There she was, 86 years old, lying flat on the narrow floor of a mine-sub investigating the wreck of a liner sunk in World War I.

"Luckily I had brought my gardening trousers," said Sheila Macbeth Mitchell. "I wore them aboard the Calypso too, and as I would sit next to Captain Cousteau in my trousers at dinner I would think of my days in India when one Dressed for Dinner no matter what."

Mrs. Mitchell is one of the half-dozen still-living survivors of the Britannic, sister ship of the Titanic, which was sunk by enemy action Nov. 21, 1916, while serving as a hospital ship in the Aegean Sea.

The story of Jacques Cousteau's search for the wreck and of the great-grandmother's inspection trip in his diving saucer will be told in an hour-long special Nov. 22 at 8 p.m. on PBS.

She was 26 years old, a nurse and one of 1.136 persons aboard the great ship when it was hit. They were carrying no wounded, though a day later there would have been as many as 3,500 wounded soldiers aboard for passage from the island of Lemnos to Naples.

Nov. 21 was a beautiful day, sunny and clear. Shelia Mitchell had just gotten up, according to her diary:

"Up late - so only managed to get two spoonfuls of porridge before: Bang! and a shiver right down the length of the ship . . . Everyone jumped to their feet . . . When the siren sounded, I went off to my cabin for my belt and also took my pillow, eiderdown and the first coat I could pick up."

She still has the eiderdown. She also has a piece of a handsome carved chair which a sailor pulled out of the water for her when she was in a life-boat.

"The engines were working until practically the end, doing all they could to beach the ship which unfortunately proved impossible, and she sank about a mile from land. Many boats were drawn into the propellers, and two were cut in half by them and destroyed."

It was the propellers that killed most of the 30 casualties. One who tumbled from her boat in time to avoid the crushing blades was a stewardess who already had come through the Titanic sinking four years earlier.

Britannic sank in 50 minutes, partly because the portholes had been left open.

"I could see the portholes from the mini-sub," Mrs. Mitchell recalled. "We went along the whole length of the ship and saw where the torpedo or mine hit, over the coal bunker."

Thrilled at her adventure - which began when her daughter saw Cousteau's query a year ago in The Sunday Times and brought her to Athens four days later for a helicopter flight to the Calypso - Sheila Mitchell peered through her viewing port in the tiny undersea craft. She saw the tilted deck, the anchor, the rusting flanks of the ship, the torn superstructure festooned with green algae.

"Only the captain's bathroom was free of it, the tiles, so glossy and clean as if they'd just been polished. But the ship was a dead thing, you know. I was really more interested in all the life around me: a most adorable lobster waving its gills, a great ugly red fish . . . We were simply surrounded by goldfish. And the coral everywhere: It was like an underwater garden."

Her husband, John, nearly 91, couldn't make the trip with her (nor could the other Britannic survivors whom Cousteau found), but adventure has always been part of Sheila Mitchell's life. One of nine children of a Victorian English machinery designer, she was born into an energetically unconventional family. Her uncles were painters and musicians, her sisters artists and professional golfers.

In 1908 she went to Paris as an art student, learned French, lived with a family of musicians - a pupil of Debussy, Mme. Gallier, kept an eye on her and her sister. Fleeing from a dilettante life when World War I broke, she became a nurse, served in London Hospital and later the hospital ship. After her rescue she worked behind the lines in France.

"I went skiing in Switzerland with my brother after the war," she said. "My family was always considered a bit advanced: I wore men's riding breeches, which wasn't done in those days."

Married in 1920, she removed to India with her husband, a finance official with the Punjab government. Once she hiked 200 miles into the Himalayas to see some rare religious festivals. She and her husband have lived all over Europe.

In Scotland the Mitchells are best known for their genealogical investigations. So far they have recorded 50,000 gravestone inscriptions from 10 counties in Schotland, producing 14 mimeographed books packed with data taken from pre-1855 graves.

"We got lots of inquires from America. Americans all want to find a king among their ancestors."

She is quite impatient with this craving for kings and Magna Carta signers. Her own Macbeths have nothing to do, she emphasized, with that Thane of Glamis who was so maligned by Shakespeare. Her Macbeths were doctors, many of them, for generations and generations.

But it's the present that interests her most. She wears a Calypso medal-lion on her scarf, and she is needle-pointing a special design to give Captain Cousteau when she sees him again in Los Angeles.

"Such a nice man," she said. "Such a charming man."