What was going on when I was born?

The four candidates for Nassau County Executive clashed yesterday over the role of county government in the management of the Long Island Lighting Company, the future of the utility's nuclear power plant and political contributions by county employees. During a one-hour debate at The New York Times, Francis T. Purcell, the Republican incumbent, and his Democratic challenger, John W. Matthews, were cordial, but on several occasions they engaged in heated verbal sparring. They agreed only that they did not approve of the way Lilco was being managed, but they differed sharply on whether the county government should force a replacement of the top officers at the utility. The Liberal Party candidate, Jack Olchin, said he strongly supported the Shoreham nuclear plant, while Dr. Raymond J. Vuolo of the Right to Life Party said the importance of the issue had been exaggerated.

The Chrysler Corporation today reported record earnings for the third quarter of $316.2 million, or $2.75 a share, up 21 percent from $261.6 million, or $1.88 a share, in the comparable period last year. It was the eighth consecutive quarter of record earnings for the nation's third-largest auto maker. The Chrysler report brings the combined earnings of The Big Three to $1.15 billion for the July-September period. But for the General Motors Corporation and the Ford Motor Company, the high cost of incentive programs in the form of low financing rates produced declines in operating income. G.M., the industry giant, actually lost money on its car-making operations.

John A. Walker Jr. pleaded guilty today to charges that he spied for the Soviet Union and that he recruited his son, friend and brother into an espionage operation that the authorities have called one of the most damaging in American history. Under a plea agreement approved by a Federal judge today, Mr. Walker admitted his role in the spy ring and is to be sentenced to life in prison. In return, the judge agreed to a reduced prison term of 25 years for his son Michael L. Walker, a Navy yeoman who faced up to two life sentences and more than $500,000 in fines. Will Give Complete Account Mr. Walker, a retired Navy communications specialist, told Federal District Judge Alexander Harvey 2d that he would give Government investigators a complete account of the material that he and his associates delivered to the Soviet Union in 17 years of espionage. He also agreed to testify in other cases, including the trial of Jerry A. Whitworth, a retired Navy radioman described as Mr. Walker's closest friend, who is charged with stealing secrets that were delivered to Soviet agents.

Markets Phibro-Salomon is cutting back its commodity trading unit, Philipp Brothers, for the second time in a year. About 600 jobs will be lost, and two men in their early 30's who made their mark in sugar trading will become Philipp's chairman and president. Phibro-Salomon will change its name to Salomon Inc. [Page D1.] A flood of Treasury notes and bonds will be unleashed beginning today when the Treasury starts a three-part financing totaling $17.75 billion. The size and hasty schedule surprised dealers and helped reduce bond prices by more than a half-point. [D22.]

Merrill Lynch & Company, parent of the giant financial services organization, yesterday reported a 52 percant drop in net income for the third quarter despite a 5.4 percent increase in revenues. Net income fell to $38.4 million, from $80 million in the third quarter of 1984. Weak stock market volume in the latest quarter hurt Merrill, just as at other brokerage houses.

TOWARD the end of his long life, Edmond Halley was writing of his prediction that the comet he studied in 1682 would return in 1758 or 1759. He knew he would not live to see if his calculations proved to be correct. But he expressed the hope that ''candid posterity will not refuse to acknowledge that this was first discovered by an Englishman.'' ''Candid posterity'' has been, in one sense, generous to Halley. His name is forever associated with comets. People may misspell his first name (his will had it with an ''o''). They may mispronounce his last name (it's Halley as in ''alley'' or perhaps - the argument may never be settled - as in ''hawley,'' though never as in ''hayley''). Nonetheless, he is widely remembered through the dazzling comet bearing his name, the most celebrated comet of all. Edmond Halley did not discover this particular comet, which is racing in for its once-in-a-lifetime visit to the inner solar system. He did something more important. He determined that comets do not travel straight lines or parabolic orbits, passing through once never to be seen again; their orbits are elliptical, a sort of squashed circle. Many comets thus make periodic visits, he concluded, and by plotting with care the characteristics of their elliptical orbits, which he did with ''his'' comet, it was possible to predict their many returns.

Despite high interest rates, stable prices and Federal incentives to encourage thrift, Americans are saving a smaller portion of their incomes than at any time since the early 1950's. The annual savings rate plummeted during the summer to 2.9 percent, less than half that for eight of the past nine years, and the rate for September came to only 1.9 percent. When corporate pension funds are excluded, Americans are probably withdrawing more from savings accounts than they are putting in. The recent sharp decline owes much to cut-rate financing offered by Detroit on new cars. The borrowing to pay for them severely affected the personal savings rate.

King Hussein of Jordan and Yasir Arafat, chairman of the Palestine Liberation Organization, met for two and a half hours here tonight to discuss strains in their already uneasy alliance. The meeting at the Royal Palace, at which both leaders were accompanied by a large number of aides, broke up apparently without a resolution. More talks were scheduled for Tuesday. ''It won't be solved in one meeting,'' Hani al-Hassan, one of Mr. Arafat's chief political advisers, said.

''The way we hit, we couldn't beat Molly Klutz.'' - Whitey Herzog, manager of the St. Louis Cardinals.

Phibro-Salomon Inc. yesterday announced the second major shake-up in a year at its Philipp Brothers commodities trading subsidiary, cutting hundreds of staff and installing new management. Taken together, both parts of the shake-up mark an enormous pruning back of Philipp Brothers, which just four years ago acquired Salomon Brothers intending to create a financial powerhouse. But Salomon Brothers, Wall Street's largest investment banking firm, has gained the upper hand so decisively that yesterday Phibro-Salomon said it plans to change its name to Salomon Inc. Philipp Brothers, one of the largest and most respected concerns in the secretive world of physical commodities dealing, will be slimmed down sharply as it refocuses on its basic business, trading raw commodities. 600 Jobs to Be Cut The moves will slash 600 staff members worldwide from Philipp Brothers' staff of some 3,000. Nearly all of those reductions, according to Robert S. Salomon Jr., a Phibro-Salomon managing director, will come from the company's marketing and distribution operations, a low-margin business in which it largely acts as a middleman. On a smaller scale, it is also negotiating to sell a Brazilian pig-iron manufacturing operation, Mr. Salomon said.

A dispatch on Friday about the United Nations' 40th anniversary misstated the American position on resolutions on the Middle East. The United States opposes references not to a ''just settlement'' but to Palestinian ''self-determination.''

An article in SportsMonday on Oct. 21 about the World's Masters Games rowing competition in Toronto last August stated the achievements of Dave Challinor and J. William Middendorf 2d. Challinor won a bronze medal in the double-scull event with William Killhour. Middendorf and an Australian teammate won a gold medal in the paired oars.