The estate of John Hay Whitney has given eight important pictures--among them works by Seurat, Balthus and Picasso--to New York's Museum of Modern Art.

The donation to the Modern is the third gift made by the estate of the late diplomat, publisher, sportsman and collector, who died last February.

Eight other Whitney pictures--one each by Eakins, Whistler, Hopper, Bellows, Rousseau and Henri Edmond Cross and a pair of Derains--were given, in December, to the National Gallery of Art. A comparable gift to Yale University--a Degas, an Eakins, a Gauguin, a Pissarro and two Picassos--was announced at the same time.

Whitney and his wife Betsey, who received much guidance from the art historian John Rewald, formed a remarkable collection, especially strong in paintings by the French Impressionists and Fauves. The cream of their collection--including all the paintings in the three recent gifts, as well as perhaps 50 others still owned by Betsey Whitney--will be the major summer show at the National Gallery of Art. "The John Hay Whitney Collection" will open May 29.

Additional Whitney gifts may well be forthcoming. John Wilmerding, the National Gallery's deputy director, said yesterday: "We hope someday to receive another group of pictures. And I believe it was Mr. Whitney's wish that additional paintings, held by Mrs. Whitney during her lifetime, eventually will be given to Yale and to the Museum of Modern Art."

The Modern was given two early Picassos, "Head of a Sleeping Woman" (1907) and "Still Life with Fruit and Glass" (1908). Also in the gift are Vuillard's "Les Brodeuses" (1895-96), Utrillo's "La Rue des Abbesses" (1910), Tamayo's "Woman" (1938) and a pair of pointillist pictures--one an 1885 seascape by Seurat, the other an 1892 picture by his follower, the Belgian The'o van Rysselberghe.

Thirty-seven objects by the American artist Joseph Cornell have been given to the Art Institute of Chicago by collectors Betty and Edwin Bergman. This donation, too, is a first installment. The Bergmans, who own the world's most comprehensive collection of Cornell's boxes, collages and dossiers, intend to give most of it to the Chicago museum, which they have long supported. Eight Cornell objects and one Cornell dossier, all from their collection, are now on view in Washington at the National Museum of American Art.