HOW DO you launch a new symphony orchestra at a time when the United States already has some 1,500 symphony orchestras? How do you do it most particularly in New York, which already has one world-class orchestra under the direction of Zubin Mehta and a variety of other less-known but worthy ensembles? "It helps to have an extremely thick skin," says 27-year-old Rohan Joseph, who will be bringing his new orchestra, the American Philharmonic, to the Kennedy Center Concert Hall on Friday night.

"You run into a lot of critics and cynics who tell you it simply cannot be done," Joseph says."My feeling was that if you can get a group together to accept you as a conductor, you have a right to stand before them."

A few years ago, Joseph, a native of Sri Lanka who came to New York in 1970 to study music, decided that he was a conductor, not a pianist. It was not an unreasonable decision, though he made his piano debut in a Liszt concerto at age 16. Besides piano lessons under some of New York's best teachers, he had studied conducting and had conducted at music festivals in upstate New York. But when he began applying for positions as an assistant conductor, he found the job market nonexistent for a musician of his experience.

Lukas Foss, who was then the conductor of the Brooklyn Philharmonia, was sympathetic if not helpful. He told Joseph that if he wanted an orchestra to conduct, he would probably have to start one of his own. So Joseph went out and did it.

How the new orchestra will sound at the Kennedy Center remains to be seen, but its Carnegie Hall performances have drawn generally good notices from the New York critics, who are not usually pushovers. Besides commenting on the technical proficiency of the orchestra and its youthful enthusiasm (the players' average age is 28), they have found particular subjects for praise in the string tone and the conductor's rapport with the players and sense of style. One critic called him "an utter madman on the podium," but this seems to have been intended as a compliment.

Joseph drifts quickly into superlatives when describing his orchestra. It acts and sounds, he says, "like an enormous string quartet." The subject of quartets reminds him of a prominent fan: "Arnold Steinhart of the Guarneri thinks its first-class," he says. "We have the best double-bass section in New York -- by far. There are 10 of them -- as many as the Berlin Philharmonic has -- and they are the pride and joy of the orchestra. This is really a cooperative effort on the part of 104 musicuans; morale is very high, turnover is very low and the quality is very consistent from one concert to the next."

He began in 1978 with no money and only two woodwind players who knew and respected his work, a clarinetist and a bassoonist. Word of the new enterprise spread slowly through the New York free-lance grapevine, and by the fall of 1979 he still had no budget but there were 89 players -- many of them regular substitutes for the New York Philharmonic or Metropolitan Opera orchestras. They began rehearsing (without pay) once a week in a high-school auditorium, and he set about acquiring a board of directors, which is the time-honored way of getting money.

If it does as well as the most affluent American orchestras, the American Philharmonic can hope some day to make about half of its expenses in ticket sales, but affluence is still in the remote future. For the moment, says Jan Harpel, one of the orchestra's 18 board members, "it's a financial and logistical nightmare. Financially, it's the old question of the chicken or the egg; you can't get money until you've established yourself and you can't establish until you've performed, and it takes lots of money to perform."

The first corporate sponsor was Gulf and Western, where Joseph earned his living as a computer programmer. With Gulf and Western at the head of the list, other corporations such as Mobil, American Can and United Airlines joined in. The orchestra's next major fund-raising effort will be a special gala concert in Carnegie Hall April 9, with Victor Borge as guest conductor and a top ticket price of $40.

The financial situation is beginning to look better, but it is still not exactly good. Rohan Joseph continues to earn his living as a computer programmer at Gulf and Western.

"We still have an unpaid rehearsal every Tuesday night," says Joseph, "although the orchestra is getting more on its feet, financially and in reputation. The players have agreed to keep that rehearsal unpaid to remind us of how we started. This has the complete sanction of the musicians' union -- Local 802 -- as long as the players sign a waiver."

According to Chase Morrison, the orchestra's principal cellist, its membership is drawn from an almost unlimited supply. "For every player who got in, there are three or four more around town who are just as good but didn't make it -- enough musicians who play well to fill at least three more symphony orchestras." Payment to the players "has been at least scale for each concert," she says, "but it's been different each time, depending on what has come in. Some of the orchestra members teach, and some try to do free-lance work wherever it turns up, including other orchestras as far away as Poughkeepsie and Scranton; some are substitutes or regulars on Broadway, and our principal oboist has just finished a job subbing as second oboe in the New York Philharmonic. In general, we do whatever will help to pay the rent."

By January of 1980, the orchestra was ready to make its public debut at the Brooklyn Academy of Music. The box office only brought in about $860 for that concert (a bit less than $10 per player), but critical reaction was good and the orchestra continued to grow, in size and in ambition. Last fall, when it began its first full season, it had 104 members and was planning a series of four concerts at Carnegie Hall as well as its first out-of-town date, this week at the Kennedy Center. "Our first concert at Carnegie Hall only sold $1,974 worth of tickets," says Joseph, "but the second one, when we played Bruckner's Seventh, was sold out."

Bruckner was the composer whose music first inspired Joseph with the desire to be a conductor, back in 1977, and he may become a specialty of the new orchestra.His Third Symphony was the featured work in the American Philharmonic's first Carnegie Hall concert, and will be the piece de resistance again for their debut at the Kennedy Center -- along with Mozart's 23rd Piano Concerto in A (with Lili Krauss as soloist), the Brahms "Academic Festival" Overture and the second performance of the "Yellowstone" Overture by Richard Adler of Broadway fame, which received its world premiere from the American Philharmonic in November. This is a program of very generous proportions, and unless Joseph uses lightning tempos (which would be odd in a Brucknerian), the audience should figure on well over two solid hours of music.

It will be a long day for members of the orchestra, who are treating the Washington performance as a day trip to save the expense of 100-plus hotel rooms. "There agreement to do this is consistent with the sacrifices that the orchestra has made thus far," says Jan Harpel. "They will be coming down by bus at 11 a.m., and on the bus they will eat box lunches prepared by volunteers. Then at midnight, they will get back on the bus, to arrive back in New York at about 4 a.m. We can't afford to put them up overnight, and they know we can't afford it and they are willing to do it this way. Although they are very young, these musicians know what is important and where they should be playing. They want to play in Washington."