What was going on when I was born?

UAL Inc., the owner of United Airlines, agreed yesterday to buy the Hertz Corporation, the world's biggest car-rental company. United is already the nation's dominant air carrier. The surprise acquisition, valued at $587.5 million, would make UAL, which already owns the rapidly expanding Westin luxury hotel chain, one of the most important travel companies in the country. The announcement, made jointly by UAL and the RCA Corporation, which owns Hertz, came only three days after a costly 29-day pilots' strike against the airline had ended.

An article June 4 about groups petitioning the Federal Communications Commission to deny Ted Turner's bid to take over CBS incorrectly included one group. The American Legal Foundation filed comments with the commission supporting the takeover bid.

A Washington dispatch on page 1 Sunday reported that a letter to The New York Times by Patrick J. Buchanan, the White House director of communications, criticized Governor Cuomo for his position on President Reagan's tax program. Mr. Buchanan gave the letter to a Times reporter with the understanding that it could be used as the basis for a news article. The article should have explained the circumstances under which Mr. Buchanan made the letter available. Letters addressed to The Times that contain news are sometimes used as the basis of articles rather than published in the columns of the editorial page devoted to letters to the editor. Page D1

TUESDAY, JUNE 18, 1985 Companies The owner of United Airlines agreed to buy Hertz from RCA for $587.5 million. United is the nation's largest air carrier and Hertz is the world's biggest car-rental company. The acquisition would make UAL Inc., United's parent, one of the most important travel companies in the country; it also owns the Westin luxury hotel chain. The company noted that 80 percent of all car rentals come in connection with an airline trip. [Page A1.] Four big New York banks are expected to be fined by the Treasury today for failing to report thousands of large cash transactions in recent years, banking sources said. The expected fines - against Chase, Manufacturers Hanover, Chemical and Irving Trust - are expected to be from $200,000 to $400,000 for each bank. Banking sources said a fifth major bank was resisting a fine. [A1.]

The crew of the space shuttle Discovery roared into orbit today to help develop arms for President Reagan's proposed shield against nuclear missiles, to launch satellites and to perform a variety of experiments. In their first key assignment, the astronauts successfully launched Morelos-A, a communications satellite for Mexico. The success was seen as particularly crucial for the shuttle program, which recently has been plagued by satellite failures and increasing competition from abroad in the launching of satellites. ''Great job,'' Mike Mullane of mission control radioed the crew. ''You've got a lot of appreciative folks down here. Thanks a lot.''

His sudden propulsion into the vortex of the hijacking drama has confirmed what Beirut watchers have known all along - that Nabih Berri, a soft-spoken, mild-mannered, 46-year-old lawyer is perhaps the most powerful man in Lebanon. His leadership of the mainstream of the Shiite movement gives him political power that outstrips that of the Christian President, Amin Gemayel. As head of the Amal militia, he has battlefield strength to contend with the Palestinians or the Druse fighters of Walid Jumblat. Mr. Berri, who retains a green card entitling him to work in the United States and whose first wife and six children live in Dearborn, Mich., long plotted a steady, moderate course. It was not until Israel invaded Lebanon in the summer of 1982 that he came into his own as a political force.

The Supreme Court, in a decision with broad implications for the enforcement of the Federal law against age discrimination in employment, ruled today that airlines may not force flight engineers to retire at age 60. The vote was 8 to 0. About half the major airlines in the country now refuse to permit flight engineers to work past age 60. The flight engineer is the third member of the cockpit crew in jet airplanes, and does not fly the plane unless both the pilot and co-pilot are incapacitated. The Federal Aviation Administration has long required pilots and co-pilots to retire at age 60, a rule that was not at issue in the case.

If a beam of green laser light flashes up from Hawaii to the space shuttle Discovery as scheduled on Wednesday, it will be the most prominent experiment yet conducted as part of President Reagan's Strategic Defense Initiative program to develop a defensive shield against nuclear missile attacks. The experiment is the latest milestone in a series of tests aimed at learning how to send a laser beam through the turbulent atmosphere with great precision, a matter of critical importance if some of the most visionary ''Star Wars'' weapons are to succeed. But the experiment also symbolizes dozens of rapid advances being made in a broad range of technologies that will be needed if the United States is ever to build a defensive system that could knock down incoming enemy missiles at various points along their flight paths toward this country. Top Government scientists say that experiments completed or reported in recent months, and new ideas emerging from the nation's laboratories, have made them increasingly confident that the United States will ultimately be able to develop at least some of key weapons, sensors, materials and other technologies needed for a workable defensive system. ''There has been progress in all of these areas over the last six months or so,'' Dr. Gerold Yonas, chief scientist for the Strategic Defense Initiative Organization, which manages the ''Star Wars'' program for the Pentagon, said recently.

THE young Emperor Nero became known as one of the worst Roman rulers by ordering his mother's death, persecuting Christians and Jews and committing other cruel and bizarre deeds. And, of course, it has also been suggested that he even gave a musical recital, with himself as sole performer, while Rome was ablaze with a fire he had caused. Nero's behavior has come under fresh scholarly discussion, nourished by recent study of ancient Roman chronicles, sculpture, ruins and coins. Though he is still seen as profoundly ruthless, new research makes him seem more understandable by emphasizing that his reign was shaped by his serious passion for the arts, among other personal traits, and by complicated political problems. But experts still voice varying opinions as to Nero's mental balance and his general behavior during his first years in power.

Merger talks between the Burroughs Corporation and the Sperry Corporation were called off yesterday after Sperry said it wanted more time to consider Burroughs's offer. The announcement immediately sent Sperry's stock sharply lower as arbitragers, who bought an estimated 4.5 million Sperry shares in recent days on hopes of a successful combination, began bailing out of the stock. On the New York Stock Exchange, Sperry closed at $51.375, down $4.125, on a volume of 2.3 million shares, while Burroughs closed at $56.125, up 87.5 cents. In a statement issued yesterday morning, Sperry said it had received a merger offer from Burroughs in which Sperry shareholders would have received $65 in Burroughs stock for every Sperry share they held. When the Sperry board responded by requesting more time to allay ''customer base and antitrust concerns,'' Burroughs withdrew its offer and the talks were terminated, the Sperry statement said.

''He wanted to live in the greatest country in the world and take advantage of all its freedom, but he didn't want to be loyal to it.

At the time of their marriage in 1971, J. Seward Johnson and his third wife, Barbara Piasecka, were by any standard the unlikeliest of couples. The bridegroom, who was 76 years old at the time, was heir to the vast Johnson & Johnson health-care fortune. But Mr. Johnson, an enigmatic and private person even to those who knew him best, had always appeared far more interested in oceanography, philanthropy and women than in the baby powder and Band-Aids on which his wealth was built. His Polish-born bride, then 34, who called herself Basia, had arrived in the United States only three years earlier, speaking little English and with just $100 to her name. She took a job as chambermaid at the Oldwick, N.J., estate where Mr. Johnson and his second wife had been living for 30 years. By winning his affection, she soon supplanted her.