obviously considering a protest, but, after a glance at Archimedes, yielded. Then Hieron nodded as well, satisfied. 'Take the prisoner to the quarry, and put him in his brother's place,' he commanded the two guards. 'Captain Dionysios, I disagree entirely with your assessment as to who was responsible for this incident, but, with hindsight, there were not enough guards on the quarry. We relied too heavily on the prisoners' wounds. Take another half-file, and improve matters. Agathon, ask Nikostratos to come here and write some letters: I need to double the watch on the seawall. Archimedes…' The king hesitated. 'Perhaps you'd care to stay to breakfast?'

Archimedes shook his head.

'Then, please, use my house as your own if you wish to rest a little and compose yourself before going home.'

The guards escorted Marcus out. He went quietly, though his expression was one of shame and bewilderment, not at all appropriate to a man who has just heard that he is to be freed from slavery and returned to his own people. Dionysios left with him, to rearrange the security for the quarry. The secretary Nikostratos came in to take Hieron's letters, and Archimedes went out into the garden. He was glad of a chance to rest and compose himself before venturing into the streets. He felt more shaken and confused by what had happened than he would have thought possible.

He was sitting beside the fountain, stirring the water with his fingers, when Delia came into the garden on her way to breakfast. She stopped short, her breath catching, and watched him a minute in silence.

Ever since Hieron had promised his exceptional engineer wealth and honor, something which she had dismissed as impossible had been insinuating itself to her as possible after all, and she had not known what to do. She was wretchedly aware that just because her brother wanted to keep Archimedes in Syracuse did not mean that he wanted to marry his own sister to a middle-class teacher's son. But a devious, untrustworthy part of her mind had begun to whisper to her that even though Hieron might not actually want her to make such a marriage, he would probably accept it if he had to- if, for example, she declared that she loved Archimedes, and Archimedes threatened to go off to Alexandria if Hieron refused his permission for the match.

Like the secret meetings, it was something she should never have contemplated. She owed her brother a political advantage from her wedding. He had given her a great many things, and that was all she had to give in return. And he deserved whatever advantages he could get. Hieron had taken a city shattered by the Pyrrhic Wars, a bankrupt city which had lost its fleet and its treasury, its citizens rebellious and its army mutinous, and he had made it strong and whole and prosperous again. That in itself was extraordinary enough, but to have done it without violence or injustice- that was an achievement unparalleled in the history of Syracuse. She knew what she ought to do; she'd known all along: tell Archimedes that they must not meet again, and resign herself to her fate. But when she thought of him, she had no resignation in her at all.

But the thought of going to Hieron, of admitting what she'd been doing and what she wanted to do, of facing his anger- or, worse, his bewildered pain- appalled her.

She also had no idea whether Archimedes wanted to marry her. She felt sometimes that he loved her, sometimes that he must despise her as shameless- it was shameless, the way she'd thrown herself at him! Did he really want to go to Alexandria? Did she want to be the chain that kept him in Syracuse? She was afraid to see him again, afraid that if she suggested this impossible scheme he would turn it down.

In the end she'd decided to talk to his sister, to see if she couldn't discover what he thought about her. That had been a disaster. Philyra didn't appear to have heard anything about her, good or bad, and, what was more, had disliked her. She wasn't sure why, though she supposed she'd mishandled the interview; she often did. And Queen Philistis disapproved of the invitation, though she'd had to concede that it was perfectly proper. She had stayed in the room the whole time Philyra was there, frowning whenever Archimedes was mentioned. Philistis disapproved of Archimedes generally- a conceited young man, she thought, who was being treated with altogether more honor than he deserved, and who had had no business disturbing her husband at the end of particularly exhausting day and making accusations of deceit. Hieron thought it important to cultivate the man, so Philistis was cooperating, but she did not like it.

And now here was Archimedes himself, rumpled and tired and staring sadly into the basin of the fountain, while around him the early-morning light cast fresh shadows through the leaves of the garden.

Delia stepped forward, and he looked up. He blinked at her vaguely, without surprise, his mind still fixed on whatever he had been contemplating in the water.

'Good health!' she said, struggling to keep her voice steady. 'What brings you here so early?'

At that he grimaced, scrunched up his shoulders, and got to his feet. 'Nothing pleasant,' he told her unhappily. 'My slave Marcus helped two Roman prisoners to escape. One of their guards was killed, a man I knew, a good man.'

'Oh, by the gods!' she exclaimed with concern; then added quickly, 'I'm sure my brother doesn't blame you for something your slave did.'

He shook his head, but remained hunched unhappily. 'He's being locked up in the prisoners' place- Marcus, I mean- though Hieron has implied he'll be exchanged or released with the other Romans. I- feel ashamed.'

'It's not your fault if a slave does something wicked!'

He shook his head. 'Not like that at all! I never really noticed Marcus before. He was always just there. But he's really quite an extraordinary man. He's actually a Roman citizen, and the reason he helped those men escape was that one of them is his brother. He could have escaped as well, but he didn't because he didn't want to betray Syracuse. And I realized that that's exactly like him. He had an obligation to his brother and an obligation to Syracuse, so he fulfilled both as well as he could, and then stood there expecting to die for it. He didn't even complain about it. He's always been absolutely honest and scrupulous. I should have noticed. But I don't notice people, even when they're under my eyes. All I notice is mathematics.' His voice had filled with disgust.

She did not know what answer to make to this. She went over to the fountain and sat down on its rim. 'I suppose mathematics is rational, and people aren't,' she said. He gave a rueful snort. 'You know the song of the Sirens?

' 'Halt your ship and stay to hear our song.

For sailor none in his black ship has gone from listening to our honey-voiced call but goes his way delighting, knowing more…

For we know as many things as come to pass upon the fertile Earth.' '

His voice lowered, and he continued:

' 'So they cried with lovely voice and clear and I wished with all my heart to hear and commanded my friends to set me free… instead they bound me with more chains.'

'Mathematics is a siren. It's probably just as well that most of the world has its ears stuffed with wax and can't hear her. I'm saying this now as though I'm ashamed of it, but I won't change. The moment she sings to me again, I'll ignore everyone and everything else.'

She was silent for a long moment, thinking about him, and about herself, and about her brother. Then she repeated slowly, 'Chains. Do you know, Hieron talked about chaining you to Syracuse. Do you hate it?'

He did not answer at once. He had thought that morning that Hieron was summoning him as though he were a slave, and he'd been surprised by his own sense of outrage and betrayal. He had not realized how much he had started to believe that he would stay in Syracuse and work with the king. With the king; that was the point. Not for him. He had been more or less resigned to being under another man's command when he'd thought it unavoidable, but that resignation had been crumbling as he came to appreciate his own power. The way Hieron had tried to manipulate him had impressed him. He hadn't liked it, but it had been interesting, as elegant in its way as a geometrical proof, and it had seemed to him a clear indication that the king genuinely preferred persuasion to decree. And he had begun to like Hieron himself- the subtlety, the quick perception and efficient action, the good humor. And then there was Delia. She was worth staying in Syracuse for, if he could get her, and he had begun to wonder if he might. After all, Hieron had promised him almost anything.

But was that only another trick? The position Hieron had been inventing for him had impressed him as something more than the kind of straightforward contract he could get in Egypt, but what if it was something less? What if it was only a counterfeit meant to cheat him? Would he be a friend of the king, an adviser, on an equal footing- or would he be a hired servant?

'I am deeply in your brother's debt,' he said at last, slowly, 'and I suspect that's where he wants me. But there's nothing he's given me yet that I can't repay- not even Marcus' life. What I can make is worth a great deal,

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