Stock prices yesterday took their biggest single-day plunge in history.

Analysts said the 39.10-point fall in the widely followed Dow Jones Industrial Average was sparked by investor fears that the decline in interest rates was over.

The decline was exacerbated, analysts said, because some computer-directed programs that call for the sale of large blocks of stock by brokerage houses and other well-heeled investors were triggered in the last hour of trading on the New York Stock Exchange. Nearly 40 million shares of stock changed hands in the last 60 minutes before the final bell rang to end trading for the day.

The Dow Jones Industrial Average closed at 1526.61, down from a record high Tuesday of 1565.71. Yesterday's absolute decline was bigger than the 38.33-point tumble the Dow Jones average took on Oct. 28, 1929, during the collapse of stock prices that ushered in the Great Depression.

But the 1929 decline represented a 12.8 percent loss in the Dow average, compared with 2.5 percent yesterday. The Dow average would have had to fall about 200 points yesterday to approximate the scale of the 1929 drop.

The sharpest rise in the Dow index occurred on Nov. 3, 1982, when it jumped 43.41 points.

Yesterday's decline in stock prices was not confined to the traditional "blue chips" that make up the Dow average. Standard & Poor's index of 500 stocks fell 5.83 points to 207.97, a record one-day decline for that gauge as well. The index of all stocks traded on the New York Stock Exchange, the most important securities trading floor in the world, fell 2.94 points to 120.2.

About 180 million shares of stock were traded on the New York Stock Exchange between 9:30 a.m. and 4 p.m., with about 22 percent of that coming in the last hour.

Analysts said it was unclear whether yesterday's steep decline was a temporary setback to the latest surge in stock prices that began four months ago or was a prelude to a sustained decline in the price of securities. But most agreed that stock prices have risen so high that speculative investors -- those seeking quick gains and more skittish during inevitable price declines than buyers in search of long-term investments -- are becoming a major factor in the stock market.

"What is more important than what happened during the final hour of trading yesterday is the realization that we are in a more speculative environment. That will mean more volatility in prices," said Leslie J. Silverstone, manager of the Dean Witter Reynolds Inc. brokerage office at 18th and K Streets NW.

Despite yesterday's steep plunge, the Dow Jones average of 30 big industrial companies remains closer to the record high that it set Tuesday than to its level in early December, before it closed above 1,500 for the first time. Prices on the New York exchange even recovered slightly during the final five minutes of trading.

Most analysts said they believed that yesterday's tumble had its roots in what would be considered a "good news" report on employment issued by the Department of Labor, according to Jerry Hinkle, the chief trader for the New York securities firm Sanford C. Bernstein & Co. The Labor Department said yesterday that civilian unemployment declined 0.1 percentage points, to 6.9 percent, in December, while the number of workers on nonfarm payrolls grew by 320,000.

That triggered a sharp increase in interest rates in the bond market, as investors concluded the stronger-than-expected performance of the economy in December will spur economic growth and lead to increased demand for credit on the part of companies and consumers. The expectation of stronger growth convinced investors that interest rates would have to rise and that the Federal Reserve Board, manager of the nation's monetary policy, will find it difficult to take steps that would reduce interest rates further. Hinkle said that the recent stock market rise had been so linked to the expectation of further declines in interest rates that investors might not have digested the fact that the Labor Department report might also presage a healthier economic climate -- with higher corporate profits and dividends.

The Dow average had already fallen 15 points when economist Henry Kaufman, the executive director of the securities firm Salomon Brothers Inc., issued a statement that said the economy seems to be improving and that he expected no further declines in interest rates. Although Kaufman's short-term forecasts are often wrong, his track record is better than that of most prognosticators, and his pronouncements often have a major impact on stock prices and interest rates.

After Kaufman issued his statement, shortly before 3 p.m., stock prices went into a tailspin.

Then the computer-directed programs linked to futures contracts based on the Standard & Poor's index began to dominate trading, further driving down stock prices. These programs are used by some big brokerage houses that are trading for their own accounts, rather than for customers, and by some big "pools" of money controlled by big investors.

By the afternoon, the futures contracts based on the S&P index were priced less than the issues themselves. When the spread becomes wide enough, the trading programs call for investors to sell the stocks underlying the S&P index and buy the cheaper futures contracts. Heavy selling continued until the spread between the futures contracts and the S&P index narrowed.

"The recovery in the final minutes of trading may reflect the end of the computer-directed selling," one analyst said.

More than twice as many stocks declined in price as rose yesterday, during the fifth-busiest trading day in NYSE history.

Price declines were less marked on the American Stock Exchange and the over-the-counter market, where securities are bought and sold broker-to-broker rather than on an organized exchange through a middleman.

The Amex market value index fell 2.63 points to 247.26, a 1 percent decline. In the over-the-counter market, the National Association of Securities Dealers Nasdaq composite index fell 1.65 points to 328.09, a 0.5 percent decline.