'But a map is not a globe,' he continued, peering at me over the top of the great spinning ball. 'All maps entail distortion. Mercator makes his meridians run parallel to each other, but everyone knows that meridians are not parallels like latitudes are.'

'Of course,' I murmured, made dizzy by the sight of the globe, which was still revolving swiftly, its axle squeaking as seas and continents reeled past. 'Meridians converge at the poles. The distances between them shrink as the lines extend north or south of the equator.'

'But Mercator's meridians never converge.' He was pecking at the map once again. 'They remain parallel to each other, something that distorts east-west distances. So Mercator changes the distances between the latitudes as well, increasing them as they move away from the equator and towards the poles. We therefore speak of his "waxing latitudes". The result of these alterations is a distortion towards the poles. Landmasses in the far north and south are exaggerated in size because the parallels and meridians are distended so that the grid of parallel lines and right angles can be preserved. Mercator's projection is therefore well and good if one is sailing along the equator or in the lower latitudes but not much use to someone exploring the high latitudes.'

'Not much use,' I was nodding eagerly, 'to someone exploring the northwest passage to Cathay.' I was remembering how, as a boy, I used to trace the voyages of Frobisher, Davis and Hudson-those great English heroes-through the ice-ridden Arctic seas and labyrinths of islands represented at the top of Mr. Molitor's globes.

'Or the sea route to the northeast through Archangel and Novaya Zemlya. Yes. Or the southwest passage to the South Seas through the Strait of Magellan or round Cape Horn.'

He was turning the sheets of the atlas and jabbing with a forefinger at the passages. When he raised his head and squinted at me I could smell his decaying teeth along with the fustiness of his threadbare garb. And for a second I thought I saw, reflected in one of his spectacle lenses, a shape in the bow-window behind me: a lone figure leaning forward as if to peer through the glass. But then Mr. Barnacle lowered his head and the reflection was lost.

'You see, all of these new sea routes, if they exist, will be found in the high latitudes, near the poles, places where Mercator's projection is next to useless. For this reason mariners have never discovered them. It's also the reason why the Spaniards and the Dutch have been at work on new and better methods of map projection. In 1616 the Dutch discovered a new route into the Pacific between the Strait of Magellan and Cape Horn, the so-called Le Maire Strait'-he was licking his finger and fumbling to unfurl another sheet-'which lies along the fifty-fifth parallel. Their fleets used the new passage to sail into the Pacific and attack the Spaniards at Guayaquil and Acapulco. So such routes were of obvious strategic importance,' he said, 'but a clue was needed to find them, something that would guide navigators through the labyrinths of islands and inlets.'

Such, then, was the legend that had been favoured by Mr. Molitor: mathematicians and cartographers in Seville, in the service of Philip II, had, round about the year 1600, perfected a new method of map projection, one that preserved Mercator's grid while doing away with its distortions, so that navigation became easier in the higher latitudes. New and shorter routes to Cathay and India might thereby be discovered, along with the famous lost continent, Terra australis incognita, which was thought to lie somewhere in the South Seas, in the high latitudes south of the equator.

'And Ortelius?' I was studying the upside-down atlas, hoping to guide him back to the matter at hand. 'He would have known about this new projection?'

Mr. Barnacle nodded vigorously. 'Of course he would have known about it. He was the Royal Cosmographer, after all. He may even have helped devise it. But when Philip died in 1598, Ortelius left Spain for Bohemia. Possibly he hoped to pass the secrets of the new method, for a price, to the Emperor Rudolf, or even to someone else. Prague was filled with fanatical Protestants in those days, enemies of Spain and the Habsburgs. And so perhaps he was murdered by Spanish agents as his reward.' He shrugged and clapped the volume shut. 'The rumour is compelling but impossible to verify as the plates have since disappeared. Some say they were stolen, but that cannot be verified either.' He smiled, thinly and helplessly, then shrugged again. 'Nor do any of the books themselves survive. The few copies ever printed are all thought to have been either lost or destroyed when Prague was pillaged during the Thirty Years War.'

No, I thought, shuffling through his doorway a few minutes later and back into the heat, thinking of the water-damaged volume in the queer little laboratory: not quite all of the copies had vanished. But as I wandered aimlessly back towards Charing Cross I wondered if I had not wasted my time after all. For what connections could exist between Ortelius's Theatrum and the Hermetic text I had been hired to locate? Between a new map of the world and a manuscript of ancient wisdom? But then I recalled what Mr. Barnacle had said about the age of discovery and wondered if I had stumbled upon a connection, however remote, with Sir Ambrose's expedition to Guiana, if in fact the voyage ever took place.

I thrust the thought from my head. I decided that my imagination, like my feet, had taken me too far afield. It was time to return home.

It must have been after six o'clock when I hailed a hackney coach outside the Postman's Horn (in whose tiny garden I had consoled myself with another pint of ale under a mulberry tree) and began making my way back towards London Bridge through the knots and streams of evening traffic. I fell asleep after a few minutes but was roused, somewhere along Fleet Street, by the sound of shouting. The traffic must have been even thicker now, because for minutes on end the hack barely moved. I dozed again but found myself awakened once more, this time by the abrupt, two-toned bleat of a horn. I sat upright and drew back the curtain, expecting to see the Fleet Bridge with Ludgate beyond it. Only we were no longer in Fleet Street.

I thrust my head outside the window and peered up and down the street. We must have taken a wrong turn. I didn't recognise any of the taverns and alehouses overhanging the street, or even the street itself, a narrow, deserted channel darkened by billows of black smoke.

'Driver!' I rapped on the roof of the coach. Had the idiot lost his bearings?

'Sir?'

'Where the devil are you taking us, man?'

He had swivelled round in his seat, a big bear of a fellow with a thick neck and sun-peeled nose. He was grinning uneasily through a set of wooden dentures.

'An accident in Fleet Street. Cart-horse dropped down dead, sir. So I thought that if you pleased-'

I interrupted him. 'Where are we?'

'Whitefriars, sir,' he replied, teeth clicking. 'Alsatia. I thought I'd come back up to the Fleet Bridge from Water Lane, sir, and then-'

'Alsatia-?'

The narrow passage had now assumed a more sinister aspect. I knew of Alsatia's unsavoury reputation. It was a dangerous hinterland beside the noxious sludge of the Fleet River: a dozen-odd streets and God only knew how many back courts and alleyways, all claiming exemption from the jurisdiction of the City's magistrates and justices by right of a charter granted earlier in the century by King James. The result of these privileges was that the quarter now gave sanctuary to criminals and villains of every description. Bailiffs and catchpoles entered at their peril, as did anyone else foolish enough to wander south of Fleet Street. The horn that awakened me must have been, I supposed, a signal from one of their look-outs, a warning to the others that strangers had arrived in their midst. Although the quarter now seemed innocent enough in its faint gilding of antique-gold sunlight, I was taking no chances.