The fog was a living thing that night—a yellow, choking miasma that had crawled up from the Thames to swallow the city whole. From the window of our sitting-room at 221B Baker Street, the gas-lamps below appeared as nothing more than sickly, nebulous smudges in the gloom. It was a night for warm fires and old brandy, yet the atmosphere within our quarters was as unsettled as the weather without.
Sherlock Holmes was in the grip of one of his darker hyponchondriacal fits. For three days, the London criminal classes had remained disappointingly stagnant, and my friend had paid the price in a currency of agonizing boredom. He sat now in his armchair, his thin, aquiline nose buried in a volume of Napier's logarithms, though I knew his mind was far from the printed page. He had not spoken for three hours, save for an occasional caustic remark regarding the "appalling lack of imagination" currently displayed by the city's burglars.
"My dear Watson," he said suddenly, his voice cutting through the silence like a scalpel. "The arrival of a man in a state of terminal terror is usually a precursor to a most interesting evening. I suggest you put down your British Medical Journal and prepare your bag."
I looked at him in surprise. "I heard nothing, Holmes. Not even the rattle of a hansom."
"Your ears are tuned to the obvious, Watson. You missed the frantic, uneven footfalls on the pavement three minutes ago, followed by the hesitant fumble at the door. Mrs. Hudson is currently experiencing some difficulty with him in the hallway, if I am not mistaken."
As he spoke, the sound of a sharp, strangled cry drifted up the stairs, followed by a heavy thud that vibrated through the floorboards. I was on my feet in an instant, my medical instincts overriding my curiosity. Holmes followed, though his pace was more measured, his eyes already alight with the predatory gleam of the hunter who has caught a scent.
We found them on the landing. Mrs. Hudson stood pressed against the wall, her hands flew to her mouth in a gesture of horror. At her feet lay a man, sprawled facedown. He was dressed in the uniform of a Continental courier—a heavy, brass-buttoned greatcoat stained with the salt of the Channel and the soot of the railway.
"A doctor, Mrs. Hudson! Quickly!" I cried, dropping to my knees beside the man.
I turned him over, and the breath caught in my throat. He was young, perhaps no more than five-and-twenty, but his face was a mask of such profound exhaustion and terror that he looked decades older. His skin was the color of wet parchment, and a thin line of frothy, blood-flecked foam bubbled at the corners of his mouth.
"Is it a wound?" Holmes asked, looming over us. He did not look at the man's face, but rather at his hands, which were clenched with such force that the knuckles were white.
"No," I muttered, tearing open the man's tunic to listen for a heartbeat. "His pulse is thready—galloping. It is a collapse of the nervous system. Or poison. Look at his pupils, Holmes—they are dilated to the point of vanishing."
The courier's eyes suddenly flickered open. They were glassy, unfocused, staring at some point beyond the ceiling. His lips moved, but the sound that emerged was a mere rasping rattle.
"The... the limit..." he hissed. "The variable... is... zero..."
With a final, violent convulsion that nearly threw him from my grasp, the man's body went limp. I pressed my fingers to his carotid artery, waiting for a flicker of life that did not come.
"He is gone," I said, looking up. "The poor devil. Whatever he was running from, it caught him at our very door."
Holmes was already crouched by the body. He ignored my professional verdict, his long, sensitive fingers prying open the man's right hand. Inside the palm, crumpled into a tight ball and damp with the sweat of the dead, was a scrap of thick, vellum-like parchment.
"Common grief is a thing for the clergy, Watson," Holmes remarked dryly as he smoothed out the paper on his knee. "The investigator must find his solace in the evidence. Tell me, what do you make of this?"
I rose and looked over his shoulder. I had expected a note—a plea for help, perhaps, or the name of an assassin. What I saw instead was a series of intricate, maddeningly precise diagrams. They were not sketches of places or people, but mathematical constructs. Lines curved in ways that defied the traditional laws of geometry; symbols I vaguely recognized from my university days were intertwined with others that seemed entirely alien.
In the center of the parchment, written in a cramped, precise hand, was a single equation:
$$\lim_{x \to \infty} \left( \frac{\Phi(n)}{\Delta} \right) = \text{Regis}$$
"Non-Euclidean geometry," Holmes murmured, his voice hushed with a rare note of genuine interest. "And look here, Watson. The ink is still slightly tacky. It was written recently, perhaps on the train from Dover."
"What does it mean, Holmes? It looks like the work of a lunatic."
"On the contrary, it is the work of a genius. A genius who is concerned with the stability of structures. Observe the way the lines converge toward that central point. It is a calculation of a breaking point."
He stood up, his gaze sweeping over the dead man. With the toe of his slipper, he nudged the courier's left arm. The sleeve pulled back, revealing a series of small, precisely spaced bruises along the forearm—the marks of a struggle, or perhaps something more clinical.
"He did not die of poison, Watson," Holmes said, his eyes narrowing. "Nor was it a simple nervous collapse. Look at the carriage of his head. There is a slight swelling at the base of the medulla."
I leaned down and felt the area. He was right. There was a hard, localized inflammation at the very top of the spinal column.
"A needle?" I suggested.
"A very specific kind of needle. One designed to deliver a shock to the respiratory center. It is a method of execution that leaves almost no trace, practiced by those who value discretion above all else."
Holmes walked to the window and looked out into the fog. He was no longer the bored, lethargic man of an hour ago. He was a coiled spring, vibrating with a dark energy.
"The courier comes from Vienna, via Paris," Holmes said, his back still turned to me. "His boots are caked with a specific red clay found only in the construction sites of the Ringstrasse. He traveled in haste, forgoing sleep. He carries a cipher that speaks of the 'Limit of the King.' And he is murdered on our doorstep by a method known only to the most advanced state laboratories."
"State laboratories?" I echoed. "Surely you don't mean..."
"I mean, Watson, that the game is no longer afoot. It has begun to gallop. This boy was a variable in an equation he did not understand, and he has been cancelled out to prevent the solution from being reached."
Holmes turned back to the room, his face set in those hard, clinical lines I knew so well. He picked up his magnifying glass and bent over the parchment once more, his focus so intense that the rest of the world seemed to cease to exist for him.
"This is not a crime of passion, or of greed," he whispered, almost to himself. "It is a crime of logic. The most dangerous kind of all."
A sudden, sharp rap at the front door made us both start. It was not the hesitant knock of a client, but the authoritative, rhythmic strike of a heavy cane.
"The police?" I asked.
"No," said Holmes, his eyes fixed on the door. "Lestrade does not carry a Malacca cane, nor does he walk with the heavy, measured tread of a man who weighs the fate of nations in his pocket."
The door to our sitting-room swung open before Mrs. Hudson could announce the visitor. There, framed in the doorway, stood a figure that brought a chill to my heart even more profound than the death we had just witnessed.
It was Mycroft Holmes. He looked more massive than ever, his grey, introspective eyes clouded with a shadow I had never seen before. He did not look at his brother, nor at me. His gaze fell directly upon the dead man on the landing.
"You have the paper, Sherlock?" Mycroft asked, his voice a low, rumbling bass.
"I have it, Mycroft."
"Then you must burn it. Now. Before the shadows in the street realize that the courier reached his destination."
Holmes held the parchment up, his thumb tracing the non-Euclidean curves. "And if I refuse?"
"Then," Mycroft said, stepping into the room and closing the door with a finality that made the windows rattle, "you will find that the British Empire is a very small place to hide from a ghost."
At that moment, from the street below, came the sound of a single, sharp whistle—a signal that was answered from the rooftops by the cold, metallic click of a rifle bolt being drawn back.