The platform at Victoria Station was a scene of frantic, freezing chaos as the morning boat-train prepared for its departure. Great clouds of white steam hissed from the locomotives, instantly freezing against the iron framework of the glass roof. The winter storm had followed us from the river, casting a fresh blanket of granular snow over the luggage barrows and the heavy woolen coats of the travelers.
Mary stood beside me on the frost-lined platform, her hands tucked deep within her beaver-skin muff. There were no tears in her eyes; the long resolution of her father's Andaman mystery had given her a profound understanding of the world Holmes and I inhabited. She looked up at the dark carriage window where Holmes was already arranging his traveling maps.
"You must go, John," she said softly, her voice carrying clearly through the din of the shunting engines. "The Professor is the final link in the chain that bound my father to Major Sholto. Until his shadow is removed from Europe, no hearth in England is truly safe."
"I shall return before the spring thaws, Mary," I promised, kissing her cheek before swinging myself aboard the first-class compartment just as the guard’s whistle blew its shrill, piercing note.
The train jolted forward, clearing the platform and gathering speed as it plunged into the yellow, frost-bitten fogs of the South London suburbs. Holmes sat opposite me, already enveloped in his long traveling cloak, a large ordnance map of the Bernese Oberland spread across his knees. He had not spoken since we left Baker Street, but his long, thin fingers were working with a tireless energy, tracing the red ink lines that marked the alpine passes.
"The Professor has a three-hour start on us, Watson," Holmes remarked, his eyes never leaving the map. "He took the early packet boat from Newhaven to Dieppe while we were still clearing the soot from our lungs at Charing Cross. By tomorrow night, he will have reached Geneva, and by the weekend, he will be securely entrenched in his mountain redoubt near Meiringen."
"And what is his objective there, Holmes?" I asked, adjusting my heavy traveling rug over my knees. "Why draw us to the heights of Switzerland in the dead of winter?"
"Because the mountains are an absolute equation," Holmes replied, looking up with a flash of analytical fire in his grey eyes. "In London, a criminal must contend with the friction of the police, the fog, and the accidental observations of the street populace. But in the high Alps, the elements are pure. There are only two forces—the hunter and the prey—separated by a sheer vertical drop of a thousand feet of ice. It is the perfect laboratory for a final mathematical demonstration."
He reached into his breast pocket and drew out the heavy blue paper sheet we had found at Baker Street. He turned it over, revealing a small, intricate sketch drawn on the reverse side. It was a precise topographical diagram of a narrow mountain path, clinging to the edge of a monstrous chasm where a roaring glacial waterfall was marked in dark, heavy strokes.
"The Reichenbach Falls," Holmes murmured, his voice dropping to a low, solemn cadence that sent a sudden thrill of dread through my chest. "That is where the coordinates terminate, Watson. He is waiting for me at the edge of the abyss, where the water never freezes and the noise of the torrent drowns out the voices of men. Let us see if our analytical faculties can survive the altitude."
