New York - Bus Number 4 rounds the corner, and you see the square, gray tower silhouetted against the sky. Then you see the winding cobblestone path; the gardens filled with age-old herbs, the gnarled trees bursting with blossoms; the Gothic windows shimmering in the sun.

The rocking and rolling ride is over. It's the end of the line. You've traveled back - way back - in time. And you've ended up at the Cloisters, an imposing structure right out of the Middle Ages.All it takes is a bus token and you can enter an era when monastic orders were at their height; an era when pious monks by the hundreds were cloistered away on mountaintops and in secluded river valleys. The Middle Ages - most scholars date it from Constantine (311-337) to the beginnings of the Renaissance - was a remarkable moment in history marked by religious zeal and great art and architecture. And the Cloisters, a serene and unexpected sanctuary in America's busiest city, beautifully commemorates the bygone period.

Located in Fort Tryon Park on the Hudson River, the Cloisters looks exactly

actly like a fortified medieval monastery on the outside. A monastic atmosphere permeates inside, too. Entering the main door, you find yourself in a dim, echoing hall with vaulted ceilings. There are candles. There's the distant sound of soft, melodic chanting. There's a hint of incense in the air.

It would not be surprising in such a setting to see monks in flowing robes disappearing into the shadows. But the Cloisters sequesters none. Rather, it houses saintly statues and countless other treasures - the world's most monumental repository of sculpture, paintings, tapestries, objets d'art, ornate icons, stained glass, altar pieces and challises from medieval times.

The medieval museum, celebrating its 50th anniversary this year (it opened on this site in May of 1938), also is a remarkable repository of architectural jewels. Complete or nearly complete rooms and sections from European chapels, abbeys and monasteries can be found within the walls. Long ago most of their original sites were pillaged or irrevocably damaged by time. But these impressive remains - these columns, arches, fountains and the like - have found compatible new surroundings.

The collection at the Cloisters came about thanks to the efforts of many dedicated individuals. But the initial dream began with an American sculptor, George Grey Barnard.

When he lived in Europe, notes Bonnie Young in "A Walk Through the Cloisters," Barnard collected much of the architectural material seen in the medieval museum today, including the columns and capitals of the Saint-Guilhem, Cuxa, Bonnefont and Trie cloisters. The huge pieces from historical ruins in southern France were eventually shipped to America. As for Barnard, he kept returning to Europe, avidly continuing his treasure hunt.

According to Kate Simon, author of "New York Places and Pleasures: An Uncommon Guide," Barnard had a great talent for treasure hunting. He could unearth masterpieces in the most unlikely places. Two lovely carved virgins were found supervising a chicken coop and encouraging a larger yield of eggs. A magnificent carved torso was serving as a scarecrow. Barnard bargained with farmers. He negotiated for semi-defunct sections of monastic enclaves. And gradually he assembled a monumental, priceless collection.

The collection was set up in 1914 in Barnard's own Cloisters museum located in a brick building on Fort Washington Avenue. But operating such a place was not an easy task, and in the '20s the sculptor's treasures were put up for sale. A newspaper asked: Is this gem of French art to be torn from the environment so patiently and lovingly created for it and sold to some more enterprising city? The reply to that question came in 1925 when John D. Rockefeller Jr., donated funds to the Metropolitan Museum of Art for the purchase and continued exhibition of the collection, to which he added some 40 medieval sculptures from his own private trove.

The Cloisters first opened under the Met's auspices in 1926. Subsequently, when Rockefeller presented to New York City the land that became Fort Tryon Park, he reserved the northern hilltop for the construction of a larger and better-developed museum of medieval art.

The design for the structure was entrusted to Charles Collens, the architect of the Riverside Church in New York. Collens' first consultant in the planning was Joseph Breck, assistant director of the Metropolitan Museum. Upon Breck's death in 1933, James J. Rorimer took over the responsibilities.

It took four years to complete construction. Finally, in 1938, the Cloisters was opened to the public. It is not a copy of any particular medieval structure, emphasizes Robert Goldsmith of the museum staff, but an ensemble of rooms and gardens that suggest the European originals.

With Goldsmith as a guide, we walked through covered passages looking out to scenic garden spaces. (The term "cloisters" refers to covered passages around open spaces; areas that traditionally connected the church to the chapter house, refectory and other parts of the monastery.) We passed through the Fuentiduena Chapel, largely devoted to Spanish Romanesque art. We saw the Saint-Guilhem Cloister with its series of columns and capitals from the Benedictine abbey of Saint-Guilhem-le-Desert, near Montpellier, France. We viewed the Cuxa Cloister, the largest cloister in the museum, with architectural features from Saint-Michele-de-Cuxa, which once housed monks in the Pyrenees. We admired stained glass windows in the Gothic Hall and tapestries in the Nine Heroes Tapestry Room and the Hall of the Unicorn Tapestries; saw a fountain shaped like a cross in the Trie Cloister; looked out toward the scenic Hudson in the Bonnefont Cloister; peered through glass roundels adorned with a variety of religious scenes in the Glass Gallery.

In some areas we could see examples of early Romanesque architecture, typical of the 11th and 12th centuries and distinguished by round arches and an absence of windows and light. In others, the Gothic movement was obvious with its emphasis on great windows of stained glass and pointed arches.

"There's something here for everyone - the scholars who are interested in art and architecture and just ordinary people who want to escape city pressures for a while," Goldsmith noted. "We offer concerts, lectures, a variety of seasonal events. During this anniversary year, we're really going to be busy and hope to focus more public attention on this great museum. "

The anniversary will be marked with an updating of books about the Cloisters. There will be a new brochure about the place, informative symposiums, gala dinners and parties, fresh landscaping, new stained glass windows in some areas and a new labeling of artistic objects in the collection to make their historical significance more precise.

The biggest birthday gift of all, of course, will be a brand new treasury area - climatically controlled, scientifically lighted - that will increase display space about 55 percent. The enlarged treasury (it opened this month) will allow museum personnel to bring many art objects out of storage that the public has never seen before.

"We're extremely pleased about the treasury," said William D. Wixom, chairman of the Cloisters, as we rode in a creaking "medieval elevator" to his spacious offices in the building's tower. "The search for significant medieval things didn't stop with Barnard or Rockefeller. We're continually hunting for new pieces of sculpture and art to improve our collection. Not long ago, we discovered a wonderful 14th century challis in London. It was an exciting experience to make this acquisition."

Wixom, who has been a dedicated fan of the Middle Ages since college days, is so enthusiastic about the new acquisitions and all the items in the collection, that he has a hard time picking personal favorites. Perhaps the unicrorn tapestries. Or the annunciation altar piece by Robert Campin. "My choices differ from day to day," says the chairman.

He also has a hard time naming his favorite time of day at the Cloisters or his favorite time of year. Early morning's wonderful with the sun glistening on the river, but so's sunset over the Palisades. As for the seasons, spring is a glorious reawakening. The gardens are at their splendid best in the summer and fall. And even icy winter has charm.

The museum is open from 9:30 a.m. to 5:15 p.m., Tuesday through Sunday, through October. Hours are 9:30 a.m. to 4:45 p.m., November through February. Admission is by voluntary donation.