IF THERE'S no business like show business, there's also no dancing quite like show dance. In the whizzing legs of Broadway, the razzmatazz of musical theater comes by its most direct form of expression.

First thoughts may be of peppy, breezy routines, chorines in net stockings kicking with martial precision, old-time hoofers in bowlers, polo shirts and impossibly tight slacks. But show dancing can also have more than one kind of soul, as in "Bubbling Brown Sugar," or "Fiddler on the Roof," a show in which dancing is not just a "specially" but the heart of the matter.

The dancing in musicals is quite distinct in tone, form and purpose from the kind one sees on the ballet stage or in dance concerts. All the same, there's been an endless interchange from the earliest days of musicals. Michel Fokine was drafted into choreographing for the Ziegfield Follies, for instance, way back in the 'teens. George Balanchine was to go the same route in 1935, and the next year he did a Broadway show, "On Your Toes," from which came the celebrated "Slaughter on Tenth Avenue" sequence that's still in the repetoire of his New York City Ballet. Balanchine choreographed 21 musicals, including "Cabin in the Sky" of 1940, which featured the Katharine Dunham troupe.

Asurprising number of landmark musicals are associate with the leading creative figures of American dance art - "Oklahoma" and "Carouse," for instance, with Agnes de Mille, "West Side Story" and "Fiddler on the Roof" with Jerome Robbins; "Kiss Me, Kate" and "My Fair Lady" with Hanya Holm; "As Thousands Cheer" with Charles Weidman; "Annie Get Your Gun" with Helen Tamiris; "Silk Stockings" with Eugene Loring; "Street Scene" with Anna Sokolow, and so on.

Of course, the infiltrataion worked both ways. Show-biz and jazz idioms have made their way into countless ballets and modern dance compositions - Balanchine's "Who Carpes?" for example, or Twyla Tharp's "Push Comes To Shove." On the other hand, de Mille's innovative "Western" ballet, "Rodeo," was an immediate harbinger of her revolutionary musical choreograpphy for "Oklahoma," and Robbins' jazz "Fancy Free" was elaborated into the show "On the Town."

The only problem is that the choreography of American musicals is, as Lee Becker Theodore puts it, an "endangered species."

Dance is the most perishable artistic ccommodity to begin with, but even ballet and modern dance creations are perpetuated for a time by the companies that engender them. Not so with the musical stage. Though the songs of a hit show are preserved in scores and recordings, only an occasional film or revival staves off extinction for the dances of broadway.

Theodore, who danced the role of Anybodys in the original staging of "West Side Story," decided to do something about it.

Her solution, a new performing company called the American Dance Machine, has its official debut tonight at Ford's Theatre, where it is booked for a four-week run. American Dance Machine will be presenting a program of 15 dance numbers that are whimsical, romantic or spectacular by turns, from such shows as "Carousel," "Bubbling Brown Sugar" and "Cabaret." Thee dances are the work of de Mille, Bob Fosse, Michael Kidd and Onna White, among others.

And the repertory that American Dance Machine draws on may be the most comprehensive dance genre of all, taking in everything from ballet to modern, tap, jazz, ethnic, pop, social and ballroom dance idioms. There's none other that touches such a broad range of public taste.

Theodore, who previously founded a company called Jazz callet Theater (Eliot Feld and Michael Bennett are alumni) hit upon the concept of the American Dance Machine in 1972, while she was teaching at Long Beach University. What she envisioned was a "living archive" of musical dances.

For several years, she investigated the real possibilities for fulfilling her dream, consulting with de Mille, Fosse, Oliver Smith, Gwen Verdon and many other friends in the world of musical theater. With the aid of the National Endowment for the Arts and the O'Neill Foundation, she was able to establish a troupe in 1975, and in the following year, to mount a pilot project - a film on the theatrical dances of Jack Cole, one of the great pioneers of choreography for musicals. With more grants the next year, the company resurrected several dance numbers and took to the stage for some summer performances in Connecticut and Long Island.

The restoration process involved seeking out and petitioning the help of the human repositories of this dance repertory - the choreographers and the dances of the original casts. The deeper she delved, the more Theodore realized that what was required for a long-term effort was a three-pronged approach - in order to make future performance possible, both research and training would have to be part of the enterprise.

The American Dance Machine has thus evolved beyond a company into a full-fledged academy for the conservation of musical dances. A research arm inventories past musicals, locates and explores surviving memories, holds rehearsals and documents the results by means of video and dance notation. A training unit with a faculty of Broadway and dance notables seeks out company aspirants. And the performing wing brings them to the public. As of August of last year, all three activities were being pursued at the troupe's New York quarters in Harkness House.

Still, for all its splendid lineage, musical dancing is a phenomenon unto itself, and until American Dance Machine came along, no one had tried to give it autonomous life. Though the company soloists include three experienced Broadway dancers and Janet Eilbe, a principal of the Martha Graham troupe, there are no "name" performers among the dancers. The program consists fundamentally of excerpts, and it's hard to tell in advance how well they'll work apart from their original settings.

In the meantime, the American Dance Machine is proceeding under the only assumption it can sensibly hold - that a public that has given the musical theater so high a place in its affections will be delighted with its dance highlights. After the run at Ford's there is talk of a New York engagement and a national tour. In any event, Washington is seeing a bold experiment launched.