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which allowed the binomial, (a + b), to be raised to any power
n
.

Although the theorem was proved by the Norwegian mathematician Niels Henrik Abel in the early part of the nineteenth century, Mr Poul Anderson in his article ‘A Treatise on the Binomial Theorem’, published in the
Baker Street Journal
in January 1955, has suggested that Moriarty was working on the basic idea of number itself and that he had developed a general binomial theorem which could be applied to other forms of algebra.

Moriarty was also the author of
The Dynamics of the Asteroid
, a book which ascended to ‘such rarefied heights of mathematics’ that it was claimed there was ‘no man in the scientific press capable of criticising it’. An asteroid is a tiny planet revolving round the sun between the orbits of Mars and Jupiter. While it is too small to affect the orbits of the nine major planets, their gravitations simultaneously influence the orbit of the asteroid, although no general mathematical solution had been formulated to express even the effect of three of these planets (the three-body problem), let alone the nine.

In the same article, ‘A Treatise on the Binomial Theorem’, Mr Poul Anderson has suggested that Professor Moriarty had discovered a general solution for the orbit of an asteroid together with a set of equations which could be applied to any similar body, as far as even the
n
-body problem. Mr William S. Baring-Gould has further suggested that Moriarty may have anticipated Einstein’s equation E = mc
2
, which prepared the way for the development of the atomic and hydrogen bomb, and that he may also have supplied the theoretical groundwork for man-made satellites and space stations.

Whether this is true or not, it is clear Holmes was correct in describing Professor Moriarty’s powers as ‘phenomenal’, although he had deliberately chosen to dedicate his genius to a much more sinister purpose than research into pure mathematics. Instead, he had set up an international criminal organisation of over a hundred members, including pickpockets, blackmailers, cardsharpers and murderers, which he ruled over with a rod of iron. The punishment for any transgression of the organisation’s rules was death.

His Chief of Staff was Colonel Sebastian Moran, son of Alexander Moran, the former British minister to Persia. Born in 1840, Colonel Moran had been educated at Eton and Oxford University and later joined the First Bengalore Pioneers,
*
an Indian Army regiment. He had served with some distinction in several campaigns and had been mentioned in despatches. He was also the celebrated author of two books,
Heavy Game in the Himalayas
and
Three Months in the Jungle
, and was considered one of the best shots in the world, a skill he was later to put to deadly use.

Although there was no open scandal, he was obliged to retire from the army and, on his return to England, Moriarty recruited him into his organisation to carry
out those top-class crimes which none of the ordinary gang-members would undertake. Holmes, who considered him the second most dangerous man in London, suspected him of being responsible for the murder in 1887 of Mrs Stewart from Lauder.

Professor Moriarty paid Moran the huge sum of £6,000 a year, more than the Prime Minister’s salary. It was money Moriarty could well afford, for his criminal activities brought him considerable wealth. By tracing some of Moriarty’s cheques, Holmes had discovered he had six separate bank accounts and suspected he owned twenty in all, the bulk of his fortune being invested abroad in Deutsche Bank or Credit Lyonnais.

The problem was finding evidence which would prove Moriarty’s guilt. It was not an easy task. Holmes had visited his rooms on three occasions, twice legitimately, using different pretexts for calling on him but leaving before the Professor returned home. Although Holmes does not give details, he hints that on the third occasion he broke into Moriarty’s rooms during his absence and searched his papers but found nothing incriminating. Holmes does not make it clear where these rooms were situated, whether at the university, possibly Durham, or in London where Moriarty may have kept a separate establishment for his use during the vacations. As his criminal organisation was London-based, this is perfectly feasible, in which case Holmes would have timed his visits to coincide with Moriarty’s presence in the capital.

Nor is it clear how Holmes first heard of Moriarty,
although it may have been through a man known by the pseudonym Fred Porlock. The surname is probably a reference to the man from Porlock who called on the poet Samuel Coleridge and interrupted his composition of ‘Kubla Khan’. Or Holmes may have already been aware of Moriarty’s existence through his own enquiries and established contact with Porlock himself. Whatever the circumstances, Porlock was a useful informer inside Moriarty’s organisation, what in the language of John le Carré’s spy fiction is referred to as a ‘mole’.

Porlock, a ‘shifty and evasive’ character, was a minor member of Moriarty’s gang, a pilot fish to his whale, a jackal to his lion. Out of what Holmes refers to as ‘a rudimentary aspiration towards right’ but principally for financial gain – the ‘judicious stimulation of a ten-pound note’, as Holmes ironically calls it – Porlock was willing on occasions to supply Holmes with advance information of Moriarty’s plans. These sums of ten pounds, a large amount of money in the 1880s, were presumably paid out of Holmes’ pocket and were always sent in cash to Camberwell Post Office. Communication between them was in code, using a system which is virtually unbreakable. The message was composed of a set of figures which referred to a page, to lines on that page and to the position within those lines of individual words contained in a certain book, the identity of which was known only to the correspondents. Anyone not knowing which book had been used to compile the cipher had little hope of unscrambling the message.

In the Valley of Fear inquiry, Porlock sent the coded
message but lost his nerve at the last moment and failed to supply the name of the volume on which the code was based. It took all of Holmes’ ingenuity and knowledge of ciphers, on which he was an expert, in addition to some invaluable assistance from Watson, to deduce that the code was taken from a page in
Whitaker’s Almanac
.

Breaking through the web of evil which surrounded Professor Moriarty was to prove a much more difficult task. As Holmes says of him, he had a brain which might have made or marred the destiny of nations. This is an interesting echo of his comment on Mycroft’s role. In fact, the two men had much in common. Both possessed great mathematical skills. Both men also concealed their true activities, Mycroft as adviser to Her Majesty’s Government, Moriarty as head of an international criminal gang.

But it is between Sherlock Holmes and Professor Moriarty that the closest parallels can be drawn. In
The Hound of the Baskervilles
, Holmes refers to himself as a ‘specialist in crime’, an epithet which could be applied with equal accuracy to Moriarty; but while Holmes had dedicated his own phenomenal powers to the fight against crime, Moriarty had concentrated his on building up a Mafia-style underworld organisation, the sole purpose of which was the perpetration of crime.

The struggle between the two men was to assume the epic proportions of the primeval contest between the forces of good and evil, Holmes on the side of the forces of light locked in mortal combat with Moriarty who ‘had all the powers of darkness at his back’.

None of this was apparent to the casual observer. Outwardly, Moriarty was harmless, a respectable Professor of Mathematics from a provincial university, known only as the learned author of two brilliant but abstruse publications which had caused quite a stir in academic circles. Inspector MacDonald, who called on him after hearing of him from Holmes, found nothing suspicious about him. Indeed, he thought Moriarty would have made ‘a grand meenister with his thin face and grey hair and solemn way of talking’. In the opinion of MacDonald and his colleagues in the CID, Holmes had a bit of a bee in his bonnet over the man.

Holmes’ description of Moriarty, when he finally came face to face with him, is much less flattering. He was extremely tall and thin, Holmes tells Watson, with a high, white, domed forehead, sunken eyes and rounded shoulders from his years of study. Clean-shaven, pale and ascetic-looking, he had something of the professor in his features, although his habit of pushing his head forward and swinging it slowly from side to side gave him a repulsive, reptilian air. Holmes found his style of speech, which was soft and precise, more threatening than an overtly bullying manner.

During his interview with Moriarty, MacDonald was also impressed when, the conversation having turned to the subject of eclipses, the Professor was able, with the aid of a reflector lantern and a globe, to make ‘it all clear in a minute’, proof of Moriarty’s undoubted skill as a teacher.

But what MacDonald failed to take sufficient note
of was the painting which hung behind the Professor’s desk. It was a portrait of a young girl by the French artist Jean-Baptiste Greuze. A similar painting, entitled
La Jeune Fille à l’Agneau
, had fetched FF1,200,000, more than £4,000, at the Portalis sale in 1865.
*
How could the Professor afford to buy such a painting on his salary of £700 a year?

The answer was simple. Like Jonathan Wild

before him, Moriarty sold his own criminal expertise and that of his organisation for a commission, either on a promise of part of the spoils or as a down-payment for organising the crime before it was committed. In the Birlstone case, he had been paid by the Scowrers, an American secret society intent on destroying the power of the railway and colliery owners in Vermissa Valley in the States, to hunt down and organise the murder of Birdy Edwards, a.k.a. John McMurdo, a Pinkerton detective who had infiltrated the Scowrers and brought about their downfall. Using the alias John Douglas, Edwards had fled to England, where
Moriarty’s organisation had traced his whereabouts. But the attempt on his life failed when Douglas killed his would-be murderer, Ted Baldwin, a former Scowrer member, in self-defence.

This case, a full-length account of which Watson later published under the title
The Valley of Fear
, was the first direct contact Holmes had with both the Pinkerton National Detective Agency, set up in the States by Allan Pinkerton in 1850,
*
and, more importantly, with Moriarty and his gang.

Douglas later disappeared overboard from the
Palmyra
when on his way to South Africa with his wife, after being acquitted of Baldwin’s murder. Holmes attributed Douglas’s death to Moriarty, convinced he had stage-managed the apparent accident in order not to appear to have failed in his commission. As Holmes remarks, ‘You can tell an old Master by the sweep of his brush. I can tell a Moriarty when I see one.’

Holmes’ comparison of Moriarty with Wild was apt. So, too, was his comment that, ‘The old wheel turns and the same spoke comes up again.’ It had all been done before and would be done again.

Moriarty’s methods, such as the use of the paid professional ‘hit-man’, the investment in overseas banks of illegal money and the iron discipline exerted over gang members, are those still used by contemporary criminals. Even Moriarty’s ploy of deliberately seating a person he was interviewing so that either the light from the window or the desk lamp fell directly on his face while his own features remained in shadow, is a stratagem still used by secret police the world over.

Holmes himself was looking into the future when, at the end of the Valley of Fear inquiry, he assures Cecil Barker, Douglas’s close friend and associate, that Moriarty can be beaten.

‘But you must give me time – you must give me time.’

It was to take Holmes another three years before that promise was fulfilled.

*
Although Watson’s account was hardly noticed by the critics at the time, the annual itself was such a success that the publishers issued
A Study in Scarlet
in a separate edition in 1888.

*
The Diogenes Club has been variously identified as the Athenaeum or the Travellers’, which were also situated in Pall Mall. However, both were established too early for Mycroft Holmes to have been a founder-member.

*
Holmes himself was a good mathematician. While travelling down to Devon on the Silver Blaze inquiry, he was able to calculate in his head the speed of the train from the time it took to pass the telegraph posts which were set sixty yards apart.

*
Bengalore is spelt Bangalore in some American editions. There is no such regiment as the First Bengalore Pioneers. Because of Colonel Moran’s subsequent criminal career, Watson has clearly changed the name in order not to bring shame on Moran’s former regiment.

*
Holmes was mistaken over the name Portalis. In fact, it was the Pourtalès Gallery of Art, a private collection owned by the Comte de Pourtalès-Gorgier, which was sold at auction in 1865. The painting referred to by Holmes, entitled
Innocence
, which was bought by an anonymous buyer, was later proved to be a copy of the original by Greuze. It is at present in the Wallace Collection in London.


Jonathan Wild (c. 1682–1725) was a master criminal who organised a gang of London thieves, setting up their robberies and charging a fifteen per cent commission on the sale of the proceeds of their thefts. He betrayed anyone who refused to co-operate with him to the authorities. He was hanged at Tyburn in 1725.

*
Allan Pinkerton (1819–1884) was born in Glasgow. After emigrating to the States in 1842, he was appointed deputy sheriff of Cook County. Eight years later he set up his own detective agency. One of his detectives, James McParlan, infiltrated the Molly Maguires in Pennsylvania (1873–6) and secured evidence which led to the break-up of this organisation of coal-miners, allegedly engaged in terrorism. This closely parallels John Douglas’s infiltration of the Scowrers.

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