On a balmy day in June in 1964, Paul Mellon, the philanthropist, addressed the graduating class of the Foxcroft School in Middleburg. His subject was unusual. Mellon spoke of Pleasure.

He protested "over-seriousness and over-conscientiousness." He praised quiet meals, "dunes and waving dune-grass," books and long hot baths. He even mentioned romance -- despite "the illusory convention that people as old as commencement speakers, or as young as schoolgirls, don't know about things like that." And then Mellon, who described himself as "a kindly, graying man," gave his youthful audience a clue to his career.

He said: "What this country needs is a good five-cent reverie."

For more than half a century, Paul Mellon has persistently, effectively, expensively, practiced what he preached.

It has cost more than 5 cents. It has cost Mellon and his family's foundations the best part of $1 billion.

Tomorrow, 47 years after he first became president of the National Gallery of Art, Mellon, 77, will announce that he is stepping down as chairman of the board. The museum on the Mall, founded by his father, bears Paul Mellon's stamp. He guided the design of both its East and its West buildings. He has given it grand pictures and large amounts of money. Behind its careful installations, its garden courts and fountains, its kindness to the public, one can feel his taste. The museum has been his job.

But there is more to him than that.

If you have ever consulted the oracles of the "I Ching" (a book he paid to publish), or kibitzed at the chess tables in Lafayette Square (his foundation paid for the square's refurbishment), or wandered the dunes of the Cape Hatteras National Seashore (he helped to buy that land), or read Kenneth Clark's "The Nude" (he published that as well) you are in Paul Mellon's debt.

Many of his gifts -- for wildlife sanctuaries in Massachusetts, archeological digs in Athens, windowboxes in New York -- have been personal, eclectic. Nelson Rockefeller exhausted much of his vast fortune trying to become president. The Hunt brothers exhausted much of theirs trying to corner the silver market. Mellon pursues other goals. He has all his life invested in quality and quiet. He has never labored to make his fortune grow. Instead he has helped give giant sums away.

He has probably spent more scrupulously and imaginatively promoting public reveries than any man alive.

The figures are staggering.

Calculate them this way: Begin with the $199,812,250 in cash and art distributed between 1930 and 1980 by his father's foundation; for all those 50 years Paul Mellon was a trustee. Include the museum stocked with British art that he gave to Yale in 1977; that single gift alone was worth perhaps $150 million. Add the $6 million he gave to the Virginia Museum in Richmond and the $35 million he spent on the East Building, and the like sum from his sister, the late Ailsa Mellon Bruce (1901-1969). And don't forget Sky Meadows, the 1,200-acre state park in the Blue Ridge, which Mellon gave Virginia. Include his pictures, too. He has formed two astonishing collections, one French, the other British. He may well be the most accomplished collector this country has produced.

He gives books away as well. To Oxford, which has long owned half of John Locke's library, Mellon gave the other half. To Yale he has given all his books on alchemy and magic. These were private benefactions, as have been all his gifts of art.

Now consider only his family's chief conduit for giving, the Andrew W. Mellon Foundation. It was formed in 1969 by merging Ailsa's foundation, the Avalon, and his, the Old Dominion, with the bulk of her estate. Since 1969, that foundation has spent $369,426,947 on "education;" $152,243,579 on "cultural projects;" $104,919,800 on "medicine and public health;" and $50,280,500 on "conservation and the environment."

As of Dec. 31, 1984, the total amount appropriated by that A.W. Mellon Foundation and its predecessors had reached $858,063,003.

One of his accomplishments looms above the others.

Paul Mellon has made our lives a little bit like his.

To comprehend him rightly, you have to love what he loves -- old books, old pictures, Yale, England and fine horses, the fields of Virginia, intellectual excitement, the empty-mindedness of exercise, good words, good food, good manners, women of high spirit, sporting competition and puttering round the house.

Mellon's benefactions grow from his affections. Wandering through Sky Meadows is not so very different from wandering his own land, his sweet 4,000 acres in Fauquier County. Sitting in the National Gallery's garden courts is not so very different from sitting in his sitting room, with the air scented by flowers and grand pictures near at hand.

Paul Mellon is at home at Oak Spring, his country house near Upperville. He is dressed for country living, shiny penny loafers, a shirt of light-blue cotton open at the throat. He has just read aloud a clipping from the Daily Telegraph of London -- "Farmer, 84, Dies in Mole Vendetta." His eyes crinkle when he laughs.

He is a trim, attractive man, soft-voiced and attentive. He writes poems for his friends, and sometimes, on the spot, produces little well-made drawings. You might think he would attract hot currents of resentment, greenish waves of envy, but he seems to have no enemies. He is largely apolitical. He has deflected importuners by insisting on the best. He strikes those who encounter him as self-deprecating, mild and impeccably polite. It is hard to speak of Mellon without making him appear too good to be true.

Patrick, his Norwich terrier, is sleeping at his feet. The floor is bright with sunlight. Despite the grandeur of the paintings -- the Degas, the van Gogh -- the room is warm and welcoming. He is pouring drinks for guests, Mellonian Martinis, one-third gin ("I like the taste") and two-thirds Russian vodka ("they say vodka's better for you"), premixed and then nearly frozen. Outside, in all directions, woods and tended meadows roll toward the horizons. The shade trees in the fields were planted by his wife, Rachel Lambert (Bunny) Mellon. So, too, were the potted lilies-of-the-valley growing at his elbow. They perfume the air.

The van Gogh above the fireplace, one of many he owns, depicts a green field of wheat and a bright, very blue sky. "It used to hang in the hallway," says Mellon. "Once Liza, my stepdaughter, brought in some friends from Foxcroft, and one observed it there and asked, 'Oh, who paints?'

" 'Nobody,' said Liza. 'Da buys them at the store.' "

All of Mellon's houses -- two in Upperville, two in Washington, one in New York, another on Antigua, another in Massachusetts, and even his transatlantic Gulfstream jet -- are filled with pictures large and small. Though he has given 35 paintings by George Stubbs to Yale, he retains 15. More than 90 other pictures, including six Monets, two Gauguins, two Cassatts, a Seurat, a Renoir, a van Gogh -- and Ce'zanne's imposing, tree-trunk-rough portrait of the artist's father -- already have been given to the National Gallery, but he has so much fine French art left, one would hardly know they're gone.

Armed with money, good advice and the rights of first refusal from the best of the world's dealers, Mellon has assembled what may well be the finest hoard of School of Paris paintings still in private hands. Degas is a favorite. In one room in the "Brick House" on the Upperville estate are 46 of his remarkable wax sculptures.

He sometimes makes mistakes. He owns one pleasing still life signed Henri Rousseau, which is not a Rousseau after all. The signature is forged. Mellon likes it anyway. It hangs above the fireplace in his house in Washington.

On Nov. 16, 1983, 44 Mellon pictures were sold at Christie's in New York for $12.14 million. One Manet was knocked down for $3.96 million, then a record for the artist. "We didn't like them," said Mellon, who credits "90 percent" of his interest in French pictures to the interests of his wife. "That doesn't mean they were bad pictures. But they weren't our type."

Mellon has two children, Timothy, 42, who lives in Connecticut, and Catherine M. Conover, 47, of Washington, who was once married to Sen. John W. Warner Jr. (R-Va.). Neither of Mellon's children has shown much interest in museums or collecting.

Almost all his art, says Mellon, will eventually be distributed to Yale, to the Virginia Museum or to the National Gallery of Art.

The money comes from Gulf, Alcoa, the Carborundum Co., Koppers, the Mellon Bank in Pittsburgh, from coal, steel, street railways, and from a century or more of well-scrutinized investments.

Forbes magazine, which ranks Paul Mellon 38th among the wealthiest Americans, says that his "well-hidden" net worth is "believed to exceed $600 million."

His grandfather's people were Northern Irish Presbyterians "of the common industrial class . . . notable only for good habits and paying their debts," or so wrote Thomas Mellon (1813-1908). He was 5 when he came to this country, to Poverty Point, Pa. It was through banking and the law and capitalist finance that he began to build the family fortune. His two sons, Richard B. and Andrew W., made it grow and grow.

By 1923, Andrew Mellon was the country's third largest taxpayer, ranking just behind J.D. Rockefeller and Henry Ford. He wore a thick chinchilla overcoat and what his son remembers as a thin "ice-water smile." In 1931, in the depth of the Depression, his net worth was estimated at $200 million.

Paul Mellon might have drifted toward philanthropy by following his father, but the path he followed wound through poetry, romance, psychiatry and dreams.

He met Mary Conover Brown (1904-1946) on a visit to Manhattan in 1933. She had been educated at Vassar and the Sorbonne. Even in old photographs one feels her beauty's glow. They were married in 1935. They spent their honeymoon on a houseboat on the Nile. Their wedding rings were fashioned in one of the souks of Cairo. She changed his life.

In an effort to cure what she thought might be psychosomatic asthma, she entered Jungian analysis. Her husband joined her. Then in 1937, the Mellons met Carl Jung.

The Swiss psychologist and mystic had come to lecture in Manhattan. Paul was in the audience. Something eerie happened. Jung was speaking on the Tao symbol when Mellon, staggered, realized that he had just experienced that Yin-Yang symbol in a dream.

He still recalls it clearly: "It was a very moving sort of dream . . . It had to do with some foreign city, and with a river going through this city, and with colors . . . There were white mountains in the background, and this blue, this very blue river going through the center of the city. When I saw Jung draw that symbol on the blackboard, well, naturally . . ."

But did the symbol appear in the dream?

"The dream was the symbol," said Mellon.

John Walker, a childhood friend of Mellon's, and a former National Gallery director, has written that "perhaps as a result of Jung's analytical psychology Mellon became one of the best balanced and, as far as an outsider can know, one of the happiest of human beings."

Mellon does not make such claims for his years with Jung. "He was a wonderful person to talk to, and his theories about alchemy and so forth were very interesting intellectually. But I don't think I was affected very much, let's say, psychologically."

Be that as it may, the Mellons' encounter with Jung, the first of many, led to the establishment of the Bollingen Foundation, one of the more interesting chapters in 20th-century philanthropy.

In 1941, Carl Jung wrote of Mellon: "I always had the impression that he had the psychology of somebody who was waiting to be picked up by something which wasn't yet in sight." Bollingen was a seed. In 1941, Mellon was in the army, and his most impressive personal philanthropies still were yet to come.

Before it was wound down in 1969, the Bollingen Foundation, named for Jung's tower retreat on the Lake of Zurich, published 100 extraordinary books in 275 well-made volumes. These included the "I Ching," Joseph Campbell's "The Hero With a Thousand Faces," Andre' Malraux's "Museum Without Walls," "Ibn Khaldu n: The Muqaddimah," D.T. Suzuki's "Zen and Japanese Culture," Kenneth Clark's "The Nude" and Vladimir Nabokov's translations from Pushkin. It also helped to pay for hundreds of other publications.

Elias Cenetti, who received the Nobel Prize for literature in 1981, was given his Bollingen Fellowship in 1955. Sculptor Isamu Noguchi got his to study "leisure" in 1949. Marianne Moore, the poet, Siegfried Kracauer, the theorist of film, Meyer Schapiro, the art historian, and more than 300 other scholars and men of letters, many of the best of them refugees from Hitler, also received grants.

Bollingen, occasionally, wandered into trouble. In 1948, a jury (whose members included T.S. Eliot, Katherine Anne Porter, Robert Penn Warren and Robert Lowell) awarded the Bollingen Prize in poetry to Ezra Pound. It was not a popular decision. Pound had broadcast anti-Semitic and anti-American talks from Mussolini's Italy during World War II. Rather than being tried for treason, he had been judged insane and sent here to St. Elizabeths Hospital. Then-Rep. Jacob K. Javits (R-N.Y.) demanded an investigation. The Daily Worker suspected a conspiracy among the government, the "anti-Semites Pound and Eliot," and "the giant Mellon industrial and financial interests." The Mellons battened down the hatches and rode out the storm. In 1949, the Bollingen prize in poetry went to Wallace Stevens.

Paul Mellon credits Mary Mellon -- "the inspirational initiator, the founding nurturer" -- with all of Bollingen's accomplishments. But it was he who continued its activities long after her death, following a heart attack, in 1946. And he had always paid the bills.

Bollingen prefigured much of Mellon's later giving. In the early 1960s he would pledge himself to English art much as Mary Mellon had pledged herself to Jung. The Mellon-funded Center for Advanced Study in the Visual Arts recalls such Bollingen-supported assemblages of scholars as Jung's Eranos symposia.

Bollingen was in many ways a highly personal endeavor. Many of Paul Mellon's later philanthropies -- Sky Meadows in the Blue Ridge, the Yale Center for British Art, the Cape Hatteras National Seashore, and his decision that the Old Dominion Foundation should give $662,500 to the American Friends Service Committee and $300 to the YMCA -- seem personal as well.

It is not easy to detect the moment in his life when his full commitment to philanthropy began.

Once, while at Yale, when "at least five" of his friends happened to accompany him to the tailor's, Mellon suddenly suggested, "Wouldn't you boys each like a polo coat? I'd admire to stand treat." His father was to some degree made a scapegoat during the Depression, and Andrew Mellon's tax trial (he was charged with tax fraud, but acquitted) also may have spurred the son toward wholehearted public giving. Another inspiration was surely Mary Mellon.

On June 29, 1938, Paul and Mary each had private appointments with Jung. It is not known what Mellon spoke of. But Mary later reported that her first words were "Dr. Jung, we have too much money. What should we do with it?"

Those who meet Paul Mellon in the course of business find him self-contained, elusive and fastidious. His offices at the Gallery, in both its East and its West buildings, always have felt indefinably different, perhaps homier than the others. He explains why. In his offices, as in his homes, he hangs the art himself.

He likes to swing the hammer. He likes to drive the nails. Forgoing tape measures and spirit levels, he "eyeballs" installations. He calls hanging pictures his "occupational therapy." At times he has been so immobilized by art -- with drawings leaned against his legs and canvases in either hand -- that he's had to call for help.

He is discussing a small, exquisite, penciled self-portrait by Ce'zanne. He takes it from the wall. Half a dozen nail holes wink out from the plaster. The picture, more than once, has been shifted half an inch or so first this way, then that.

Tomorrow: The Private Paul Mello