The message picked up by the control tower was as bizarre as it was alarming. “Everything looks strange,” said the pilot. “It looks like we’re entering white water. We’re completely lost.” There were a few more crackles and then silence. It was December 5, 1945, and the five aircraft of Flight 19 — a military training mission from Fort Lauderdale, Florida — had vanished.

The disappearance of Flight 19 became one of the world’s most enduring aviation mysteries. No wreckage was found, despite an extensive search, and nor were any bodies recovered. The aircraft and their 14 crewmen seemed to have disappeared into thin air. There was frenzied speculation, and, before long, the birth of an extraordinary myth: an area of ocean that became known as the Bermuda Triangle, in which unexplained and seemingly paranormal incidents occurred with alarming frequency.

Now, seven decades after their disappearance, the truth about the aircraft and the Bermuda Triangle can be revealed. It is a tale of fantasy, duplicity and wishful thinking — one that brought enormous wealth to a handful of individuals.

Within hours of the five Avengers disappearing from the radar, a PBM-Mariner seaplane was sent on a search-and-rescue mission. Its pilot made a routine radio call at 7.30pm indicating his position. Soon afterwards, the Mariner also vanished from the radar. Neither the aircraft, nor her 13 crew, were seen again.

The disappearance of six aircraft in one day was mysterious enough, but a further three aircraft went missing in the same area in 1948 and 1949, and a yacht, the Connemara IV, was found adrift and without its crew in 1955. A few years later, two US Air Force Stratotankers also disappeared.

The media began to speculate: citing compass variation, tropical storms and the Gulf Stream’s unpredictable currents. But one theory caught the imagination: all the losses had occurred in about 2.5 million square kilometres between Miami, Puerto Rico and Bermuda.

In February 1963, a freelance writer, Vincent Gaddis, wrote a sensational article for “Argosy” magazine claiming that supernatural forces were at work in this triangular bit of ocean. Gaddis’s article contained much speculation, little evidence and precious few facts. But his timing was perfect: “The Deadly Bermuda Triangle” was published shortly after the two Stratotankers were lost. “The mysterious menace that haunts the Atlantic off our south-eastern coastline has claimed two more victims,” wrote Gaddis. “Before this article reaches print, it may strike again, swallowing a plane or ship, or leaving behind a derelict [vessel], with no life aboard.”

The article was a masterpiece of conspiratorial fantasy, suggesting that dark forces were at work. “Despite swift wings and the voice of radio, we still have a world large enough so that men and their machines and ships can disappear without trace.”

Others were quick to cash in. Scores of books were published — many became bestsellers — with the most popular being Charles Berlitz’s “The Bermuda Triangle”, published in 1974. It sold 20 million copies in more than 30 languages — blaming the losses on aliens and survivors from Atlantis. Berlitz’s theories were so popular that when Steven Spielberg made “Close Encounters of the Third Kind”, he depicted the Flight 19 aircrews as having been abducted by aliens.

At the time of the loss, much attention was focused on the squadron’s leader, Lieutenant Charles Taylor. An accomplished pilot with 2,500 hours of flying experience, he had an unblemished record as an instructor. His student pilots were also highly capable, having clocked up some 300 hours of flying time. The aircraft were fully fuelled and had passed all their pre-flight checks.

They took off without incident at 2.10pm and were soon heading due east, towards Abaco Island in the northern Bahamas. Snatches of the radio conversations between the crews allow for a partial reconstruction. Around 3.40pm, one was heard asking for a compass reading. “I don’t know where we are,” was the response. “We must have got lost after that last turn.”

Minutes later, Lt Taylor said: “Both my compasses are out and I am trying to find Fort Lauderdale, Florida.” He attempted to locate his position by studying the islands below. “I am over land but it is broken,” he said. “I am sure I’m in the [Florida] Keys, but I don’t know how far down.”

His words give the first inkling of the disaster to come. His aircraft had strayed from their planned route due to faulty compasses: Lt Taylor was almost certainly looking at the Bahamas. By swinging east — as he now did — he was heading out into the Atlantic. A dissenting voice was heard on the radio. “Dammit, if we could just fly west, we would get home. Head west, dammit.”

Someone, it seems, knew that they were on course for disaster. The ground staff made frantic efforts to contact Lt Taylor, but their messages were not picked up. They eventually triangulated Flight 19’s position and it was alarming. The aircraft were north of the Bahamas, miles from land. “All planes, close up tight,” radioed Taylor at 6.20pm. “We’ll have to ditch unless landfall. When the first plane drops below 10 gallons, we all go down together.”

The final moments of Flight 19 must be speculation: the aircraft presumably ditched into the ocean, where conditions had deteriorated since they left Fort Lauderdale. The choppy sea would have soon swallowed the heavy Avengers. The US Navy immediately opened an investigation into the missing Avengers, as well as the PBM-Mariner. The latter aircraft was widely held to have exploded in mid-air — a hypothesis reinforced by the testimony of Captain Shonna Stanley of the SS Gaines Mills: he saw a ball of fire in the sky at exactly the time the search aircraft went missing.

As for the Avengers, it was concluded that human error and compass malfunction caused the tragedy. Lieutenant Taylor had wrongly believed himself to be over the Florida Keys; each change of course took his formation further out to sea. He had previously been based in Miami and was unfamiliar with the Fort Lauderdale topography.

One by one, the Bermuda Triangle’s supposed mysteries have been solved. The Connemara IV was washed out to sea (without its crew) during a hurricane and the two Stratotankers collided and crashed in the Atlantic. And Lloyds of London said losses were no higher there than in any other area. But Gaddis refused to accept the findings and set to work on his supposition that supernatural forces were responsible — and the Bermuda Triangle was born.

The Telegraph Group Limited, London 2015

“Fascinating Footnotes From History” by Giles Milton is published by John Murray, £15.

Strange phenomena — and how to explain them

Nostradamus’s prophecies: Written in verse, the letters of 16th-century French philosopher Michel de Nostredame have long been credited with predicting the French Revolution, the rises of Napoleon and Hitler and the 9/11 attacks on the Twin Towers. The vagueness of the descriptions have encouraged conspiracy theorists — despite so many prophecies, not least the end of the world in 1999, never coming true.

Crop circles: There are countless theories as to how crops come to be flattened in elaborate patterns of geometric lines and circles. But rather than being a supernatural phenomenon, or created by the landing gear of extra-terrestrial spacecraft, the only known cause is human.

Mary Celeste: Speculation over what happened to the crew of the brigantine, found adrift in the Atlantic in 1872, has been fuelled by a lack of evidence to support suggestions of piracy or mutiny. In 2006, a UCL scientist posited that an explosion caused by alcohol leaking from the cargo could have caused “a pressure-wave type of explosion”, killing the crew.

Spontaneous human combustion: According to hundreds of accounts, people have caught fire and burnt slowly, without scorching their surroundings. One theory for it — which leaves a yellow, foul-smelling grease surrounding the remains — is a build-up of methane that is ignited by enzymes or static electricity. But many scientists believe the victims died after falling asleep with a cigarette, suffocated and, in a slow-burning process known as the wick effect, were cremated.

“Blue or gold dress?”: #Dressgate divided a nation this year, when a party dress appeared to be blue and black or gold and white, depending on the environment and screen on which the digital photograph was viewed. (It was, in fact, blue and black.)

Area 51: A remote area of desert in Nevada is a magnet for conspiracy theorists, who believe post-war US governments hid evidence of alien life there. Recently released documents, however, show it was used during the Second World War as a gunnery range for pilots.