic legitimacy underpinning the House of Saud and never enjoyed by the American-imposed shah, the time-tested alliance between the Saudi religious and political establishments as compared to the longstanding hostility between the two in Iran, the vast network of personal ties and allegiances linking the 4,000-strong Saud clan to the kindom's various tribes and families, which had no parallel in the shah's Iran, and the vast sums of money invested in the health, education and social welfare of all Saudis, a policy also never duplicated by the shah.

"I don't see any indications of any instability as a businessman," says William Fifer, chairman of the American Businessmen's Group of Riyadh who has been involved with Saudi Arabia for a decade now. "As far as internal stability and security go, I am not in the least bit worried."

Yet the unknowns of Saudi political life are so glaring and manifold that such statements seem more declarations of faith than anything else. For example, no outsider really seems to know what is going on within Saudi religious circles, despite the central role played by the powerful ulama and despite the real-life drama played out in Mecca two years ago when 300 heavily armed Moslem extremists seized the Grand Mosque and held it for two weeks.

The Saudis themselves dismiss that black episode as their "Jonestown," an aberration in Saudi behavior as atypical and horrifying to them as the mass suicide of hundreds of wayward cultists in Jonestown, Guyana, was to Americans.

"Jouhaiman Oteiba (the Mecca leader) was a shadow across the country that was so ugly no one wants it to happen again," declared Mahmoud Safar, the deputy minister of higher education. "It got no support from the people.... (But) it showed there was group of people who lost track and did not understand what was going on in the country. The chance of it's being repeated is very, very remote."

Saudi officials say they now watch their potential Moslem extremists much more closely for danger signs. Above all, the government has deliberately sought to coopt many of their demands for stricter religious observance, including the removal of many Saudi women from office jobs alongside men.

The general presumption is that the Islamic Right has either been pacified or taken in hand. But few, if any, westerners are in a position to know what the mood among such extremists really is, any more then they did in Egypt on the eve of Sadat's assassination.

Another crucial unknown is the Saudi military, not only as a combat-ready fighting force but as a pillar of security for the House of Saud. No expense has been spared to see to its wellbeing, either in arms or material comforts, as reporters who stayed in the well appointed air force noncommissioned officers' living quarters outside Taif during the Islamic conference last January saw firsthand.

At the same time, the Saud family watches closely over the 75,000-strong armed forces. There are princes serving throughout the various branches, particularly the elite air force, and this in itself provides an inbuilt security apparatus no other Middle East leader can match.

In addition, the 45,000-man army is divided up in military cities being built in various parts of the kingdom, all but one far from the capital. Protection of Riyadh itself, as well as the oil fields, is the special duty of the tribally based, 12,000-man national guard. But there is also a 1,000-strong royal guard hovering around the ruling family.

All this seems a finely crafted system of checks and balances to prevent a military coup from ever taking place. But whether it would serve equally well to stop a surprise attack by a small group of religious fanatics, the kind that succeeded in gunning down Sadat during a military parade in Cairo, is an unanswerable question.

Diplomats and other tend to parry it by arguing that the House of Saud is so vast, with so many potential heirs to the throne standing by, that even a Cairo-style attack on its top leaders would not bring it down.

Perhaps least of all is known about the deliberations and decision-making process within the royal family itself. The dynamics of major policy decisions are totaly hidden behind thick curtains of silence. Unlike Washington, little leaks out of Riyadh.

One recent case in point was the eight- point Middle East peace plan of Crown Prince Fahd. The first major really risky international initiative of the royal family, it must have been preceded by prolonged discussions. Yet what is known in Western diplomatic and intelligence circles about its origins and authors, or which members of the royal family, if any, had misgivings seems minimal even four months after its publication. Conflicting reports abound.

When it comes to the inner sanctum of the royal family, Saudi Arabia is still very much a jealously guarded secret kingdom.

All these imponderables leave one mostly with impressions and guesstimates when it comes to predicting the House of Saud's stability or longevity. In many ways, Saudi Arabia, with its vast wealth and tiny population, with its limitless opportunities for money-making and its puritan social mores, looms unique among Third World countries.

Certainly there are not the visible signs of stress and strain that so badly scarred the face of the shah's Iran: neither the poverty, the omnipresent secret police nor the demonstrating students either inside or outside the country.

"I don't know of any political prisnoers here per se," said one Western analyst.

The worst threat to the House of Saud, according to some long-time residents, is probably an invisible one: the moral crisis of a highly religious society, many of whose members enjoy a lifestyle in private, or abroad, that stands in shocking contradiction to Wahhabi dictates.

But whether there is another Jouhaiman in the making remains today the ultimate mystery of Saudi Arabia.

When it comes to predicting its stability, one is likely finally to agree with the comment of one American businessman living here: "This isn't Iran, but this is the Middle East, and the only thing you can expect in the Middle East is the unexpected."