Investors, encouraged by lower interest rates, shattered the eight-day-old trading record on the New York Stock Exchange and pushed up the Dow Jones Industrial Average another 7.52 points.

Shortly after the New York exchange closed at 4 p.m. yesterday, the Federal Reserve Board gave further momentum to the drop in interest rates that has sparked the market's climb. The nation's central bank cut the discount rate it charges financial institutions that borrow from it to 10 percent from 10 1/2 percent.

The Fed move was seen as a confirmation that it continues to approve of the sharply lower level of interest rates. By itself, however, the discount rate cut does not necessarily indicate that the Federal Reserve wants rates to fall further, analysts said.

The Fed itself said the rate was cut in order to bring it "into better alignment with short-term interest rates." It was the fourth time in six weeks that the Fed has lowered the rate, which stood at 12 percent at the beginning of July.

Nearly 138.5 million shares of stock changed hands on the New York Stock Exchange yesterday, as such institutions as insurance companies and pension funds continued frenetic trading. The previous record trading day was Aug. 18, when 132.7 million shares were bought and sold. Yesterday was the fourth day in a row that more than 100 million shares were traded on the New York exchange alone.

Yesterday also produced a record number of transactions -- 89,751 -- eclipsing a 43-year-old record of 83,100. In 1939, when individuals dominated trading, most trades were for 500 shares or less. Today, an institution usually buys and sells in blocks of 10,000 shares or more. Yesterday, for example, in one trade alone 1 million shares of Exxon Corp. changed hands. In another, 700,000 shares of Sony were traded.

Yesterday's market performance was influenced by a statement from Merrill Lynch's chief analyst Robert Farrell, who said he felt the Dow Jones average could climb to the 925 to 950 range. Farrell, one of the most accurate overall market forecasters, had been skeptical of the rally.

The Dow average topped 900 briefly yesterday, but fell back in later trading. Volume was so heavy that the tape that records transactions was behind most of the day. At the end, the tape was 18 minutes late.

Since the current rally began last week, investors have concentrated their buying on the high-quality, blue-chip stocks traded on the New York Stock Exchange. Since Aug. 12, the widely followed Dow Jones industrial average has climbed 115.49, a gain of nearly 15 percent. Yesterday's close of 892.41 was the highest the index has been since last Dec. 4, when it finished the day at 892.69.

Although individual investors and foreign investors are starting to join the party as the record number of transactions indicates, the massive stock market rally so far is mainly a creature of giant institutional buyers, according to Jerry Hinkle, the chief stock trader for Sanford C. Bernstein & Co., a brokerage firm that specializes in trading stocks for institutions.

"The breadth is wide, the volume is unprecedented, but there are still a lot of participants not playing the game," said Robert Stovall of the brokerage firm Dean Witter Reynolds.

James Balog, senior executive vice-president of Drexel Burnham Lambert Inc., said that when the rally began stock prices were severely undervalued, but now the "catchup phase is over."

Balog said there is still a "lot of euphoria" on Wall Street, but that the underlying economy still is weak and the surge in stock prices will end as investors begin to think anew about the problems in Mexico, Argentina, the banking community and the corporations.

The Federal Reserve's discount rate cut should prompt major banks to trim their prime lending rate further. The prime rate, the key interest rate on which banks base their loan charges to businessmen, is at 13 1/2 percent today, compared with 16 1/2 percent two months ago.

The stock market yesterday shrugged off the bankruptcy filing of the Manville Corp., one of the 30 companies whose stocks are listed in the Dow average.

Overall, 1,183 New York exchange stocks rose in price while 457 declined. More than 260 stocks set new highs, while one stock hit a new low.

The most active stock was Cities Service, the subject of a tentative $53-a-share takeover by Occidental Petroleum. Nearly 3 million Cities Service shares changed hands. Citgo stock closed at $46.50, up $1.50.

The New York Stock Exchange's own index closed at 68.01, up 0.62.

On the American Stock Exchange, volume totalled 10.5 million shares, up sharply from the 7 million shares traded Wednesday. The Amex index rose 4.74 to 276.37.