WITH EARLY PHOTOS by Diane Arbus and Richard Avedon, "The New York School: Photographs 1935-1963, Part III" is a third more filling. It's grittier, with stronger images than the previous two parts at the Corcoran.

Although the photographers weren't called the New York School, their work paralleled that of the Abstract Expressionist painters, who were. They were just as convinced of the uniqueness of their vision.

Their commercial work -- their magazine work -- was seen. But the photos on display here have rarely if ever been on view, opening a door to what the photographers called their "private world."

The show focuses on five photographers represented by 144 works, along with flashbacks to the 11 photographers in Parts I and II.

These are documentary photos that defy caption. They capture a moment -- and the question that comes up like an itch wanting to be scratched is why this moment? It cannot always be defined.

Don Donaghy discovered accidents -- fragments of vignettes in Philadelphia, or any city: the junction of electric wires at a pole, dry black ooze inching toward a drain, matrons clustering on a park bench like pigeons, a woman's sensible shoes passing a cracked window in a momentary glint of sunlight.

Bruce Davidson's documentary of the Brooklyn Gang is loose, impressionistic. He reveals the teenagehood of teenage hoods, lighting up, necking under a boardwalk and showing their softer side: his arm tattooed with an eagle, a young scamp pets a pigeon.

There's something vague about these photos that sideswipe the subject and hit it from non-traditional angles. So we look at them that much longer.

Leon Levinstein's vision is people. A misshapen whale turns out to be a man's bare back. From an angled viewpoint, Levinstein focuses on bald heads and couples embracing. From another viewpoint askew, he sees a man with the saddest eyes gently holding a doll with a cracked head.

The powerful Arbus pictures are the sort that one feels embarrassed to stare at; obese ladies photographed secretly in a Coney Island bathhouse mirror, female impersonators doing a poor makeup job. And freaks -- the circus fat man, the dwarf lady and the three-legged man; he's real, because only nature could invent the dangle of flesh below his third knee. He's happy, but think of his tailor.

In Arbus' early photos, says John Gossage, a photographer and guest curator of the show, "she defines the details she is going to deal with for the rest of her life." But not so Avedon, whose slick portraits of the rich (and now, the not-so-rich) have made him a household name.

In the time frame covered by this show, he was experimenting, becoming. Here are the earliest Avedons, made in Italy just after World War II when he was learning to be a photographer. Out of focus, a grinning boy on one side of the composition balances and plays off an olive tree on the other side. Taken in 1947, the photo speaks to regeneration and rebirth.

But the world shifts, and by 1963, Avedon's work has evolved to the hopelessness of a wizened madwoman in a Louisiana mental institution, or of the double-chinned woman in Times Square who shows Avedon the newspaper headline: "President Shot Dead."

THE NEW YORK SCHOOL: PHOTOGRAPHS, 1935-1963, PART III -- At the Corcoran Gallery of Art through January 5, 1986.