The stock market surprised the experts and soared today in heavy trading, as the Dow Jones Industrial Average jumped by 37.07 points to 944.26, its second-largest one-day gain in history.

"This is extraordinary," said Steward Pillette, associate research director at Drexel Burnham Lambert Inc. Few on Wall Street could precisely define reasons for the dramatic gains in trading activity, which totaled almost 94 million shares on the New York Stock Exchange.

Stock prices had sagged over the past two weeks, with the industrials average losing about 39 points from its dramatic 158-point rally of August and September, and there was little evidence even by midday today that a major move was underway. Further confirmation of the economy's weak condition is expected on Friday, when the government announces the unemployment rate for September.

But about 3 p.m., the blue chip stocks that are used to tabulate the industrial average began to shoot up, as did many other stocks favored of late by large institutional market investors.

None of the 30 stocks that make up the industrial average declined, while 28 gained. The increase in the industrial average has been topped only by the dramatic 38.81-point gain on Aug. 17.

Among the reasons given for today's buying spree was an expectation of further declines in interest rates. The Federal Reserve Board's Open Market Committee met Tuesday to consider goals for the growth of the money supply for the next six weeks, and although there was, as usual, no announcement of decisions, the market today apparently assumed that the Fed is easing monetary policy to help the economy recover, some analysts said.

The federal funds rate on loans of uncommitted reserves among banks -- reflecting the availability of money in the banking system -- fell as low as 8 1/2 percent today, and market analysts took that as a sign of easier monetary policy. Yesterday the rate averaged 10.27 percent.

The decline in the federal funds rate helped trigger substantial gains in bond prices.

Other factors that contributed to the rally were positive announcements by several blue-chip leaders, including International Business Machines Corp. IBM said that its third-quarter results would be better than expected, despite the strength of the dollar, which depresses the value of its overseas business. Consequently, IBM stock rose by 3 7/8 closing at 79.

There was also some speculation that investors are continuing to move into stocks as money market fund interest rates fall. Analysts also suggested that investors were buying stocks to help cover option positions that expire at the end of the week.

But as the market's move began this afternoon, it was clear that few wanted to miss a rally that pulled stocks to their highest closing point since Aug. 13, 1981. "These marketeers, having missed the first 157 points, stopped waiting and bought stocks because they were afraid they would miss another explosive rally," said William M. LeFevre, vice president-investment strategy at Purcell, Graham & Co. Inc.

Pillette also noted that a widely predicted dip in the industrial average to about the 880 level did not materialize, as the market's pull-back ended at about 886. "People just stopped waiting," Pillette said.

As a result of all the activity, more than four times as many stocks gained as lost ground on the New York exchange, where the composite index gained 2.14 to 72.20 and the average price per share rose by 88 cents. Volume rose by 24 million shares from yesterday's figure.

In particular, Johnson & Johnson began to recover from the Tylenol situation, trading at 3.24 million shares, more than double that of American Telephone & Telegraph, the second-most-actively-traded stock. J&J closed at 41 7/8, up 2 7/8, while AT&T rose 1 3/4, ending the day at 58 1/2. Eastman Kodak surged by a dramatic 7 5/8, closing at 94 1/4.

The American Stock Exchange's market value index gained 5.14 to 288.28. Volume rose to 6.06 million shares from 4.78 million yesterday, and the average price per share jumped by 20 cents. There were 410 stocks gaining, while 156 declined, with 218 remaining unchanged, an indication that the rally focused on the blue chip stocks that make up the Dow industrial average.

Nationwide turnover in NYSE-listed issues, including trades in those stocks on regional exchanges and in the over-the-counter market, totaled 107.51 million shares.

Standard & Poor's index of 400 industrials soared 4.62 to 140.68, and S&P's 500-stock composite index was up 3.99 at 125.97.

The NASDAQ composite index rose by 3.21 to 191.28.