President Carter stood last month on the village green of George Washington's ancestral home in Washington, England, and shoveled some soil around the base of tulip tree that had been brought from Washington's Mount Vernon, Va., home.

British Prime Minister James Callaghan waited nearby to plant an English sapling, a simple gesture of friendship between the two countries.

But now, the five-foot sapling that Carter planted has wilted and died, a State Department spokes-woman reported yesterday.

The sapling, scion of the 120-foot Independence Tree believed to have been planted by George Washington at Mount Vernon could not adjust to the change in climate, according to State Department protocol officer Midge Burke.

"They had three surgeons look at it last week. It was still wilted. It's not going to survive," she said. "The tree was a symbol of good relations between the two countries."

The sapling, together with a seedling, had been flown by transport from Andrews Air Force Base and shared a compartment with Secret Service agents and their vehicles.

At a well-orchestrated ceremony on the village green, the president placed a few shovels of soil aroung plant, as Callaghan planted an English tulip tree nearby.

The State Department said it is going to send a second sapling from Mount Vernon to the ancestral home in February. This time it will be newly-appointed Ambassador Kingman Brewster who will weild the shovel, Mrs. Burke said.

It is not first time diplomatic gestures of good will had trouble rooting in foreign soil.

"The Prince of Wales in 1860 planted and English Oak near Washington's tomb on the occasion of his visit. That tree also died. The British ambassador planted a replacement and that tree is still living today, so we have a sort of precedent for the occasion," Burke said.

The tulip poplar, actually a member of the magnolia family, was a favorite of George Washington's. The planting of the 120-foot progenitor of the ill-fated sapling is recorded in his diary of February, 1785.

"Monday 28 planted all the Mulberry trees, Maple trees, and Black-gums in the Serpentine Walk, and the Poplars on the right walk, the sap of which and the Mulberry appeared to be moving," the diary records.

One of the populars at Mount Vernon is called the Independence Tree because at the time it was transplanted in 1785 it was believed to be 10 years old, placing its birth at about the time of the American Revolution, according to Mount Vernon's resident director, Harrision M. Symmes.

Thousands of seeds from the Indepenence Tree were sold last year during the nation's Bicentennial, Symmes said.