As the members of the National Symphony Orchestra's board of directors don their tuxedos and gowns for tonight's glittery opening concert, they have more than Brahms' Third to think about: to wit, a $5 million projected shortfall, which requires $500,000 a month in fund-raising, just to stay afloat.

In addition, the orchestra has committed itself to raising a $3 million endowment by the end of the year -- a commitment it wrote into a formal agreement with the musicians union, which itself has agreed to take a salary freeze. The financial situation is "not at the panic level," says the orchestra's president, Leonard Silverstein, but it's "too close for comfort, given the importance of the orchestra and its position in the nation's capital."

For several seasons, the NSO has been caught in a financial bind with expenses steadily outrunning income and a deficit slowly, inexorably accumulating. Now, with a new management team and promising budget reforms, it has been sideswiped by other people's tragedies.

"Our total earned income for the last season was $3.8 million," says manager Henry Fogel. "It would have been over $4 million except for the $250,000 in ticket sales we lost because of the Wolf Trap fire. We had not yet announced our plans for a benefit performance next spring hosted by Princess Grace, but we expected to earn another $100,000 to $150,000 with that."

Fogel's assignment is not raising money so much as keeping expenses in line, and he has been busy on that project. "The total expense budget for next year," he reports, "is $300,000 less than this year, and the earned income will go up. The gap between earned income and expenses will be $1.3 million less." It will still be considerable, according to projections for the season now opening: $10.286 million in expenses; $4.95 million in earned income.

Why is the NSO so short of funds? Silverstein reaches into his memory for an illustration: "There was a fellow named Cabot who lived in Georgetown for 30 years, died a while ago and left a million dollars to the Boston Symphony. Naturally, that breaks my heart." In Boston, it is traditional for Cabots to give money to the Boston Symphony. Traditions like that (and an adequate supply of families as wealthy as the Cabots) have yet to be established in Washington. A few miles up Interstate 95, the Baltimore Symphony has just opened a new hall named for Joseph Meyerhoff, who contributed a cool $10 million for its construction as well as the prime downtown lot on which it stands. The National Symphony is still looking for its Cabots and its Meyerhoffs. Also for substantial, regular corporate supporters. And a lot more. A state government, for example, like the ones that support all the other symphony orchestras.

"I've asked myself and asked management," says Silverstein, "what is the difference between us and the other orchestras that are in the black, in effect. One difference is that they are complete sellouts at most of their concerts; they have larger communities . . . Another is acceptance for 100 years or more of history. And there are recordings; we have just now broken the barrier on recordings. It's a direct dividend from the European tour; Deutsche Grammophon heard us in Hamburg. The other thing is the orchestra's endowment. Pittsburgh has the Heinz family, who have been very generous in their own way to this orchestra. They have Heinz Hall now, and an endowment of some $30-odd million as I understand it. Another critical thing is, every one of those orchestras has a state government to provide support, and they have major industrial companies that are willing to step up and help as a community-pride gesture."

If Washington lacks factories, though, it abounds in offices; thousands of corporations are represented in this city, and if they give most of their arts contributions to people back home, Silverstein hopes that they can be persuaded to give a smaller amount to the orchestra in Washington. Over a period of years, he expects the orchestra to find a stable financial base through a large number of relatively small corporate contributions. The problem is to hold on while this infrastructure is built up.

"There are enough companies around, given the time and the staff organization to reach them, that would manage some modest support for the orchestra, which wouldn't interfere with their support of their local institutions." As for businesses that have their headquarters here, there isn't one, says Silverstein, "that has given the kind of support that I feel should be justified."

Among the orchestra's assets that don't get written down in ledgers, according to Silverstein, one of the foremost is the "spectacular personality" of music director Mstislav Rostropovich. "Slava is terrific in lending himself to any sort of legitimate promotional activity," says Silverstein. "Not all star conductors are like that. Von Karajan, they tell me, you can't even talk to."

Then there is the board, which has a two-tiered structure: a small group that acts in the traditional decision-making role of a board of directors and a larger group whose primary function is to generate support for the orchestra. "It's not that anyone has to be rich to be on the board," according to Silverstein, "but we have the obligation -- with a $500,000-a-month gap -- either, as they say, to give or to get. At least $10,000 per year . Now, that isn't honored every time, and some people are not in a position to solicit. With 75 people on the board, that's $750,000; that doesn't go anywhere near to it . . . There's work to be done. I expect every board member to work. If they don't want to work, they don't belong on the board."