MANY YEARS ago, the redoubtable Marjorie Merriweather Post announced grandiloquently at a luncheon one day that "The National Symphone Orchestra is going to become equal of any orchestra in the United States."

But when her son-in-law, Leon Barzin -- for decades the conductor of the country's chief training orchestra, the National Orchestra Association -- asked her how the NSO was going to equal those in Boston, New York and Philadelphia, the famous hostess fell silent.

She would have found the beginning of an answer three weeks ago, when Mstislav Rostropovich opened the NSO program with Samuel Barber's Second Essay for Orchestra. That performance revealed that the National Symphony today is consistently offering a more polished, more refined, more powerful kind of playing than ever before.

The new sound and polish might have shown up last year had that season not been plagued by a strike and various unexpected changes in conductors. But now the effect is unmistakable.

Various sections gleamed in the Barbar Essay, a work written with the specific intention of showing an orchestra in its best light. The French horns had a noble sound, matching the finest to be heard anywhere. The cellos and viola sections -- both increased to 12 a year ago, and the double basses now grown to 10 -- provided not merely more sound, but a live, glowing tone and kind of playing that has been evident more and more in recent National Symphony concerts.

The brass section, which for years was group of unbalanced sounds, now has an even, substantial quality of real luster. The woodwinds, strengthened by several new players -- notable first flute Toshilo Kohno -- easily hold a special place of honor.

The violin section -- the orchestra's largest single choir -- is the one that has most needed further refinement as well as strength. In all three concerts so far this season, the violins have made it clear that they, too, have an added quality. In Barber, in Berlioz, in the opening night's Schumann and Tchaikovsky, and in last week's "Petrouchka," there was a not-to-be-missed difference in tone which was clearly coming from practically the entire section.

Beyond question some of the improvement must be credited to the system of rotating the players, other than the first stands, throughout the section, as is now done in many of the country's top orchestras.

Rostropovich talked about some of the reasons for these marked improvements a few days ago. "Each Sunday I keep having master classes. The musicians come and play whatever they want -- in the last weeks I have heard the Brahms Horn Trio and a Mozart Flute Concerto. We talk about how best to play.

"And now the assistant principals take more responsibility and play more," he added. He stopped for a moment and then, beaming, went on. "Absolutely the orchestra is different from two years ago. I was never so happy as after the first rehearsal of "Petrouchka.'" Like Beecham and Furtwangler, Rostropovich insists that inspiration often comes during a rehearsal.

Many of the musicians share Rostropovich's euphoria. They talk about the kind of charismatic leadership he gives them. They point out with pride the things the New York critics say about the orchestra compared to the reviews it got before Dorati and Rostropovich began their improvements. Many of the string players speak with appreciation about the rotation system, through some of them were opposed to it at first. (The double bass section adopted the plan even before it became a part of the contract.)

The new, younger players note that they chose to come to play under Rostropovich, which is a complete reversal from the days when the orchestra lost many of its best musicians to the orchestras of Cleveland, Philadelphia, Boston, and the Metropolitan Opera.

The members of the orchestra also appreciate the fact that within recent seasons they have recorded for London, Columbia and Deutsche Grammophon records under Dorati, Rostropovich and Leonard Bernstein, and they take special pride in the fact that it was this orchestra that Bernstein chose for the world premiere and subsequent recording of his "Songfest."

These developments come at a propitious time. The orchestra is facing, as always, its biggest non-musical problem: finances. Like the orchestras of Boston and New York, Nation Symphony subscriptions are down this year. It is not hard to see why: Last year's strike robbed the season of the first five weeks, all of which were to have been played under Rostroovich, who is, after all, the orchestra's chief drawing card.

Leonard Bernstein's cancellation of the concerts he was to have conducted the final week of the season also had its effect on prospective subscribers, as did his even more devastating decision (from the standpoint of concertgoers) not to conduct this season's final four weeks. Not only did those cancellations disappoint potential ticket buyers, they also caused a delay in getting details of the season into ads and direct mail.

Joyce Idema, the National Symphony's director of public relations, said last week that "People no longer automatically buy the full series of 24 subscription concerts. All over the country orchestras have found that far more subscribers buy sets of 12 or 6 -- they come on series called "Gold," or "Red," or "Blue," or "Celebrity," or whatever else attracts best in a given city."

"The National Symphony's runaway best-seller," Idema added, "is the Friday night series. Last year we had six. This year there are eight. It is very clear that people in Washington want to go out on the weekends."

Moreover, "Ticket prices are so high now," she said, "that people just hesitate to put all their ticket money into a 24-week series. They buy half instead so they will still have some money to go to other things. It is not like it was when the National Symphony was almost the only big series in town."

Austin Kiplinger, president of the NSO board of directors, has the orchestra's total financial picture comstantly in mind. He said last week that "my chief concern -- the most troublesome question for all the performing arts in Washington -- is 'Who is responsible for our federal city? I write about politics and I understand this thing. Nixon ran against Washington, and Carter is running against Washington. But there has to be a point at which you recognize that your capital is there competing with Vienna and London and Moscow and Paris."

He believes Congress should take a more active role in looking after the Symphony's finances: "I did some checking and I found that the Indiannapolis Symphony gets a higher percentage from taxes than the NSO. Economists know that out standards of living rise along with the technology and investments. But this does not happen in the arts. Yet in the arts, our real costs rise and will continue to rise. We have to supplement our income with assistance from other sources."

Rostropovich believes that there are other factors that have caused subscriptions to drop: "The American people are very sensitive to problems of inflation, of gas shortage. This is true in Boston too, and in many other cities." He also sees a connection between the contents of his programs and numbers of subscribers.

He observed, "In the Bicentennial, there was much American music and new music played. Some people did not like so much. We do not want people not to subscribe because of what we play."

gThere may very well have been too much new music played in the Bicentennial Year. But it was far more a matter of the wrong music having been played. Certainly works by Orrego-Salas and Roy Harris, which drove people from the hall, should never have been programmed, and there were others that were hardly better.

It is the job of the music director to find American music and other repertoire that is of a quality that entitles it to the time required for rehearsal and the effort needed to present it persuasively so that audiences will enjoy it. There is no shortage of such music, but one poor piece often has an immediate negative effect at the box office.

At the moment, however, National Symphony players' morale seems high for a number of reasons. Next April they will make a tour of Japan, by far the longest as well as the most prestigious foreign tour the orchestra has ever made. The NSO now attracts some of the star guest conductors of this country and Europe and there is no area of the repertoire in which it does not play with authority. Much of this improvement was well started during Antal Dorati's beneficial years with the orchestra. Under Rostropovich the improvement, as well as the essential enlargement of the orchestra, has placed the NSO on a new plane of operation

Nonetheless, Rostropovich and the NSO board should find a way to have him here more of the time. Rostropovich has compiled a chart that shows that he spends more time with the National Symphony than Seiji Ozawa with the Boston Symphony, Georg Solti with the Chicago Symphony, Andre Previn with the Pittsburgh, or, he might have added, Carlo Maria Giulini with the Los Angeles Philharmonic.

But unhappily, 4 of the 16 weeks Rostropovich is spending with the National Symphony this season will be in Japan, which does not help audiences in Washington. He is excited about plans for the orchestra's 50th anniversary season, coming up next fall, and in that season he will be with the orchestra for 19 weeks. He is planning to repeat the very first program the orchestra played, dedicating that program to the orchestra's founder and first conductor, Hans Kindler. Howard Mitchell, who was Kindler's successor, the conductor over the longest number of years in the orchestra's history, and the conductor under whose baton Rostropovich first appeared with orchestra in Washington, has been invited to conduct, as has Dorati.

New works have been commissioned from William Schuman, Alberto Ginastera, Jacob Druckman, and Peter Mennin. It is probable that there will be a special concert marking Aaron Copland's 80th birthday in November, of 1980, and Leonard Bernstein has agreed to return as guest conductor in the orchestra's big anniversary, after his sabbatical from conducting.

It is now clear that if the National Symphony has not lived up to Marjorie Merriweather Post's grand claim, it has certainly become one of the top orchestras in the country. How many orchestras are at that particular "top" is still the great question.