Eighty-seven years of all-white rule of Rhodesia came to a quiet, undramatic close yesterday.

At a ceremony held behind the closed doors of Indenpendence House, a new multi-racial government - headed jointly by Prime Minister Ian Smith and three black nationalist leaders - was sworn in to lead Rhodesia during the transition to black majority rule.

No reporters or photographers were permitted to witness the ceremony, and few Rhodesians - black or white - were even aware that the historic event was taking place.

It appeared that the Smith government was anxious to avoid any possible display of white opposition to the first stage in the internal settlement agreement, which guarantees black majority rule and elections based on universal adult suffrage by Dec. 31.

Ironically, before the three black leaders became part of the nw government's four-member Executive Council, they had to swear an oath of allegiance to the 1969 constitution promulgated by Smith after his government unilaterally declared the colony of Rhodesia independent from Britain.

"There are times when you have to swallow your pride to achieve the highest good and this was one of them." Bishop Abel Muzorewa, who heads the United African National Council, later told reporters, "I think it is a miracle that this has taken place at all."

Then referring to black plans to change the name of Rhodesia to Zimbabwe, Muzorewa vowed that on Dec. 31, "We weill swear an oath of allegiance to Zimbabwe."

Prime Minister Smith, for his part, termed teh ceremony marking the end of all-white rule another "mile-stone in our history."

"This is the way it is going in Rhodesia, isn't it," Smith remrked."One's got to be realistic. We live in a changing world. We'll make it go."

A few hours agter the ceremony, the four members of Rhodesia's new governing body held their first meeting in the Cabinet room next to the prime minister's office in downtown Salisbury.

THe immediately decided by drawing lots that Smith would serve as the first council chairman, to be followed at four-week intervals by Chief Jeremiah Chirau, the Rev. Nidabanningi Stthole and Muzorewa.

Muzorewa told reporters after emerging from the first 90-minute session of the council that the transitional government would give top priority to convincing the black Rhodesian guerrillas still fighting under the umbrella of the Patriotic Front to support the internal settlement and lay down their guns.

He said that as soon as the "mechinery of peace" was set up,a formal appeal would be launched asking the guerrillas to come home from their bases in neighboring Zambia and Mosambique, and informing them of the benefits awaiting them.

The fate of the internal agreement signed here 18 days ago may well hang on the success of this appeal. Without an end to the worsening guerrilla war, it is highly unlikely that elections for a black majority government will ever held, and there is fear that a civil war with foreign involvement will develop.

Muzorewa, however, scoffed at attacks on the internal settlement by the leaders of the Patriotic Front guerrillas, Joshua Nkomo and Robert Mugabe, and showed little interest in President Carter's recent proposal for a summit meeting of all Rhodesian leaders in New York.

"We are in the process to full majority rule in December," Muzorewa said. Sithole, Chirau and white Rhodesian officials displayed a similar lack of enthusiasm for a meeting with the Patriotic Front leaders, while in the Zambian capital of Lusaka, Nkomo also declared he as not interested in attending such a summit.

The prospects for a New York confernce thus appeared particularly grim as U.S. Ambassador to the U.N. Andrew Young arrived in southern Afric yesterday in last-ditch effort to salvage for a Rhodesian settlement.

The ever-optimistic Young, however, said in a Dares Salaam, Tanzania, tht he hoped plans of action for internationally acceptable political settlements for Rhodesia and Namibia would be created within 30 days.

Tnazanin sources said that Young assured President Julius Nyerer that the United States still regarded the Anglo-American proposals announced last summer as the best basis for any Rhodesian settlement.

The formal end of all-white rule here, begun 87 years ago withthe establisment of a British colony under John Cecill, came in a strange atmosphere of "nusiness as usual" combined and improvisation.

It was only a few hours beforehand that reporters were informed and hen the ceremony was to take place. Aside from the 30 toso members of the press corps who were left standing outside the gates o Independent House during the ceremony, life in Salisbury proceeded as if nothing of importance was happening.

A black Anglican bishop, Patrick Murindagomo, was chosen to administer th oath of allegiance to the new ministers. Rhodesis'swhite President, John Wrathall, should have performed this function, but he was apparently unacceptable to the three black leaders.

Despite the creation of an Executive Council to govern Rhodesia during the transition, Ian Smith will remain prime minister until establishment of a black majority government at the end of the year, and the white-dominated Parliament will also continue in power until new elections are held - probably in the fall.

Smith and Muzrorewa told reporters that the new interim government's cabinet, composed of an equal number of black and white ministers, would be chosen within the next few days.

Each of the three black nationalist leaders probably will name five persons from his faction to sit in the Cabinet alongside 15 white ministers. Each ministry will be run jointly by a black and white minister.

The main task facing the transitional government is completing the writing of a new constitution that must be submitted to the $260,000 whites here for their approval even before elections take place.

The old white cabinet held what was probably its last meeting early yesterday morning, but did not make public what decisions it had taken prior to being disbanded.

At the same time, there were reports that Smith had quietly revamped his War Council - the body responsible for the conduct of the government's anti-guerrilla campaign - to reduce its size from 10 to five and exclude all ministers before the establishment of the transitional government.

This would mean that the new black ministers and members of the Executive Council would not be in a position to exercise much influence over the conduct of the war. Smith denied to reporters any knowledge of such a change having been made in teh War Council, and said decisions regarding the war would be made by the Executive Council