The Sand-Reckoner

13

Marcus was literally put in his brother's place, in the middle of the three sheds at the quarry, with Fabius' leg irons clamped about his own ankles. The other prisoners were astonished when he arrived, and suspicious of his account of himself. He did not much care, and spent most of his first day in prison asleep. The guards woke him around noon, when they chained each prisoner to the next as part of the newly increased security. The sawn-through planks of the shed wall had been replaced even before he arrived, and another two guards now took their place in each shed, at the far end, where they could keep an eye on everything the two on the door might miss. Marcus did not much care about that, either. He did not much care about anything. He supposed he ought to feel glad and excited- it seemed that he might, after all, be a free man again and still live- but he was too exhausted. The sheer effort it would take to adjust to his own people again, even if they didn't kill him, appalled him. He ate the meal the guards brought him and went back to sleep.

He woke with a sensation of being watched and sat up abruptly. Archimedes was squatting at the end of his mattress, hands hanging over knees and an anxious expression on his face. On all sides the other prisoners were watching the visitor with impassive suspicion, and a guard was hovering nervously a few paces away. In the dimly lit shed it was hard to tell, but Marcus thought that it was evening.

"I'm sorry to wake you," said Archimedes.

"I've been asleep all day," replied Marcus, embarrassed. He did not know what to say; the other seemed almost a stranger to him. Yet he knew Archimedes as intimately as he knew Gaius: he had watched him grow from childhood to manhood, and they had shared lodgings and short money in a foreign land. But though he had only rarely thought of Archimedes as his master, his own slavery had always defined the relationship between them, and now by Hieron's judgment he had never properly been a slave at all. With that tie cut, he could only flounder in a sea of shapeless emotions.

"I, uh, brought you some things," Archimedes said, as embarrassed as Marcus. He set a bundle down on the end of Marcus' mattress.

Marcus saw at once that the bundle's wrapping was his own winter cloak. He drew it over and unknotted the corners. Inside was his other, winter tunic, a terra-cotta statue of Aphrodite he'd bought in Egypt with money from the water-snails, and some other small knickknacks he'd picked up over the years. There was also a small leather bag that chinked and a long oblong case of polished pine. He stared at the case, then picked it up and opened it: it held Archimedes' tenor aulos. The hard sycamore wood was darkened about the stops, polished with use. He looked up in shock.

"I, uh, thought maybe you could teach yourself to play it while you're here," said Archimedes. "It would be something to do while you're waiting to be exchanged."

Marcus picked up the flute; the wood was water-smooth in his hands, and warm. "I couldn't, sir," he said. "It's yours."

"I can buy another. I can afford one, after all. And you have a good sense of pitch; it's a shame to waste it. I don't know why you never learned an instrument before."

"It's not a Roman thing to do," Marcus told him helplessly. "My father would have beaten me if I'd asked it."

Archimedes blinked. "Because of all the jokes about flute boys?"

"No," said Marcus, in a low voice. "No- he'd say it was unmanly to waste time studying music. He'd say that music is a luxury, and luxury corrupts the soul. He tolerated it at work, or as an amusement, but he always said that the only studies worthy of a man are farming and war."

Archimedes blinked again, trying to accommodate his mind to this bizarre idea. Greeks too believed that luxury corrupted, but Greeks didn't consider music a luxury. It was an essential: without it men were not fully human. "Do you not want it, then?" he asked, giving up.

Marcus ran one calloused thumb along the flute, then whispered, "I do want it, sir"- and his heart suddenly rose. Going back to his own people need not mean giving up everything he'd learned. Why shouldn't he play the flute? He had never agreed with his father anyway! "Thank you."

Archimedes smiled. "Good. I've put three reeds in the case. They should last you a little while. If you're here for a long time, I'll bring more- or you can get your guards to buy some. And when you're able to manage this one, you'll want a second flute. You can decide for yourself what voice it should be. There's some money." He gestured vaguely at the leather bag.

"Thank you," said Marcus again. "Sir, I'm sorry."

Archimedes shook his head quickly. "You couldn't abandon your own brother."

Marcus met his eyes. "Perhaps not. But I did abuse your trust and put you in danger. I think Fabius would have killed you if he'd realized who you were when you came in. I should never have brought him to the house, and never have given him the knife. So- I'm sorry."

Archimedes looked down, his face going red. "Marcus, my trust deserved to be abused. Do you remember when we came back to Alexandria after making the water-snails? How I told you to take all the money back to our lodgings? My friends said later that I was an idiot to trust you with so much, but it had never even occurred to me that you might steal it."

Marcus snorted. "It occurred to me!"

"Did it? Well, why not? After all, it would have been freedom and independence. But you didn't. You took it home, and then nagged me for days to make me put it in a bank. And what I meant to say was, I had no right to trust you that far. It was arrogant. I had never done anything to earn that sort of loyalty. As a master I was negligent and careless. Yet I relied on you absolutely, and never considered that you deserved any credit for not failing me. So- I'm sorry, too."

Marcus felt his own face go hot. "Sir…" he began.

"You don't need to call me that."

"I was in your debt for a great many things even before this morning. Music is one of them; mechanics is another. Yes, that is a debt. I don't think I've ever enjoyed any work as much as I enjoyed making the water-snails. Since this morning I owe you even more. If I'd been anybody else's slave, I would have been flogged and sent to the quarries. The king treated me leniently because you pleaded for me- you know that as well as I do. I have no way to repay what I owe. So don't burden me with your apologies as well."

Archimedes shook his head, but did not respond. After a moment he changed the subject and asked, "Do you want me to show you how to play that flute?"

There followed a short lesson on how to play the aulos: fingering, breathing, the positions of the slide. Marcus played a few wobbly scales, then sat stroking the silken wood. Its touch was a promise for the future, and gave him unexpected hope.

Archimedes cleared his throat uncomfortably. "Well," he said. "They're expecting me at home. If you need anything, send me word." Marcus opened his mouth, and Archimedes said urgently, "Don't! You've been a member of my household ever since I was a child. Of course I want to help you if I can."

Marcus realized suddenly why he had felt so numb. He was losing home and family for the second time in his life.

"Please tell them at the house," he whispered, "that I'm sorry. And tell Philyra I hope she will be very happy, with Dionysios or whoever she marries. I wish you all much joy."

Archimedes nodded and got to his feet. "I wish you joy, Marcus." He turned to go.

The sight of him turning away suddenly filled Marcus with an almost panic-stricken urgency. Something between them was unresolved, and the thought of being left with that undigested lump of emotions terrified him. He jumped to his feet with a clank of irons, and called "Medion!" — then bit his tongue, realizing that he had used the family nickname for the first time.

Archimedes didn't appear to notice the slip. He looked back at Marcus inquiringly, his expression just visible in the growing dark.

For a moment Marcus did not know what to say. Then he held out the flute. "Could you play me that tune you played last night?" he asked.

Slowly, Archimedes reached out and took the instrument. He adjusted the slide. "I really need the soprano as well," he said apologetically. "It won't be the same without it." But he set the flute to his lips and at once began the same sweet dancing tune which had filled the courtyard the night before.

Everything in the shed seemed to hold its breath. One of the guards, who had gone to fetch a lamp, came back with it and stood silent in the aisle listening. All around the eyes of prisoners gleamed in its light, drawn into the dance, and then bewildered by the inexplicable grief that crept into the tune. The melody was clearer on a single aulos, the shifts of tempo and mode more precise. There was the same sense of disintegration, and the same almost miraculous resolution. At last the same sad march faded softly into silence. Archimedes stood for a moment with his head bowed, looking at his fingers on the stops.

"And now I wish you joy," said Marcus, quietly into the quiet.

Archimedes looked up, and their eyes met. The unresolved thing between them solved itself, and the ties severed. Archimedes smiled sadly and handed the flute back to Marcus. "May you indeed find joy, Marcus Valerius," he said, stumbling a little on the alien family name.

"And you, Archimedes son of Phidias," said Marcus. "May the gods favor you."

Archimedes walked home from the quarry through the dark streets slowly. He did not want to think about Marcus, so he thought about the tune he had played. A farewell to Alexandria, he'd called it. He did not like the way his mind seemed to be making up itself about Alexandria, without consulting him. Even before Delia. If Delia…

He lost himself for a moment in the memory of kissing Delia, then went on, more grimly. What he needed to know was whether Hieron saw him as an ally or as a valuable slave.

The test was Delia. Hieron might refuse his permission for the match for many good reasons, but if the request was viewed as an affront, he'd do better going to Egypt if he had to slip out of Syracuse in disguise.

In the house there were lamps burning in the courtyard, and the family was waiting: Arata and Sosibia spinning, little Agatha winding wool, Philyra playing the lute, Chrestos sitting in the doorway doing nothing in particular. Archimedes had not been home all day, though he had sent one of Hieron's slaves to the house to tell the family what had happened, and to tell Chrestos to pack up all of Marcus' things and bring them to him at the catapult workshop. He had not wanted to talk to his family: not about Marcus, and not about Delia- yet. Now they were all waiting to talk to him.

Arata, with her usual patience and clear sense of priorities, first asked him if he'd eaten, and when he admitted that he had not, took him into the dining room and sat him down with a plate of fish stew. But Philyra, red-eyed and sniffing, sat with her elbows on the table as she watched him eat, the slaves hovered anxiously, and even his mother was frowning with anxiety. He gave up and started telling them about Marcus after the first few mouthfuls.

"Will he be all right?" asked Philyra, biting at her fingernailsa habit which her mother had striven to break, and which only reemerged when she was deeply unhappy.

"I hope so," was all Archimedes could say. "Hieron said he's welcome to answer anything the Roman general asks him. And his brother is there to speak up for him. I would think he'd be all right." But he was not altogether certain of it. Marcus ought to be all right- but he was so uncompromisingly honest. He had not prayed for the destruction of Rome for a Tarentine mercenary; he would not pray for the sacking of Syracuse for a Roman consul.

But perhaps the Roman consul would not ask it. Marcus would be returned in company with eighty other prisoners, and his brother would, presumably, be in the army to welcome and protect him. He ought to be all right.

"They're barbarians," said Philyra, blinking at new tears. "They might do anything to him! Can't he just come back to us? It wasn't his fault- you did tell the king that, didn't you, Medion? I mean, it was his own brother, or he wouldn't have…"

"The king has already been very lenient," said Arata quietly. "For your brother's sake, Philyrion. We can't ask more. After all, a man was killed because of what Marcus did."

Archimedes cleared his throat unhappily, then said, "When I saw Marcus just now he, uh, said to tell everyone that he was sorry and that he wished us all much joy. And he said he hoped you would be very happy, Philyrion, with Dionysios or whoever you marry."

Philyra pulled her torn nails out of her mouth and stared, and he realized that he hadn't told her about Dionysios.

"Dionysios only offered last night," he said defensively. "I was going to tell you this morning."

He told her about Dionysios then. There was considerable discussion of the man and his offer, and eventually it was agreed that Archimedes would invite the captain to dinner so that the rest of the family could have a look at him. But when the others went to bed, Philyra sat for a while alone in the courtyard under the stars, playing upon the lute, and it was not Dionysios who filled her thoughts.

"I don't want you to think ill of me," Marcus had told her, only the night before. "Whatever happens, please believe that I've never wanted any harm to this house."

She did believe it; she did not think ill of him. That morning his quiet admission had redefined courage for her. She realized that she no longer thought of him as a slave, and that when she thought of him as a free man, it was as a man she loved. A brave man, honorable and proud, who had- she could see it now- loved her.

"Remember once," she sang, carefully picking the strings of the lute,

"Remember when,

I told you this holy word?

'The hour is fair, but fleet is the hour,

The hour outraces the swiftest bird.'

Look! It's scattered to earth, your flower."

She suspected that for the rest of her life, when she remembered him it would be as something that went tragically wrong- an appointment missed, a letter mislaid, a person misunderstood with devastating and irremediable consequences. Already it was too late to retrieve what had gone by; the flower's spent petals were scattered to earth. She played on for a while, then put the lute away and went to bed.

That night a Roman force attacked the Syracusan seawall under cover of darkness. The extra guards Hieron had posted saw the stealthy movements against the gleam of the sea, however, and sounded the alarm. The Romans were inside catapult arc of fire when they were discovered, but so close to the cliff that it was easy to drop catapult shot directly onto them from the walls. A few hundred weight of stones were followed by some catapult fire canisters, which exploded and splattered the attackers with burning pitch and oil, so that the scene was lit by the burning clothes and bodies of the men who occupied it. Many of the Romans jumped into the sea to escape the fire, and were swept off their feet by the strong currents and drowned. The remainder fled. In the morning it could be seen that they had brought ropes and ladders, which had been woefully short for the height of the cliffs, and which now littered the rubble at the cliff foot, together with the bodies of the dead- and a few more wounded prisoners for the quarry.

The following night, the Romans left. The Syracusans keeping watch from the north wall saw the camp settling itself for the night in the evening, and the campfires glowed throughout the hours of darkness, but in the morning the army was gone, and only the fires remained, with the neat rows of flattened grass where the tents had been pitched.

Hieron sent out scouts to track them. He sent out a letter to the Carthaginian commander as well, writing it in his own hand, because it was still too early in the day for his secretary to have arrived at the house. He warned General Hanno that the Romans might now be heading in his direction, and offered to attack them in the rear if the Carthaginians could engage them. He had sent a similar message when the Romans first appeared outside Syracuse, inviting the Carthaginians to a similar feat, but there had been no response.

As he sealed the letter he wondered how long it would take for the Carthaginians to realize that, faced with an enemy like Rome, they needed Syracuse whole and strong and on their side. Stupidity, he thought, pressing his favorite signet into the wax that fixed the red cord binding of the letter. The Roman campaign, too, was one of blatant stupidity- if the Carthaginians had appeared in their rear, they would have been in a very sorry state. And they had left Messana only lightly guarded, with most of their supplies and all the ships that had carried them from Italy: if the Carthaginians stormed that in their absence, the whole army would be forced to surrender. It was a stroke Hieron was much tempted to himself: load his army onto his own ships, take them up the coast, sail into the Messanan harbor with some big catapults mounted on naval vessels and some incendiaries, fire the Roman ships, and storm the city!

Yes, but to do it would weaken Syracuse while the Romans were too close to her for comfort, and who knew how the Carthaginians would react? They still wanted Messana themselves. The last thing Hieron could afford to do was drive them into open alliance with Rome.

They might well have some kind of understanding with Rome already. Perhaps the reason they were doing nothing at present was that they'd promised not to interfere in any Roman campaign against Syracuse. Still, even if such a promise had been made, Appius Claudius was an awful fool if he trusted it. Just as Hanno was a fool to let what might be his only opportunity for victory slip by. Hieron's envoy had returned from Carthage with the news that the Carthaginian senate was growing impatient with their general. It was very stupid of Hanno to think that he had time to do nothing. Stupidity; it was altogether a stupid, blind, and pointless war, and Hieron felt a sick certainty that it was far from over. He tossed the sealed letter onto his desk and clapped his hands to summon a messenger.

When the messenger came in, Agathon was with him, holding a bundle of the day's other letters. The messenger took the king's letter, vowed to deliver it to General Hanno within three days, saluted, and marched out. Agathon watched him go, then set the other letters down on Hieron's desk. Hieron picked them up and glanced through them; the doorkeeper busied himself in trimming and lighting one of the lamps on the stand beside the desk, even though it was morning. Hieron paused and looked up at his slave inquiringly.

Agathon gave his sour smile. "You said you wanted to see any letters to Archimedes that came from Alexandria," he remarked. "One came yesterday. I had the customs official divert it." He pulled a small, thin-bladed knife out of his belt and began warming the end in the lamp flame.

Hieron looked down to the bottom of the sheaf, found the relevant letter, and handed it to him. He and Agathon had been in the habit of intercepting other people's letters long before he became king, and if he'd ever had any tremors of conscience over it, they had long since faded.

Agathon carefully slid the hot knife between the parchment and the wax of the seal, then handed the letter to the king with a bow. Hieron sat back and read it. Reading aloud was the usual custom of the age, but Hieron, to his slave's disappointment, read almost silently, barely moving his lips.

Conon son of Nikias of Samos to Archimedes son of Phidias of Syracuse sends greetings.

Dearest [Alpha]…

Hieron frowned slightly: "Dearest Alpha." Had the writer chosen that form of address because it was the first letter of Archimedes' name- or because it was the number one?

Dearest Alpha, you've been gone less than a month, and I swear by Delian Apollo it seems years, and empty years, too, with nothing but wet afternoons in them. I never hear a flute but I think of you, and there's not one person who's had anything remotely intelligent to say about tangents of conic sections ever since you went away. Diodotos was blathering on about hyperbolae the other day, and I told him what you'd said about the ratio, and he swelled up like a frog and asked me to prove it. And of course, I couldn't, though I gave him a list of propositions instead. He came back later saying he'd proved one, but he hadn't. I'll tell you more about that later.

The main thing I want to say is, I have a job at the Museum, and you can have one too! In fact, it's thanks to you that I now have my perch in the Muses' bird cage. The king has been investing in the most enormous engineering works at Arsinoitis, and when he went up to have a look at them, apparently the first thing he saw was a water-snail. "What is it?" asked the king. "By Zeus, I never saw anything like it in my life!" And shortly afterward, Kallimachos…

The poet? wondered Hieron. The head of the Library of Alexandria?

… Kallimachos himself came knocking at my door in a great sweat and said, "You're a friend of Archimedes of Syracuse- where is he? The king wants to meet him." So I told him you'd gone back to Syracuse, and he swore by Hades and the Lady of the Crossroads (and several other divinities I wasn't sure about; poets can't even swear like other people these days) and took me to meet the king instead. Ptolemy was amazingly civil to me, and gave me dinner, and we talked. Kallimachos was there, too, but he just sat and picked his fingernails and made eyes at the slave boys. The man's incapable of talking about anything but literature and boys. The king, though, knows quite a lot of mathematics- you know Euclid was his tutor. He said it was quite true about Euclid saying there was no royal road to geometry, he was there at the time. And he was very interested when I told him about eclipses, and asked me when the next one would be. That's nothing to do with what I'm writing you about, though. After we'd talked for a bit, and I'd told him some more about you (you can believe I sang your praises, Alpha!), he said he wished he'd known it sooner, and he asked me to write to you and invite you to come back and take a job at the Museum, with a big salary and everything. Then he offered me a job too (Diodotos is perfectly green about that) but it's you he really wants. I think it's really engineering he's after- he kept telling me how wonderful the water-snail is, and when I showed him my dioptra he wanted to buy it, and laughed and said he didn't blame me when I said I'd sooner sell my house and the cloak off my back. I warned him, though, that you weren't interested in doing any more water-snails, and he said that was fine. I know you like making machines if it isn't the same thing all the time and it doesn't interfere with geometry. Write to him, or to me if you prefer, and he'll send you the letters of authorization at once. Please, Alpha, come back quick! Why be poor in Syracuse when you can be rich in Alexandria? You could bring your family here if you're worried about them. It's much safer, anyway, with none of your garlic-eating barbarian armies about. As for me, I am pining away in your absence, or I would be if I didn't keep eating Dora's cakes to console myself. The Museum banquets are on a Homeric scale, too.

The proposition Diodotos says he proved is this…

There followed several pages of abstruse geometrical reasoning, which Hieron skipped. He read the warm farewell at the close, and the still warmer hope that the writer would see the recipient "soon, by Hera and all the immortals!" Then he refolded the letter and set it down with a sigh.

"Well?" asked Agathon.

"King Ptolemy is offering him the Museum," said the king resignedly.

Agathon picked the letter up and squinted at it. "It's not the royal seal," he observed.

"No," agreed Hieron. "The offer comes through a friend- a close friend, from the sound of it. But I don't think there's any doubt that it's genuine. Ptolemy was evidently much impressed by an irrigation device. I'll have to ask Archimedes how it works." He waved a hand at the letter. "You'd better seal that up again and return it."

"You don't want it to go missing?"

Hieron shook his head glumly. "He'd realize. I just want to see the reply." He turned back to his other letters. They were mostly business notes from within the city, but one caught his eye. He held up a hand to check Agathon just before the door-keeper left. "Note from Archimedes himself," he said; then, glancing through it, "He says the three-talenter will be ready in another three days, and he invites me to stop at his house on my way back to the city after the test-firing, either for dinner or simply for wine and cakes."

"He wants something," said Agathon flatly.

"Good!" replied Hieron. "He can have it." He tapped the invitation against his desk. "That other letter- delay it, until I've seen what he wants. Tell whoever was taking it to say it was mislaid or forgotten about until he came to clear the ship."

Agathon looked at his master dubiously. "Don't you think you're spending more on this man than he deserves?"

Hieron gave him an exasperated look. "Aristion," he said, "think a minute. I was toying earlier with the idea of a naval assault on Messana. If I wanted to do that, I would need to lash ships together and build artillery platforms- each stable for the weight of catapult or they'd come to bits when the shooting started. And I would need counters to the Messanan harbor defenses, which means I'd need somebody to reckon their distance and strength before we reached them. Then I'd need siege ladders- and they'd have to be the right height or we'd have a lot of men dead for nothing. I'd need battering rams that were strong enough to do the job and light enough to move in quickly. In other words, the whole success or failure of such a raid would depend upon my engineer. Now, Kallippos is good, but I wouldn't gamble my whole fleet on his getting it right. With Archimedes, it would be no gamble. Top-quality engineering can make the difference between victory and defeat. No, I do not think I am spending too much on it."

"Oh," said Agathon, abashed.

"You and Philistis," Hieron went on, smiling, "don't like Archimedes because you think he's been disrespectful to me."

"And he has been!" said Agathon warmly. "The other morning-"

"Aristion! If somebody came and arrested you, I'd be disrespectful!"

Agathon, who had not thought of it this way, grunted sourly.

"He has, in fact, treated me exactly as I would wish. And he told me I was a parabola. I think that's the most unusual compliment I've ever been given. I might have it engraved upon my tomb."

"If you say so," replied Agathon, who had no idea what a parabola was and remained unconvinced. After a moment he asked, in a low voice, "And the naval assault?"

Hieron shook his head, turning back to his letters. "Can't do it without knowing where the Romans are and what the Carthaginians would do if it worked. But it's still true about top-quality engineering. If it hadn't been for our catapults, the Romans would still be camped by the north wall and living off our farmers' lands."

The three-talenter wish you joy was installed in the Hexapylon precisely on time. Archimedes was not pleased with it. It was heavy to pivot, the loading mechanism was finicky, and the range was, he felt, short of what it could have been. Everyone else was delighted with the machine, however- the biggest catapult in the world! — and at the test-firing that afternoon a great cheer arose when the first massive stone crashed into the field where Romans had died only the week before. The king's son, Gelon, had asked to go with his father to see the spectacle, and his shrill cheer rose above all the others.

All the way back to the city the little boy talked excitedly to Archimedes, leaning down from the saddle of his father's horse to offer his own ideas for improving the defenses of Syracuse. Archimedes, who was sidling toward the moment when he must ask the king for his sister's hand in marriage like a dog toward a scorpion, found the child's chatter both an irritation and a relief. At least it was easier than talking to Hieron. Even if he hadn't been oppressed by the awful imminence of his outrageous request, Archimedes would have found Hieron's company wearing, for the king kept trying to persuade him to borrow a horse. Archimedes regarded horses as large, dangerous, bad-tempered animals that were very likely to throw you off and trample you, and he stayed on his own feet.

The house near the Lion Fountain had been prepared for the royal visit almost out of recognition. Arata and Philyra had been horrified to learn that Archimedes had invited the king to have cakes and wineit had been shocking enough to have such an eminent person turn up at the wake, but at least then there'd been no necessity of providing entertainment proper to the guest's station. Since Hieron could not be uninvited, however, they had set to work to uphold the family honor. The house had been swept, freshly daubed, and garlanded, and all the laundry boards and buckets removed from the courtyard, which looked quite empty and rather desolate. Sesame cakes purchased from the finest confectioner in Syracuse were oozing honey onto the best Tarentine pottery plates in the dining room, and wine from the best vintner trembled darkly in the antique red-figure mixing bowl. The slaves had been provided with new clothes, and when Hieron arrived, they stood scrubbed and uncomfortable by the door to meet him. The king, looking at them, saw that he was going to have to work at it if the visit was to be a success.

He detailed one of his attendants to take his horse down to the nearest public square and look after it, sent the rest back to the Ortygia, and came into the house accompanied merely by his son and by Dionysios, who had been invited to the afternoon gathering in lieu of a dinner party. Arata and Philyra, who were permitted to show their faces at an informal daytime occasion such as this, exchanged stilted greetings with the guests and offered them cakes and wine. There was a move to the dining room, and the slaves hurried anxiously about offering food and drink. Then Hieron said casually to Archimedes, "I've been hearing more from Alexandria about this water-snail of yours. Could you tell me how it works?"

"I have the prototype," Archimedes replied, delighted to escape the formalities. "Marcus put it somewhere. Mar-" He stopped in the middle of the summons and went crimson.

"I think it's in the storeroom," Philyra said quickly, though she too reddened.

The water-snail was fetched, and the laundry boards and buckets emerged with it to reclaim their rightful domain. Gelon, who'd been silently stuffing himself with sesame cakes, abandoned all thought of sweets and descended upon this new toy as soon as it was set up. He was invited to turn it, and after being corrected and advised to turn it slowly, he watched the water run out of the machine's head with unalloyed delight.

"By Apollo!" said Hieron softly. He crouched down beside his son and gazed at the machine. He had asked about the device to set Archimedes at ease, but now, at the sight of it, forgot that he'd ever needed any reason but his own delight in ingenious contrivances. "I think that's the cleverest thing I have ever seen in my life," he said, and looked up at the maker of it with his son's beaming childish pleasure.

Within minutes, all the remaining stiffness was gone. The king of Syracuse, his son, and soon the captain of the Ortygia garrison as well crouched in the courtyard and played with the water-snail. Gelon got wet- something he greatly enjoyed on a hot summer day. Dionysios also got wet, and had to be fetched rags to dry his armor quickly before it tarnished. Philyra giggled at the sight of the scarlet-cloaked captain polishing himself, and he looked up at her in embarrassment- then grinned at the look in her eyes. A plate of cakes was put down on the ground so that the guests could help themselves, and then, inevitably, stepped upon: Sosibia could be heard shortly afterward in the back of the house, scolding Chrestos, who was the culprit. "Oh, don't be hard on the boy!" Hieron called to her. "It's our own fault for sitting on the ground."

When the fascination of the water-snail began to thin, Philyra brought some of her brother's other machines out from the jumble in the storeroom: an astronomical instrument, a hoist, a set of gears that did nothing except turn each other. "That was supposed to be part of a lifting machine," Archimedes admitted shamefacedly, "but when you attach the weight to them, they jam."

"You built a machine that didn't work?" asked Dionysios, much amused. "I am shocked."

"He was only about fourteen!" protested Philyra. "I always loved them anyway." Fondly she rotated the top wheel. "See? They all turn at different speeds."

"Gelon loves them too," said Gelon's father dryly, observing the boy's expression of open-mouthed greed.

Archimedes cleared his throat. "Well," he said. "Umm- Gelon son of Hieron, would you like them?"

Gelon looked up at him with shining eyes, nodded, and grabbed the gears.

"Gelonion," said Hieron sharply. "What do you say?"

"Thank you!" said the boy, with all the requisite warmth.

Hieron smiled for a moment at his son's delight, then looked at Archimedes inquiringly. It was time, he felt, to hear Archimedes' own request.

Archimedes too felt that the ideal occasion had now presented itself. "Umm," he said, trying to quell the quaver in his gut. "Lord, may I speak with you a moment in private?"

They went back into the dining room. Through the window came the sound of Arata talking to little Gelon, and Dionysios asking Philyra about music. Hieron sat down comfortably on the couch; Archimedes perched on the edge of one of the chairs. Now that it had come to the point, all his new confidence was ebbing away. It had seemed better to ask his question in his own house, where he was master. But the house, even garlanded and at its best, remained the residence of a middle-class teacher, with walls of plaster and a floor of packed clay. When he compared it to the marble-floored mansion on the Ortygia, he was ashamed. He was not of a rank to ask for the sister of a king. But he cleared his throat and said, in a low voice so that the others in the courtyard would not overhear, "Lord, if my request is too bold, forgive me. You yourself encouraged me to ask above my expectation."

"I promised you anything you might get in Egypt, except the Museum," replied Hieron seriously. "If you have something to ask of me, I am delighted."

"What I want I could not get in Egypt," said Archimedes. He curled his big bony hands together and took a deep breath. "Lord King, you have a sister, who…"

Hieron looked at him in utter amazement, and all his prepared speeches went out of his head. "That is," he stumbled on, "she… I…" He again remembered kissing her, and felt his face heat. "I know I have neither wealth nor noble birth nor any other quality that makes me worthy of her. I have nothing to offer, apart from what my mind can conceive and my hands can shape. If that is enough, good. If it is not, well, I have asked you for what I wanted, and you have said no."

Hieron said nothing for a long time; he was stunned. He realized immediately that this request was something he should have foreseen, and he was shocked because he had not foreseen it. He was accustomed to thinking of Delia as a bright, adventurous child he had rescued from her grim uncle, a girl whose sharp observant mind he had delighted in for the kinship it showed with his own. He had been aware that she had reached marriageable age, but that knowledge had seemed a thing apart from Delia herself- something for the future, something beyond the war. He had been aware, too, that she was interested in Archimedes, but he had considered it a shallow interest, casual and soon forgotten. He contemplated his own failure to understand her, saddened and ashamed.

"You know," said the king at last, "that Delia is the heiress to all our father's estate."

Archimedes' face turned a deeper shade of red. "No," he croaked. "I didn't."

"In law, I am not her brother at all," said Hieron flatly. "In law, she is our father's child, and I am not. Our father was a rich man, and I have looked after his estate carefully on her behalf. The total income from it last year was forty-four thousand drachmae."

"It's not the estate that I want," said Archimedes, turning from red to white. "You can keep the estate."

"I could, if I broke the law and stole it from her," said Hieron coldly. "I have always assumed that I held it in trust for her future husband. I've never used the money from it, I've always reinvested it, to build it up for her." He paused. "You've already spoken to Delia about this, haven't you?"

"I…" whispered Archimedes. "That is- she would never go against your wishes."

"In other words, she's been lying awake at night wondering how I would reply. I thought she looked tired and miserable. Zeus!" He found himself a wine cup, ladled in a drink from the mixing bowl, and gulped down half of it. "And if I say no, I suppose you'll take yourself off to Alexandria?"

"I haven't made up my mind about that," Archimedes said slowly. "I will do all I can for the defense of the city in any case. But. Well." He paused, then said, with quiet fervor, "I am not a hired worker."

"Well, I'm not going to say yes if you plan to take her to Egypt!" said Hieron. "If you marry my sister, you're going to stay right here and make certain that you do provide me with what your mind can conceive and your hands can shape."

"You mean… you might say yes?" asked Archimedes breathlessly. Then, appalled, "You don't mean give up mathematics? I told you…"

"Yes, yes, you swore to your father on his deathbed and so forth! No, I didn't mean give up divine mathematics." He looked at the anxious young man opposite him, then set down his cup of wine. "Look," he said, "I'll tell you what sort of considerations are in my mind when I think about a husband for my sister. First, money doesn't come into it. I don't need her money. I've got plenty of my own, from various sources. And she has plenty of her own, and doesn't need to marry it. Second, politics." He flipped one hand dismissively. "It's true that there are situations where it's useful to cement some alliance with a marriage. If I hadn't married Philistis, I would probably have died in the year I became tyrant: it was Leptines who secured me the city. But on the whole, if an alliance won't hold without a wedding, it's unlikely to hold with one. And, to be honest, promising someone a half sister who isn't even related to me in law is never going to be the same as marrying somebody's daughter myself. So, politics matters, but it isn't of the first importance. What is of the first importance…" He stopped. Outside in the courtyard, Philyra was tuning her lute. "Dionysios has asked you for your own sister," said Hieron more quietly. "When you make up your mind about that, what will matter most to you?"

"I don't think I'm a very good judge," replied Archimedes, blinking. "I'm leaving that to Philyra and my mother. All I want is that Philyra should be happy- and that her husband should be a man I don't mind having as a kinsman."

Hieron smiled. "Precisely," he said softly. He picked up the cup again and rolled it between his palms. "You know that I am a bastard," he went on, looking down intently into the shallow bowl- the arch-manipulator fearfully exposing a fragment of his own heart. "I think that because of that I probably prize my kin more than those who can take them for granted. I like having a sister. I was always perfectly clear in my own mind that I wouldn't marry her to any foreigner, however important he was. I want to gain family by her, not lose it. And I want to see her happy." He took another sip of the wine, then looked back at Archimedes. "Now, it's perfectly true that you're not at all the sort of man I thought I would get as a brother-in-law. But- by all the gods! — do you really think I can raise objections about wealth and birth? You know I owe nothing to either! You would certainly be a more natural kinsman to me than someone who was merely born important. And on top of that, I like you. I want to go back and talk to Delia, and be sure that she knows her mind about this, but if she's happy about it, and if you promise to stay in Syracuse with her, then the answer is yes."

Archimedes looked at him for a long moment, disbelief slowly cracking into amazed delight, and then into an immense grin of pure joy.

Hieron grinned back. "You don't seem to have any doubt what she'll say," he observed, and was amused to see his prospective kinsman blush. "Humility is generally reckoned a becoming quality in a young man," he added teasingly.

Archimedes laughed. "And were you a very humble young man, O King of Syracuse?"

Hieron's grin became wicked. "When I was a young man, I was arrogant. I was quite certain that I knew how to run the city far, far better than the people who actually were running it." He paused, contemplating that time with satisfaction, then added softly, "And I was right, too."