Media playback is unsupported on your device Media caption Watch Holmes and Moriarty fight and plunge down the falls

One of the most famous scenes in the Sherlock Holmes stories occurs in Switzerland, where Holmes fans still gather to re-enact the detective's tussle with his nemesis, Moriarty.

It is 125 years since Sir Arthur Conan Doyle's famous detective was introduced to the world. The first Holmes and Watson mystery, A Study in Scarlet, was published in 1887.

Since then, the inhabitants of 221B Baker Street have remained hugely popular and recent film and television adaptations of the stories have introduced them to a new generation.

But there are some Sherlock Holmes fans for whom reading a book or watching a film is simply not enough to satisfy their enthusiasm. The Sherlock Holmes Society has a current membership of almost 1,200 people from all over the world, and many of them spend their free time re-enacting the key moments of their hero's life.

Image caption Sidney Paget's illustration accompanied Conan Doyle's story in Strand Magazine in 1893

And so this week, more than 70 of them, many aged over 70 themselves, were on a pilgrimage to Meiringen in Switzerland, home of the Reichenbach Falls, and scene of the final struggle between Sherlock Holmes and his arch enemy, the evil Professor James Moriarty, often called "the Napoleon of crime".

Conan Doyle couldn't have chosen a more dramatic spot to stage the encounter. The falls plummet 250 metres down into the valley and such is the power of the water that it has created great holes and cavities in the rock.

And the spot where Holmes and Moriarty are supposed to have met - now handily marked with a little statue of the detective - is the most dramatic of all. The water plunges down a full 90 metres.

On their pilgrimage, members of the Sherlock Holmes Society are determined to add their own drama to the occasion. The society's president is Guy Marriott, a retired London lawyer, resplendent in the green dress uniform of the King of Bohemia.

"The King of Bohemia appears in an early short story called A Scandal in Bohemia. The king employs Sherlock Holmes to recover some compromising photographs of him with an opera singer."

We each choose the character we like to play, he says. "I like to dress up so a military uniform really is very suitable."

In fact, a love of dressing up is something all the Sherlock Holmes Society members clearly share, and since not everyone can be Holmes himself, or Watson, or Moriarty, even the most obscure characters are joining the pilgrimage.

Jonathan McCafferty, a former barrister, has chosen to be Cardinal Tosca. The Cardinal rates just one brief mention in just one Conan Doyle story, but Mr McCafferty sees this as an advantage.

Why the Reichenbach Falls? Sir Arthur Conan Doyle and his wife spent holidays in Switzerland

He picked the waterfalls as the ideal spot to conclude the stories, in The Final Problem

The Meiringen hotel where Holmes and Watson stayed was named the English Hotel in the story

And a local church has a museum that includes the recreated study of 221B Baker St

In the BBC's Sherlock in 2012, Holmes falls from the roof of St Bartholomew's Hospital

"Since nothing whatsoever is known about me other than that I am a cardinal, every other possibility remains," he says. "Whether I was a good cardinal or given to extreme acts of wickedness and mischief is unknown. I favour mischief."

And his costume? "My outfit can best be described by the single word - red. My hat is red, my shoes are red, my socks are red."

Next to Cardinal Tosca is Queen Victoria, who is so immersed in her character that her real identity seems to have been long forgotten.

"I'm the Queen, and I'm Empress of India," she insists. "But today I'm travelling incognito."

Why, then, the crown? "When one is a queen, one has to have a crown. One's just rather hoping no-one will notice."

In fact, one of the things which makes these Sherlock Holmes fans truly endearing is that despite their enthusiasm, none of them takes themselves too seriously.

"I think they are marvellous, and slightly bonkers," says British journalist David Leask, who has come along on the pilgrimage. "These are serious people who are able to really let their hair down. Essentially, they are playing a game, they're being silly, they are having fun like children.

"Yet these are barristers, architects, business people, doing this in their spare time just for the sheer love of silliness. We could all learn something from that."

The highlight of this love of silliness is the re-enactment of the infamous moment when Sherlock Holmes meets his nemesis, Professor Moriarty, at the Reichenbach waterfalls. After a violent struggle, both men apparently disappear.

Image caption The custom kicked off in fine style in 1968, when fans travelled from London

Conan Doyle's original intention was to write off his most lucrative character in his 1893 story The Final Problem, in order to concentrate on more highbrow literature.

But his other books never enjoyed the success of Sherlock Holmes, and in 1901 Doyle, needing to make a living from his writing, revived the great detective.

Find out more You can hear Imogen Foulkes at the Reichenbach Falls on Radio 4's The World Tonight, at 22:00 BST on Monday 17 September

Or listen again afterwards using the link below BBC Radio 4 - The World Tonight

Over a century later, the struggle at the waterfalls remains one of the most famous scenes in literature and the falls today are a popular destination, not just for fans of Conan Doyle but for tourists from all over the world. A rack railway carries tens of thousands of people up to the spot each year. Today, passing tourists are in for an extra treat - the re-enactment.

Holmes (played by retired headmaster David Jones) and Moriarty (lawyer Peter Horrocks) grapple manfully with each other as the rest of the characters look on aghast.

And, as in the original story itself, the re-enactment is determined to leave open the question of who, if anyone, actually survives the apparent plunge down into the gorge.

"The conclusion of the struggle is that two bodies are seen tumbling down into the water," explains Guy Marriott.

"But it probably won't be the characters who have the struggle… we have dummies that we keep for this occasion."

And so, the final scene of The Final Problem finally re-enacted, the pilgrims treat themselves to some Swiss cheese and wine, enjoying the autumn sunshine and the stunning alpine scenery.

For Moriarty character Peter Horrocks, the chance to combine a holiday with his passion for Conan Doyle is irresistible.

"This holiday has everything," he says. "It has the beauty of the Swiss mountains, it has wonderful companionship with the other members of the society, and it has the background of the Sherlock Holmes stories."

Image caption The men fall but to their deaths?

But Queen Victoria, now revealed as Elaine McCafferty from London, admits she sometimes has a hard time telling her colleagues about her hobby.

"I shall be taking to work with me on Monday a series of photographs of Spanish beaches… I find it saves a lot of explanation."

But it's Cardinal Tosca, or John McCafferty, who comes closest to providing the real explanation of what makes playing at Sherlock Holmes so enticing.

"It gives you every opportunity for not being at all serious," he says.

"Certainly if you were to know me in day-to-day life, I would be so absolutely humdrum, but here I hope I have at least a scintilla of interest as a cardinal.

"It's a merciful release from the day-to-day troubles of the 21st Century to imagine oneself a character from a book of the late 19th Century."