It's May 10, 1941.

11pm. At Floor's Farm near Eaglesham, farmer Basil Baird and his wife Margaret are asleep.

Suddenly, there is the sound of a plane overhead and a thud.

No-one at the farm knows it yet, but that sound marks the beginning of one of the most extraordinary episodes of World War II.

Margaret Baird headed straight out of the farmhouse as soon as she heard the noise, and saw flames in a nearby field.

The farm's ploughman David McLean had also run to the scene, and in the days afterwards, recalled the details clearly.

"As I ran out to the back of the farm, I heard a crash and saw the plane burst into flames in a field about 200 yards away," he said.

"I was amazed and a bit frightened when I saw a parachute dropping slowly earthwards through the gathering darkness.

"Peering upwards, I could see a man swinging from the harness."

Everyone knew straight away that the man was a German officer, but no-one knew yet quite how important he was.

One young police officer who arrived on the scene thought he recognised the man.

"I should know you," he said. "Your face is familiar."

Indeed it was: familiar to millions of people as that of Rudolf Hess, the Nazi officer and Adolf Hitler's deputy.

Hess had flown 1000 miles in an attempt to meet with the Duke of Hamilton at his home, Dungavel House, a few miles from Eaglesham.

Hess believed the Duke would be one way of getting a chance to talk to the King.

Quite why Hess should have made the trip to Scotland has been debated ever since, but Desmond Zwar, author of Talking to Rudolf Hess, interviewed Hess through a go-between after the war and Hess told him his mission was peace.

"On his decision to fly to Scotland," says Desmond Zwar, "Hess said there was only one way out, and that the Germans could not win a war fought on two fronts.

"Hess said: 'Tell me a single young person who is in world politics today, who is not interested in bettering the situation as it stands'."

One of the troops who guarded Hess's plane after the crash, Tommy Milliken, also told of his belief that Hess had come in a genuine search for peace.

He says he remembers that the guns of the aircraft were greased up and unable to fire.

"I knew Hess had no intention of fighting," said Milliken.

"He was in a peace mission and had not come to engage in combat."

When Milliken arrived at the scene, he could see that the plane was a total wreck.

"When we arrived we could see the wreckage was totally mangled. It had been on fire and was crushed up like a concertina."

The first man to get to Hess was McLean the ploughman who, brandishing a pitchfork, took the German into the farm's kitchen. Hess was limping badly – he had broken his ankle –and was asking about the Duke of Hamilton.

Later, members of the Home Guard arrived to take him away, but Hess was still calm.

"A party of Home Guards arrived in a motor and were thrilled to hear that a Jerry was in the cottage," said Margaret Baird.

"We were standing at the side of our garden when he came round, limping pretty badly with about half a dozen Home Guards with fixed bayonets close to his back."

Hess was taken to a hall in Busby and from there to Maryhill barracks in Glasgow.

He then spent several days in Drymen Military Hospital before being moved to London, where he was interviewed by psychiatrist Dr JR Rees.

According to Desmond Zwar, Dr Rees wanted to issue a report that Hess was mentally ill, but Winston Churchill passed word down that no mention should be made of his mental illness.

Dr Rees told Zwar: "Churchill was ordering me to fake my report. But there was schizophrenia. It was real enough.

If anybody was schizophrenic they could have been repatriable under the rules of war."

In the years since, there have been conspiracy theories around the Nazi's journey to Scotland, including one that Hess was actually executed and a fake Hess put in his place, but the author dismisses this.

"That theory was forensically disproved," he says.

What really happened to Hess was that he was tried at Nuremberg for war crimes and was given a life sentence.

He then spent the rest of his life in Spandau Prison in West Berlin and died in 1987 – taking most of what really happened in Scotland with him.