It seemed that the relaxing airs of the Cup could loosen even Mummius's staid and stodgy discipline. I put my arm around Eco's shoulders and followed our host, shaking my head in wonder.

What Mummius had casually referred to as the baths was in fact an impressive installation within the house that seemed to have been built over a natural terrace on the side of the hill, facing the bay. A great coffered dome lacquered with gold paint arched over the space, pierced by a round hole at the summit that admitted a beam of pure white light. Beneath this was a round pool with concentric steps leading into its depths, its surface obscured by roiling masses of sulphurous steam. An archway on the eastern side opened onto a terrace furnished with tables and chairs, with a view of the bay. A series of doors around the pool defined a semicircular arcade; the doors were of wood painted dark red, the handles were of gold in the shape of fish with their heads and tails attached to the wood. The first door led into a heated changing room; the other rooms, so Mummius explained as we shed our tunics, contained pools of various sizes and shapes, filled with water of various temperatures.

'Built by the famous Sergius Orata himself,' Mummius boasted. 'You've heard of him?'

'No.'

'The most famous Puteolian of all, the man who made Baiae what it is today. He started the oyster farms on Lake Lucrinus – that earned him his first fortune. Then he turned out to be a master engineer at building pools and fish ponds, and villa owners all around the Cup showered him with commissions. This house contained a modest bath when Crassus acquired the estate. With Crassus's permission, not to mention Crassus's money, Lucius Licinius added an upper storey here, a new wing there, and had the baths completely rebuilt, employing Sergius Orata himself to draw up and execute the plans. I'd prefer a little grotto in the woods or a common city pool myself – this kind of luxury is rather absurd, isn't it? Impressive but excessive, as the philosophers say.'

Mummius stepped up to a brass hook cast as the heads of Cerberus and mounted in the wall. He hooked his shoes over two of the heads and hung his belt in the open jaws of the third. He pulled the heavy chain mail over his head and set about unbuckling leather straps. 'But you have to admire such feats of plumbing. There's a natural hot spring that comes out of the earth at just this spot; that's why the first owner chose to build here – that, and the view. When Orata rebuilt, he designed the pipes so that some of the pools are piping hot, while others are mixed with cool water from a different spring up the hill. You can pass from the coolest to the hottest and back again. In winter some of the rooms in the house are even heated by water from the hot spring, piped under the floors. This changing room, for example, is kept warm all year long.'

'Most impressive,' I agreed, pulling my undertunic over my head. I started to place it in one of the coffers in the wall but Mummius intervened. He called to an old, stooped slave who stood at a discreet distance across the room. 'Here, take these and have them washed,' he said, indicating my things and Eco's and pulling his own tunic over his shoulders. 'Bring back something suitable for an audience with your mistress.' The slave gathered up the garments and studied us for a moment, estimating our sizes, then slunk from the room.

Naked, Marcus Mummius looked something like a bear, with big shoulders, a broad middle and dense swirls of black hair all over his body, except where he was marked by scars. Eco seemed particularly intrigued by a long slash that ran across his left pectoral like a cleared furrow in a forest.

'Battle of the Colline Gate,' Mummius said proudly, looking down and pointing to the scar. 'Crassus's proudest moment, and mine. That was the day we retook Rome for Sulla; the dictator never forgot what we did for him. I was wounded early in the day, but fortunately it was on the left side, which allowed me to go on using my sword arm.' He mimed the action, bolting forward and swinging his right arm, causing the rather stout sword between his legs to swing heavily back and forth as well. 'In the pitch of battle I hardly noticed the wound, just a dull burning. It wasn't until late that night when I went to deliver a message to Crassus that I passed clear out. They say I was as white as marble and didn't wake up for two days. Oh, but that was over ten years ago, I was just a boy, really – couldn't have been that much older than you,' he said, punching Eco on the shoulder.

Eco smiled back at him crookedly and curiously examined Mummius for more scars, of which there was no shortage. Tiny nicks and plugs were scattered all over his limbs and torso like badges, easily discernible where they interrupted the general hairiness of his flesh.

He gathered a towel about his waist and gestured for us to do likewise, then led us from the changing room back into the great domed vault with the circular pool. The day was beginning to cool and the steam rose in great clouds from the water, hissing and smelling strongly of sulphur.

'Apollonius!' Mummius smiled broadly and strode to the far side of the pool, where a young slave in a green tunic stood at the water's edge, obscured by the mist.

As we drew closer, I was impressed by the slave's extraordinary beauty. His hair was thick and almost blue-black, the colour of the sky on a moonless night. His eyes were a vibrant blue. His forehead, nose, cheeks, and chin were perfectly smooth and followed the serene proportions from which the Greeks defined perfection. His full, bow-shaped Lips seemed to hover on the edge of a smile. He was not tall, but beneath the loose folds of his tunic he clearly had an athlete's physique.

'Apollonius!' Mummius said again. He looked back at me over his shoulder. 'I shall begin with the hottest pool,' he announced, pointing at a door across the way, 'followed by a vigorous massage from Apollonius. And you?'

'I think I'll test these waters first,' I said, dipping my foot into the main pool and quickly drawing it back. 'Or perhaps one a little less scalding.'

'Try that one, it's the coolest,' said Mummius, indicating a chamber next to the changing room. He strode away with his hand on the slave's shoulder, humming a boisterous marching tune.

We sweated and scraped ourselves clean with ivory strigils; we immersed ourselves in one pool and then in another, going from cool to hot and back again, and when we were done with our ablutions Marcus Mummius rejoined us in the heated dressing room, where fresh undergarments and tunics had been laid out for us. Mine was of dark blue wool with a simple black border, befitting a guest in a household in mourning. The old slave had a sharp eye; it was a perfect fit, not even tight across my shoulders, as I often find borrowed garments to be. Mummius dressed in the plain but well-tailored black tunic he had worn on the night he summoned me.

Eco was less pleased with his costume. The slave, apparently thinking him younger than he was, or else too good-looking to be seen bare-limbed about the house, had brought him a long-sleeved blue tunic that reached to his knees. It was so modest that it would have been more suitable for a boy or girl of thirteen. I told Eco he should be flattered if the old slave found him so dazzling that he should hide himself. Mummius laughed; Eco blushed and would have none of it. He refused to dress until the slave brought him a tunic that matched mine. It was not quite as good a fit, but Eco made do by tightening the black woollen belt about his waist and seemed happy to be dressed in a more manly garment that showed his arms and legs.

Mummius guided us down long hallways where slaves bowed their heads and stepped meekly out of the way, down one flight of stairs arid up another, through rooms decorated with exquisite statues and sumptuous wall paintings, across gardens breathing the last sweet breath of summer. At last we came to a semicircular room at the northern end of the house, set above a crag of rock overlooking the bay. A slave girl announced us and then departed.