The money-gushing conduit set up by Andrew Mellon half a century ago for the dispersal of his millions will soon go out of business, but not before delivering one last major grant -- of $5 million -- to the Washington museum that Mellon gave the nation, the National Gallery of Art.

J. Carter Brown, the gallery's director, said yesterday he had just found the check in the mail.

The money will be used to help pay for construction of the ground floor "spine" or indoor street that will, in effect, add two new small museums to the gallery's West Building.

Founded in 1930, the A.W. Mellon Educational and Charitable Trust was for years the fund that paid the gallery's major bills. It provided $23 million for the West Building's construction, an additional $11 million for a gallery endowment and works of art once valued at $50 million with which to initiate, in 1941, the gallery's collection. That $84-million benefaction, it is worth remembering, is in 1930s dollars. The trustees of the trust will distribute all the monies it has left and liquidate the trust before the end of June.

Andrew William Mellon paid for the West Building much as his two children, Paul Mellon and the late Ailsa Mellon Bruce, paid for the East Building built nearby.

The East Building has not only provided the gallery with new exhibit spaces, offices, two auditoriums and a Center for Advanced Study in the Visual Arts -- but its construction also has liberated ground-floor space in the old West Building. That floor used to house a cafeteria, offices and other support facilities no longer in use.

"The completion of the spine will probably take years," Brown said yesterday. "However, when we're finished, Washington will have two new small museums -- one for small sculptures, Renaissance bronzes and medals, the other for our holdings in the graphic arts.

"The gallery, you know, owns one of the world's three great collections of small Renaissance bronzes, but these exquisite works of sculpture rarely have been shown. Our great holdings in prints and drawings, which have been recently enriched by the unparalled collection of the late Lessing J. Rosenwald, also deserve a small museum of their own where they can be displayed in rotating exhibits.

"Eventually, the visitor will enter the West Building from Seventh Street, proceed past these two small museums, and then find himself in an indoor street of museum shops where he mnay browse among posters, prints and books. Our goal is to have on sale a postcard of everything in the place so that, if you fall in love with an image, you may take it home. But showing thousands of postcards takes a lot of room. The daylight at the end of the spine eventually will lead you to the Fourth Street Plaza and the East Building beyond."

During its half century, the A.W. Mellon Trust distributed $199,276,000, of which nearly half was given to the gallery. Before its liquidation on June 30, the trust will give an additional $20 million to 27 Pittsburgh institutions and organizations including the University of Pittsburgh, the Pittsburgh Symphony, the Carnegie Institute and the Carnegie-Mellon University.

Andrew Mellon was a Pittsburgh banker, industrialist (among th firms he helped develop were Alcoa and Gulf Oil), statesman and philalthropist who served here as Secretary of the Treasury under Harding, Coolidge and Hoover. He ended his governmental career as ambassador to the Court of St. James's.