The stock market staged another explosive advance yesterday as turnover on the New York Stock Exchange reached 63.5 million shares, easily obliterating the volume record of 52.3 million shares set just last Friday.

However, the market's 14.99 point gain, as measured by the Dow Jones average of 30 industrial stocks, was well below the best levels of the day as investors took profits during the final two hours of trading.

In the first hour alone, stocks advanced 17.33 points on a record single hour turnover of 17.5 million shares.The volume was so heavy that at one point the tape was running 11 minutes late.

Brokerage firms, however, reported no unusual problems in processing the record number of transactions.

The advance was fueled by the same buying stampede by cash-rich institutional investors and foreigners that prompted Friday's 19.92 surge, and the momentum continued into the afternoon. At around 2:30, the Dow was up nearly 23 points - close to breaking through the technically significant 820 level - but fell back to close at 810.12 for the day.

In the last three sessions, the Dow has gained 38.98 points. The last time the widely watched index stood this high was on Jan. 3 when the market closed at 818.61.

Gainers outnumbered losers by about 2-to-1 on the Big Board as 1,050 issues advanced, 536 declined and 351 remained unchanged.

The lack of any specific news developments yesterday left analysts hard-pressed to explain the phenomenal advance - an advance largely feeding on itself - other than to point to a strengthening dollar, improving investor psychology, and the herd instinct of institutional investors who have lately found themselves sitting on tremendous pools of uncommitted cash.

"There's an obvious panic with a lot of performance conscious managers out there afraid of getting caught with too low an equity position when the market is rising, noted Eric Miller, chairman of the Investment Policy Committee at Oppenheimer and Co. It's a buying panic in the true sense of the word in volume far beyond what we've ever seen."

E.F. Hutton and Co. President George Ball expressed the optimistic view that markets which advance on no news tend to have longer time spans on the upside than those which go forward on specific news events.

But other analysts cautioned that the hurting rally of the last few days could prove evanescent and the market may be extremely vulnerable if worries about inflation, interest rates, the foreign trade deficit and the lack of an energy policy which have been weighing on investors reassert themselves.

"Our view is what we are looking at is essentially a rally in a bear market downtrend, commented Paul Blamey, director of research for Becker Securities. He said his firm's technical indicators have not yet turned upward.

"I still think the gut issue in the stock market is interest rates, Blaney said, "and, despite the last two days, we're still concerned that the trend in interest rates is up."

The strong volume made brokerage house stocks favourites again yesterday. Merill Lynch was the second most actively traded stock, gaining 1 3/8 to 18 5/8. Last Friday Merrill Lynch announced it had purchased White, Weld Co., another brokerage firm. E. F. Hutton was up 1 1/2 to 16 1/4, and Paine Webber closed at 8 1/4, up 1/2.

Du Pont, which reported higher first-quarter earnings, was up 2 1/8 to 112 1/8. Other companies with improved first quarter results also gained, including Philip Morris, up 1 5/8 to 63 3/4 and Bankers Trust, which rose 3/4 to 36 1/2.

Scott paper was again the most active HYSE stock. It closed up 1/2 to 14 3/8. A block of 895,000 shares traded at 14 1/4.

The NYSE common stock index closed up 0.75 at 52.69.

On the American Stock Exchange, volume rose to 6.2 million shares compared with 5.8 million shares on Friday. The Amex index closed up 1.06 at 135.75.

Resorts International, which said it plans to open its Atlantic City Casino on May 19 or shortly thereafter, rose 7/8 to 31 7/8 on the Amex.

In the over-the-counter market, the NASDAQ composite index closed at 111.91, up 0.62.