The Sand-Reckoner

9

Four days later, Delia watched Agathon set out sour-faced and hurrying on some errand of the king's. Then she walked up to the great double door of the mansion on the Ortygia, opened it, and stepped through.

It was as easy as that: open the door and step out into the street. Nothing there, she told herself, to cause this pounding of the blood in her ears, this sense of vertigo that slowed her footsteps as she started down the road. There was nothing dangerous in what she was doing- it was just that she had never done it before.

Never before walked through that door without someone in attendance upon her. Never before set off, telling no one, for an appointment of which the household would not approve.

It was a shocking thing. She should not do it; of course she should not. But ever since the demonstration, her pretense that her interest in Archimedes was no more than that of a patroness in a potentially useful servant of the state had been vanishing like water into sand. She was chagrined at how completely she had been deluding herself. And yet, she was sure that at first she had not been pretending. When she first met the man she had simply been intrigued by him- but that had changed. It was ridiculous! She had seen him three times, spoken to him twice, played music with him once- and she felt that if she allowed him to slip away she would regret it all her life.

She had written him a note: I must speak with you. Meet me at the fountain of Arethusa tomorrow at the tenth hour. I wish you well. She had addressed it to "Archimedes, son of Phidias, at the catapult workshop," sealed it with one of Hieron's seals- he kept several about the house- and set it in a pile of the king's letters which were about to be distributed through the city. It had been fearfully easy. It was still easy: the end of a working day, the streets of the Ortygia as full as they ever were, and herself easing her way down the street, inconspicuous among the others, swathed in a voluminous cloak of linen with a fold pulled modestly over her head to conceal her face. Of course, nobody had been trying to prevent her leaving the house: nobody had ever imagined that she would do such a wanton, shameless, and disloyal thing as to arrange an assignation with a young man.

When the possibility of what she was doing had first occurred to her, she had striven to force it from her mind. It would be wickedly self-indulgent and disloyal to return all her brother's kindness to her with nothing but callous ingratitude and shame. The king's own sister went whoring after an engineer, the gossip would say. She promised herself that she would do no such thing. She did not love Archimedes- she barely knew him. She could certainly live without him!

And yet, and yet… in a way, not knowing him was the worst of it. It was as though she had been walking all her life along the same narrow streets and then, unexpectedly, at the top of a hill, glimpsed a unfamiliar and breathtaking vista. Perhaps the new prospect was as narrow and confined as the old streets when you were inside it- but if she never explored it, she would never know. That was the thing that gnawed at her: not to know, to marry some nobleman or king and have children and grow old, never knowing what she had missed.

In the end she told herself that if she did know him better, she would probably discover that she didn't much like him. Then she could go home and settle to her lot in life, not perhaps content, but at least untroubled by wild suppositions of how much better things could have been. This small, this easy, disobedience, wasn't much to pay for peace of mind, was it? And she would not do anything with the man. He wouldn't dare take liberties with her. They would talk a bit, and then she would see how silly she was being, and go home.

She had never been so frightened in her life. But she walked on resolutely toward the fountain of Arethusa.

She had chosen the fountain for three reasons: it wasn't far from her brother's house; it wasn't far from the catapult workshop; and it was enclosed by a small garden which could provide some cover for a private conversation, while remaining public enough to give her a sense of security. She did not at all believe that as soon as she was alone in private with Archimedes he would leap on her like a maddened satyr, but she had been warned of the wickedness of men and the dangers of impropriety so often that she wanted to feel that someone would hear her if she shouted. So she walked into the garden with one eye on the passersby she might have to call on: two guardsmen sharing a drink under a date palm; a couple of girls sitting on the ground by a myrtle bush; a pair of lovers kissing under a rose trellis. The girls would all be whores: respectable girls didn't sit about in public like that- like her. She tugged a fold of her cloak farther over her head, to hide herself from curious eyes.

The fountain itself was a large oblong basin of dark water, shaded by pines. The sweet water welled up silently from its depths. Tall, feathery-topped papyrus reeds grew in the shallows, a gift from Ptolemy of Egypt; in all Europe, the papyrus grew only here. Above one side of the basin towered the city wall, and at the far end, white and lovely, a statue of the nymph Arethusa gazed upon her fountain. Flowers garlanded the base of the statue, and coins gleamed in the water's depths: offerings to the protectress of Syracuse.

There were people here, too, but she noticed only one of them: a tall young man who crouched by the fountain's edge, intently regarding a collection of sticks which floated upon the surface. He was dressed in black, and his hair was cut short in mourning. She guessed that his cloak was quite a good one, since it looked heavy, but it was patched with dust and he was at that moment treading the hem into the mud. The water cast wavering reflections upon his long-boned face. He felt her gaze on him and looked up sharply. His eyes, she thought, catching her breath, were the color of honey.

Archimedes smiled delightedly and stood up. His cloak was at once pulled off by the trodden edge and collapsed about his feet, half in the water and half in the mud. "Oh, Zeus!" he exclaimed, and stood there gazing at it helplessly. His black tunic was even dustier than the cloak had been.

He had guessed that she was the one who sent that note, even though it was unsigned. I wish you well: she had sent the same message through Marcus. All through that day, working in the catapult workshop on the hundred-pounder, he had contemplated this meeting with a thrill of excitement. He had brought the cloak along that morning out of a desire to look dignified; he had been astonished to find it so shabby and dusty-looking after a day spent on the workshop floor. Now it was utterly disreputable, he looked a fool, and the king's beautiful sister was watching him from under a white linen veil, her dark eyes astonished.

Then Delia laughed. He did not like being laughed at, but for a laugh like that he would have put on a mask and gone into comic mimes. He grinned ruefully, picked up the cloak, and wrung out the damp end. "Excuse me," he said. He thought of adding, "I didn't mean to undress in front of you," but this was both so highly inappropriate and so close to what he would like to do that it threw him into confusion and made his face hot.

"Good health to you," she said politely.

"Good health!" he replied. He tried to brush the crumpled cloak straight, then gave up and simply folded it up and put it over his shoulders: his gesture toward dignity had gone wrong, so there seemed no point in persisting with it. Too hot for a cloak, anyway. "I, umm…" he began.

"Shh!" she said urgently, glancing at the miscellaneous citizens who were relaxing beside the fountain. "Can we go somewhere quieter?"

She walked rapidly away from the fountain, and he followed her. There were people everywhere, and they ended up making a complete circuit of the small garden before settling for a comparatively quiet spot under a grapevine in the shadow of the city wall. There were no benches, but Archimedes spread out his cloak on the ground and sat on the damp end himself. It could hardly get any muddier, after all. Delia sat down beside him nervously, pulling her own cloak forward again, and looking at her hands upon her doubled knees. She had worked out her excuse for the meeting. She had sent him a warning through his slave, and she was certain that the slave must have delivered it even after she told him not to. "I… wanted to speak to you," she said breathlessly. "I needed to explain." She swallowed, and risked a sideways glance at him.

He nodded: he had assumed that that was what she wanted. She had warned him to be careful of his contract. The king had not, in fact, offered him a contract- but it was only four days since his father's death, and it wouldn't have been appropriate to enter into business with him in the period of deepest mourning. Hieron had put in an appearance at Phidias' funeral, but he had made no reference either to engineering posts or to the money Archimedes had refused. So Delia had come to follow her warning with some advice. Archimedes was happy to think that she was his supporter in her brother's house. He had played with the delightful possibility that her feelings might be warmer than that, but he had dismissed the notion as wildly implausible.

"When I sent you that message, I was afraid Hieron meant to tie you to something in your contract," Delia went on. "I was wrong. I shouldn't have said anything to your slave. It was simply that he was there, and I had the opportunity. I hope it didn't alarm you." She shot him another sideways glance.

He was frowning. "King Hieron isn't going to tie me to anything in my contract?" he asked.

She took a deep breath. The least she could do to atone for her own disloyalty would be to reassure him about Hieron. "He's not going to give you a salaried position as a royal engineer at all. He thinks you'd like it better if he simply pays you well for what you do. He said that any job he gave you you'd come to regard as a prison. So, you see, I was quite wrong, and shouldn't have said anything. I should have known Hieron wouldn't do anything… unjust." Guilt at her own behavior added warmth to her tone.

"But I thought…" he began- then stopped. The frown was deepening. "I don't understand. What does the king want of me?"

"You must know you're exceptional," she said. "As an engineer, I mean."

The frown did not lighten. "I'm better at mathematics."

She thought of the ship gliding along the slipway, and laughed. "You must be very exceptional at that, then! The whole city is talking about your demonstration."

That was true: Agathon had reported it. The whole city was talking about the man who had moved a ship single-handed, and adding that the same man was now building astounding catapults for the defense of Syracuse. The threatened citizens comforted themselves with the thought of Archimedes' skill.

Archimedes made an impatient gesture with one hand. "There's nothing new about pulleys! But I've done some things in mathematics that nobody else has done before." He chewed on a thumb.

"What?" she asked.

He looked at her hopefully. "Do you know anything about geometry?"

She hesitated uncomfortably. "I can keep household accounts."

He shook his head. "That's arithmetic."

"Are they so different?"

He looked at her. She was already beginning to be annoyed when she realized that it was not a look of disgust at her stupidity, still less the condescending don't-trouble-your-pretty-head-about-that look that Leptines the Regent gave her far too often. It was a look that might have come from a stammerer confronted with an urgent need to speak: a passionate longing to be understood and the hopeless knowledge that he would not be. "Arithmetic is a natural system," he said. "But geometry is something the god of the philosophers invented to design the world. Rome, Carthage, Syracuse- we're all that"- he snapped his fingers- "to geometry. Oh gods, it's a divine and beautiful thing!"

She studied his face, the line of the cheekbones and the brightness of the eyes. She recognized remotely that it was this "divine thing" which had attracted her to him- or rather, its reflection in music. Utterly pure and inhumanly precise, it enlarged the world simply by existing. And she wanted, she had always wanted, more than her own world was willing to offer her.

"The gods have given you a great gift, then," she said, torn between admiration and envy.

"Yes," he replied, seriously and without hesitation. Then he went on, embarrassed, "You should get someone to teach it to you. I'd offer to, but I wouldn't be any good. I have tried teaching- my father used to get me to help with his students. But the students said I confused them." His hands tightened on his knees at the memory of his father's patience with those students, and the recollection of the previous day's prescribed offerings at his father's tomb. He did not want to think of his father; he had been immersing himself in catapults precisely so that he wouldn't have to think of his father, and now that the subject had come up, he leaped away from it. "I didn't mean to bore you, lady. But I'm sorry, I don't understand why you asked me here just to tell me that your brother intends to deal with me fairly. Did he send you?"

She looked at him wide-eyed, then blushed. "No," she said.

"Then I don't understand…" he began- then suddenly, looking at her, he did. She sat there, watching him, her eyes frightened and her cheeks ashamed, but the lift of her head a determined challenge. Hieron had not sent her; she had come, alone and heavily cloaked, to meet him in secret. He had not wondered at that, and he should have. The liking he'd felt for her, casual, expecting nothing, crystallized all at once into a shape with edges sharp enough to wound.

"I'm sorry," he said, awed by it, and afraid now. "I was stupid. I…"

He could not think what to say, and they looked at each other, both now blushing furiously. In the back of his mind echoed the warnings: "You were lucky you confined yourself to flutes!" "May the gods forbid that there should be anything between you and the king's sister!" What would a tyrant do to a man who seduced his sister?

What would the sister do if he refused her? Old stories swirled about his mind: Bellerophon, Hippolytos, falsely accused of rape by the queens they had rejected. Looking at Delia, he did not believe a word of it- and yet, this whole situation was unbelievable, and the stories were there, whether he credited them or not.

"You mustn't think I mean to betray my brother's trust," she said, with a sudden fierce determination. "Hieron has never treated me with anything except kindness, and I would never dishonor…" She stopped, knowing that she had already betrayed her brother's trust, already taken the first step to dishonoring the house. Only a small step, so far, but this meeting had done nothing to convince her heart of its folly: quite the reverse. "It's only that I wanted to know you better," she went on, more uncertainly- and suddenly saw that she was treating him even more disgracefully than she was treating Hieron. Even as much as she'd done already could injure him, devastate his career, and blast his reputation. The king treated him with great kindness, and he responded by trying to seduce the king's sister! Seduction was a crime, and she was asking him to risk the penalties without even a seducer's reward. Shameless, selfish, heartless! She turned away, in an absolute misery of shame, shame on all sides, and pulled her veil forward to hide the hot tears that were bursting from her eyes.

He looked at her for a moment- the tears, the confusion- and forgot, as he kept forgetting, that she was the sister of the king. He caught one of her clenched hands, and she looked back at him, her face wet and red and hopeless. The only natural thing to do seemed to be to kiss her, so he did. It was like finding the ratio, solving the puzzle, or coming home. A flurry of notes fell perfectly upon the beat, and two pitches blended into harmony.

She broke away first, pushed him back with the heel of her hand, wrapped her arms around herself and tried to separate the chaos she was feeling into coherent emotions. "Oh, gods!" she cried frantically.

"I'm sorry," he lied awkwardly: he was not sorry at all. He was enormously pleased and flattered; he was frightened and wished himself out of this- and underneath it all, complicating everything, he was enchanted by Delia, clever, witty, proud, determined girl, with such beautiful black eyes and a wonderful neat warm body whose imprint still tingled against his own. He didn't just want to go to bed with her; he wanted to sit up in bed with her afterward, talking and laughing and playing the flute. Like a new theorem, the range of possibilities ramified away from her, a ladder of inevitable connections: if and then all the way down to the final conclusive this is what was to be proved.

Only most of those possibilities were bad. After a moment he added doubtfully, "Do you really think it's wise that we should know each other better?"

"No," she said, half laughing, half sobbing. "I think it would be very stupid."

Only, only, said something in her blood, only I want to. I want you to kiss me again, I want to touch your face and run my fingers through your hair, your eyes are like honey, did you know? Ruin to you, and shame to Hieron. No.

"I thought this would convince me I didn't want to," she admitted miserably, "but it hasn't."

He sighed. No, she was no Phaedra, and he was no Hippolytos. He remembered the song he had been humming when he went to her door after finishing the Welcomer, beseeching Aphrodite to bring him this girl's love. The goddess had heard him, it seemed. Laughter-loving, they called Aphrodite, but her sense of humor tended to the black. He wished his father were alive. Not that he could have told Phidias about this- gods, no! — but at least then he wouldn't be burdened with this aching loss in the heart, this urge to find comfort. "Then what do we do?" he asked, and recognized even as he spoke that leaving the choice to her was fatally weak. Only it was perfectly clear to him what they ought to do, and it wasn't what he wanted to do at all.

She had always prided herself on her strength of mind. She might not be gracious and regal, like her sister-in-law; she might not be modest and charming, like the girls who had shared her lessons. But she had strength of mind. "We should do what's wise," she said firmlyand instantly regretted it. She looked at him and saw that he regretted it, too. She reached over and touched the side of his face, and at once he kissed her again, which was what she wanted and was not wise.

When she left the garden shortly afterward, they had resolutely made no arrangements to meet again. And yet already her mind was reflecting on how easy it would be, and already she suspected that wisdom would not prevail.

The Romans arrived before the gates of Syracuse only eight days later- twelve days after Phidias' funeral.

Archimedes had spent most of the intervening time making catapults. He had been in and out of the workshop even while he was preparing the demonstration; after the funeral he immersed himself in the work. He did not want to think about his father or his own future, still less about the net he was falling into with Delia. She'd sent him a note arranging a second meeting, and he'd told himself that he should not go, and had of course been there early. They had walked from the fountain of Arethusa to a quiet public square near the temple of Apollo, where they had sat down to play the flute- she'd brought her flutes. And they'd kissed, of course. It was innocent and very sweet, all of it, and he had no notion what was going to come of it, though he suspected nothing good. If he spent every waking moment thinking about catapults, he didn't have to worry.

The workshop hadn't been quiet before, but during those twelve days it was frantic. Extra workmen were drafted in from the army to help hammer and saw, and the catapults were assembled almost as fast they could be designed- two of them simultaneously, one by Archimedes and one by Eudaimon. The old catapult engineer had been sullen and resentful since the Welcomer passed its trial, but he gave way at every point of conflict and devoted himself to copying what Archimedes had designed: a one-talenter like the Welcomer and two hundred-pounders. Archimedes periodically went and checked that the dimensions of the copies were correct, and was rewarded with ten drachmae for every copy completed.

Kallippos, as chief engineer, had overall responsibility for the defenses of the city. This seemed to mean principally that he ordered buttressing or parapets for the walls and directed where catapults were to be sited. The copy of the Welcomer and two of the hundred-pounders went to the Euryalus fort, and another hundred-pounder to the south gate, overlooking the marshes. When Archimedes started the two-talenter, Kallippos came to see how big it really was, with a view to determining where he could put it. In fact, the machine was not as large as its designer had initially feared; the increase needed in the size of the bore was only five finger-breadths, giving a proportional increase of a quarter all round.

"We could put it almost anywhere," said Kallippos, scrutinizing the thirty-six-foot stock, which lay in the center of the workshop floor. "In the Hexapylon, for example, on the floor underneath the Welcomer."

"We could call it 'Good Health,' " suggested the workman Elymos slyly. "As in 'Welcome to Syracuse!' " He punched a palm. " 'Good health to you!' " Another resounding smack!

The other workmen laughed, and Kallippos smiled. "And the three-talenter could be called 'Wish You Joy'?" he asked Archimedes.

Archimedes blinked: he'd been trying to picture whether the catapult would fit on the floor beneath the Welcomer. "I suppose so," he said. "But look, I, um, think it will need a bigger platform. Not for the machine itself, but for the men operating it. The yard there is low, and even though the platform's on ground level you still have to climb a few steps to reach it. The, um, ammunition will be heavy, and they'll have to have a hoist to raise it. They'll need a space to stand while they lift it, and then…" He hesitated, then glanced around, found a stick, and squatted down to sketch on the dirt floor the things the catapult operators would need.

Kallippos watched intently, then squatted down next to him and began saying things like "The main roof support's about here," and "You can't put the crane on the roof- too exposed under fire." After a little while, the workmen went back to work around the two engineers; the engineers issued a few furious orders about not stepping on the sketches, then gave up, retreated to a quieter part of the workshop, and began chalking their plans upon the wall. Hoists gave way to arcs of fire and outworks. When the chief engineer finally departed, he shook Archimedes' hand warmly and declared, "I'll see to it." And when Archimedes accompanied the completed two-talenter to the Hexapylon, he found most of his suggested modifications in place.

That was the day the Romans arrived. The wagon with the catapult drew up at the fort to find the garrison buzzing with excited apprehension: a messenger had just galloped up to announce that a large Roman army was only a few hours' march away.

There had been some news of the enemy since Hieron's return to the city. Shortly after the Syracusans had left Messana, the Romans had sallied out from the city to attack the remaining, Carthaginian, besiegers. The Carthaginians, like the Syracusans, had managed to beat off the attack- and, like the Syracusans, had decided to withdraw afterward, unwilling to continue the siege without support from their allies. For a little while the Romans had remained in Messana, apparently debating whether to go after the Carthaginians or the Syracusans. When they at last made up their minds, they marched due south toward Syracuse.

The Romans had two specially strengthened legions- ten thousand men- plus the army of their allies the Mamertini, which alone nearly equaled the number of the Syracusan army. Outnumbered and facing enemies famed for their ferocity and discipline, the Syracusans had no intention of venturing into the field. Refugees from the outlying farms and villages came flooding into the city, laden with as many of their possessions as they could carry and lamenting the harvest they had been forced to abandon. As Hieron had said, the hope of Syracuse lay in her walls- and her catapults.

The captain of the Hexapylon was delighted to see Archimedes. "That's the two-talenter?" he asked, as soon as the wagon had rolled to a halt. "Good, good! See if you can get it up in time to wish the Romans good health when they arrive, hah!" And he gestured for his men to help move the catapult to its selected platform.

Between the throng of eager helpers and Kallippos' hoists, the bits of the catapult were soon in place, and Archimedes afterward realized with astonishment that he had not once had to pull on a rope himself. He was assembling the pieces when Hieron arrived with a troop of guardsmen. He came up to the catapult platform and watched silently while Archimedes threaded the pulleys. Archimedes concentrated furiously to avoid those bright interested eyes.

"Will it work as well as the others?" the king asked when the stock had been fixed upon its stand.

"Unnh?" said Archimedes, fiddling with the screw elevator. "Oh. Yes. Probably won't have the range of the Welcomer, though." He walked back along the stock to the trigger and sighted along the slide- then stood upright with a jerk. There was a vast shadow on the road northa shadow that glittered as the bright noon sun caught upon the points of the thousands of spears. He looked at the king in shock.

Hieron met his eyes and nodded. "I imagine they'll want to set up camp before they test our teeth," he said. "You don't need to rush the tuning."

In fact, the Romans were impatient. The main body of the army halted in the fields to the north of the Epipolae plateau and began entrenching, but a smaller group could be seen assembling on the road. It was easy to make out two masses of men falling into square formations, with an irregular line of other men before them.

Hieron, who was watching out the artillery port, gave a snort of dismay. "Two battalions?" he asked no one in particular. "Two- what do they call them? — maniples? Only about four hundred men. What do they think they're doing?"

As if in answer, the two squares began to march toward Syracuse, one to the left and one to the right of the road. "Anyone with better eyes than me see a herald, or any tokens of a truce?" asked the king, raising his voice.

Nobody saw any evidence that the Romans were coming to talk.

Hieron sighed and stared at the two maniples a moment longer with a look of loathing. Then he said, "Very well," and snapped his fingers. "Get the men drawn up," he ordered his staff. "There are a few things I want to tell them."

The Syracusan soldiers assembled in neat ranks in the fort yard, facing the open-backed catapult platform where the king stood. The Hexapylon had a regular garrison of a single infantry file- thirty-six men- plus servants and errand boys and hangers-on, and the king had brought four more files with him. But the crowd that assembled now numbered well over three hundred, and Archimedes realized that men from other units along the wall must have been arriving while he was busy with the catapult. Hieron had concentrated some strength here, where the first attack was expected- but not too much. All up and down the fifteen-mile circuit of the walls, Syracusans must be standing to the alert, checking the tension on their catapults and arranging supplies of ammunition. Who knew which way the Romans would turn?

Hieron strode to the edge of the platform and looked out at the rows of helmets before him, all with their cheek flaps turned up so that they could listen. Archimedes glanced over the ranks, then, feeling out of place, went back to Good Health and resumed work on the strings. Despite the king's advice, he had been rushing to get the catapult ready to fire, and now it only needed tuning. He climbed up onto the stock with the winding gear.

"Men," shouted the king, in a strong clear voice, "the Romans have decided to send some fellows up to see whether or not we have teeth. We're going to let them come as close they want to, and then we're going to bite so hard that their friends watching will shit for fear."

The soldiers gave a roar of understanding and struck the butts of their spears against the ground. Archimedes waited for the noise to die down, then struck the second set of catapult strings.

"Good!" said Hieron, drowning the note. "So don't do anything to scare them off early! No shouting, and absolutely no shooting, until I give the order. When they're nice and close, we're going to give them a warm greeting. You probably know we have a couple of new catapults here especially designed for greeting Romans. One says 'Welcome!' and the other says 'Good health!' When a two-talenter wishes you health, you'll never be ill again!"

Another roar, of laughter this time. Archimedes glanced around irritably, then tried striking the strings again.

"I want them smashed!" shouted the king, punching the air. "When the catapults have done that, the lads that came up here with me can go pick up the pieces, and carry the bits back. I want prisoners, if we can take them. But the main job today is to let the enemy know what he can expect if he attacks Syracuse. Understood?"

In answer, the men bellowed the war cry, the fierce ululation howled out just before the clash of arms: alala! Hieron lifted his arms above his head, his purple cloak flapping, and shouted, "Victory to Syracuse!" Archimedes set the winding gear down in exasperation. Hieron left the troop cheering and turned around to look at Archimedes. "I hope it is ready to fire?" he asked, in a normal tone of voice.

"It would be," said Archimedes disgustedly, "if you would just keep quiet!"

Hieron grinned and gave an apologetic go-ahead wave of the hand. One of the men who was to operate the catapult struck the fixed strings, and Archimedes hit his own strings. Too low.

He tightened them a turn and a half, struck them again, and nodded to the catapultist. The man rapped out a sharp hollow note while the first sound still reverberated, and the two notes blended low and deadly on the still air.

"It's ready!" Archimedes said breathlessly. The king smiled tightly, gave a nod, and departed to watch from the gate.

Archimedes patted Good Health nervously, then went to the open artillery port to watch. He was vaguely aware of the catapult shifting beside him as its new team of operators tried the wind-lasses and elevator to train it on the enemy's advance. In the fields beyond, the Romans were continuing their slow march up the hill toward the walls of Syracuse.

At the limit of catapult range the Romans were faced with a deep ditch and a bank; they hesitated a moment, then raised their shields above their heads and began tramping down the ditch and up the other side. The shields were painted red, and as the men descended into the ditch they looked like a swarm of brightly colored beetles.

Archimedes heard someone come up behind him, and he glanced around and recognized Straton. "Oh," he said vaguely, and looked back at the advancing Romans.

"I was sorry I missed your demonstration," said the guardsman, as casually as though they were meeting in the marketplace. "The fact is, the captain had me cleaning the latrines that day."

Archimedes glanced back at him, surprised, and Straton grinned. "I'd made some bets with the other fellows in my unit that you'd do it, and there was a bit of argument about it. The captain doesn't like arguments. But you earned me a month's pay when you moved that ship. I've come to say thanks."

Archimedes gave an embarrassed shrug. "I don't know why people thought it was so impossible. Pulleys have been around for centuries." His eyes were drawn irresistibly back to the Romans. They were well within catapult range now, and were looking more like men and less like insects. "How close does King Hieron mean to let them come?" he asked.

"You heard him!" said Straton, surprised. "As close as they're willing to come! See, they've been sent up here to have a look at us, to find out what kind of defenses we've got. They've probably got orders to fall back as soon as we start shooting. The idiots have come too close for safety already- and in loose formation, too."

Archimedes chewed his thumbnail. There was a limit to how far a catapult could be depressed: if the Romans got too close, they'd be inside the arc of fire. "What if they run for the walls?" he asked.

"Shouldn't think they will," said Straton. "If those fellows knew anything about catapults, they wouldn't have come as close as they have- and it takes a lot of experience to convince your feet that you'll be safer running toward your enemy than away from him. But if they're stupid enough to try it, we've got enough men here to wipe them out."

They both stood for another endless minute gazing down at the advancing ranks of shields: two squares in an open formation, twelve men deep, with a double line before them. It was now possible to see that the men in front were light-armed skirmishers, equipped only with a few javelins, a helmet, and a shield; the men in the rank had breastplates and heavier spears. At the front of each square gleamed the standards- gilded eagles, set upon tall poles, trailing crimson banners which juddered as the standard-bearers made their way cautiously over the uneven ground. "Idiots!" whispered Straton. "Don't they realize?"

The Romans might be idiots, but the silence of the walls was clearly making them nervous: they marched more and more slowly, and at last stopped altogether.

At his shoulder Archimedes felt the air stir as Good Health's nose dipped. He retreated from the artillery port and went back along the catapult stock to where the new team of operators stood. There were three of them: one to load, one to fire, and one to assist. All three grinned- and then the captain of the team, a tough-looking man twenty years senior to Archimedes, stood aside from the trigger. "You want to test your new catapult, Archimechanic?" he asked.

Archimedes blinked at the nickname, but nodded, then moved to the foot of the catapult to sight along the stock; the machine was already aimed and loaded, and he found himself staring through the aperture at the air above one of the Roman standard-bearers. The man was only a couple of hundred feet away. Archimedes could make out the sandy color of his beard under the wolfskin he had tied over his helmet. The standard-bearer had lowered his shield while he talked to a man in a red-crested helmet. As Archimedes watched, the light-armed troops began to move back past the two into the gaps left in the formation of the heavy infantry: clearly, the Romans had decided that they'd come far enough and should retreat. It seemed to be what Hieron was waiting for: from overhead and along the city wall came a barking order, and then the sudden crack of catapult arm against heel plate; the air darkened with bolts. The standard-bearer at once lifted his shield above his head again. From the floor directly above came the deep bay of the Welcomer- and then there were screams.

"Now, sir!" said the catapult captain impatiently. "Now!"

Archimedes fumbled at the trigger.

Good Health's voice was deeper than the Welcomer's, a fearsome bellow ending in a smash of iron. The stone was gone too fast to follow- and then the standard-bearer was down, and the missile was tearing through the Roman line behind him like a harpoon through water. Screams- they were close enough that he could hear the screams clearly, even over the whoops of glee that rose from the catapult team as they saw their target go down. Archimedes stumbled back, still staring along the stock through catapult aperture and artillery port. The standard-bearer's body sprawled backward on the ground, red-topped, helmetless- no, headless! The two-talent stone had knocked his head clean off his body and gone on to kill or maim everyone behind him in the line of fire.

"Quick!" yelled the catapultist, already winching back the string. "Reload!"

His two assistants already had the hoist ready; another stone was dropped into place. On the floor above them, the Welcomer cried out again, and Archimedes glanced along the line and found another trail of bodies traced through the Roman maniple, but not quite so far; the one-talent stone seemed to fail after claiming its four or fifth victim. As he lifted his eyes, he saw that the rear ranks were falling, too. From the parapet of the city wall the small, long-ranged arrow-shooting scorpions struck methodically at the rear of the Roman force. The Romans were still trying to protect themselves with their shields, but catapult bolts went through shields, piercing wood and leather and bronze as easily as flesh and bone. From the upper towers of the fort, the lighter stone-hurlers volleyed steadily, sending weights of ten or fifteen or thirty pounds flying with hideous force into the middle of the rank. Battered by forty catapults at once, the Romans fell like grass to a scythe.

His survey had taken only seconds; beside him, Good Health now bellowed again. Another bloody furrow tore through the Roman force from front to back; a new set of screams rose audibly above a steady background of howls and the endless percussion of arms on heel plates. "Reload!" screamed the catapult captain; and the string groaned as it was winched back again.

In the field beyond, the Romans were throwing away their shields and running away as fast as they could, but even as they fled, the storm of death followed and cut them down.

"Oh, gods!" whispered Archimedes. He had never in his life before seen anyone killed.

Straton too was staring out the artillery port, his face contorted in a grin that was more than half snarl, his fist rising and falling in sympathy with the baying of the big catapults. "Welcome to Syracuse, you bugger-arsed barbarians," he muttered. "Good health!" He straightened abruptly and flipped down the cheek-pieces of his helmet. "Almost time to pick up what's left," he said, and ran lightly down the steps to join his unit. As he went, Good Health's bellow arose again.

Archimedes retreated from the catapult platform and sat down on the steps. He thought he was going to be sick. If he closed his eyes, he could still see the standard-bearer's body lying there headless. What had happened to that sandy beard? It must be smeared all over the stone- oh, Apollo! — with the man's brains and blood… his catapult!

There was a blast of trumpets, and then the high sweet sound of a soprano aulos, piping the men out into battle. The stone-hurling catapults stopped baying, though the percussion of the arrow-firers continued, picking off the Romans as they fled. No war cry followed from the Syracusans, however. As Hieron had promised, the Romans had already been smashed: all the Syracusans needed to do was pick up the pieces. And at last even the stuttering of the scorpions ceased.

Of the four hundred-odd Romans who had advanced on the city, perhaps twenty-five men made it back to their camp. Another thirty or so who had dropped to the ground to avoid being shot surrendered to the Syracusans, and fifty-four other prisoners were carried into the city, too badly injured to walk. All the rest were dead.

Hieron went through the Hexapylon, congratulating his men. When he reached Good Health's platform, he found the new catapult's team busily loosening the strings. The machine could not be kept at full tension without strain, and it was clear that the Romans would not try another assault on the fort that day. Of the king's new engineer there was no trace.

"Where's Archimedes?" asked Hieron, glancing about with a frown.

"Gone home, lord," said the catapult captain, climbing down from the stock. "He was looking a bit green. I don't think he's seen one of these in action before- and he'd finished here, anyway."

"Ah," said the king. His frown deepened.

"He can't have been upset by that!" protested the assistant in surprise. "He built the machine- he must have known what it would do."

"There's knowing and knowing," observed Hieron quietly. "Everyone who rides, for example, knows that it's dangerous to gallop downhill. But there are plenty of cavalrymen who do it all the time, because it looks bold and dashing. Once a fellow I knew killed a horse and broke his arm in three places doing it, and after that he understood that it was dangerous."

"And never did it again?" asked the catapult assistant expectantly.

The king gave him a sharp look. "He could never again bring himself to gallop at all. He had to resign from the cavalry. There's knowing and knowing." His frown lifted as he looked at Good Health. "I noticed that this machine worked every bit as well as its brother."

The catapult captain gave a contented sigh and patted the new machine. "Lord," he said, "it's the best I've ever handled. I don't know what you're paying the fellow for it, but you should double it. We fired five times before they were out of range, and it was as easy as killing blackbirds with a sling. Three direct hits, one partial, one miss. The range is about four hundred feet. I reckon this darling must have given permanent good health to thirty or forty of the enemy. Lord, a machine like this-"

"I know," said Hieron. "Well done! We've shown the enemy a thing or two about Syracuse, eh?"

When he had finished speaking to his men and given orders for the watch on the Romans and the treatment of the prisoners, Hieron went back to the gate tower from which he had observed the assault and climbed up it to the highest floor. A single scorpion crouched there alone, its operator already gone and the tension on its strings relaxed for the evening. The king glanced out the artillery port at the Romans- now firmly entrenched for the night- then turned to stare in the opposite direction, out at the city of Syracuse.

From this angle most of the city was hidden, masked by the plateau of Epipolae. But the Ortygia thrust out into a brilliantly blue sea, and to the south he could make out the sea gates and the naval docks. The temple of Athena shone red and white, and the mansions of Ortygia made a patch of green, with the fountain of Arethusa a deeper, more vivid green by the harborside. The air shimmered with the afternoon heat, making the city look as insubstantial, and as beautiful, as a dream city in a sunset cloud.

Hieron gave a long sigh, feeling a hot sick tension ebb away. He sat down in the doorway, resting his chin on his crossed hands. His lovely city, Syracuse. Safe- for the time being.

He hated killing. He had been horrified when he saw the two Roman maniples advancing on the city, because he had known at once what he was going to do to them. He thought now of the self-satisfied face of Appius Claudius, the Roman in command, and swallowed down a lump of raw hatred. It had been an act of crass stupidity to send out those four hundred men. Claudius should have sent a few scouts under cover of darkness- or a couple of thousand men in close formation, with siege machines. But Romans didn't understand mechanics, and, being Romans, were reluctant to admit it. Claudius would probably blame his assault's failure on the men who had died in it. Not brave enough, not resolute enough, not sensible enough! Throw the survivors out of the camp and give them rations of barley instead of wheat! The general erred and the men suffered: that was the Roman way.

Claudius had probably ordered the assault at once because he was in a hurry for a victory. He was a consul, elected by the Roman people to supreme power- but only for one year, and that year was already more than half over. Hieron suspected that the decision to attack Syracuse rather than a Carthaginian city had been taken because Claudius had thought it would be quicker to take one city than to defeat a great African empire, and he wanted to return home triumphant. Appius Claudius, conqueror of Syracuse! He would be credited with a glorious victory, and have a parade given in his honor. There was no doubt a place reserved in that parade for Hieron, too: walking behind the triumphal chariot in chains.

It had been Appius Claudius and the rest of the Claudian family who had started the war in Sicily in the first place. Hieron had always made a habit of collecting gossip from Italy, and he knew that the Roman Senate had in fact opposed the Sicilian expedition. Rome had had a treaty of peace with Carthage, and the senators strongly disapproved of the Mamertini: a Roman garrison which had committed similar atrocities in Rhegium had been beaten to death by its outraged fellow countrymen. But a faction headed by the Claudii had favored the expansion of Roman power to the south and had played on Roman distrust of Carthage to persuade an assembly of the Roman people to countenance this act of brazen aggression.

"Greedy, ignorant, vainglorious fool!" Hieron said out loud- then set his teeth. It was no good hating Appius Claudius. He might yet have to humble himself before the man. Claudius must have seen now that Syracuse was not a city that could be crushed as an aperitif, before the main war began. He might now offer reasonable peace terms so as not to go home empty-handed. Hieron had to be prepared to accept any realistic offer, even if it allowed Claudius to claim a victory and get his parade. He was bound by the absolute and unalterable facts that Syracuse alone could not contend with Rome, and that she could not trust Carthage: he had to accept terms. It was no use hating. Even the gods were slaves to necessity.

Perhaps the Roman people would now regret their decision to go to war. Syracuse had humbled them once at Messana, and now had humbled them again. Those men camped out there would not forget seeing their comrades butchered before their eyes. It was too much to hope for that they would give up and go home- Rome had never abandoned a war after declaring it- but the next Roman commander might well be more flexible, even if Claudius proved stubborn.

Hieron thought again of the Romans dying under the catapult fire; remembered the two-talent stone smashing its bloody way through the rank. That must have frightened them, surely? It had frightened Hieron, and he was on the right side of it! Perhaps when the three-talenter was working he could arrange for some Romans to see it.

If he got that three-talenter in good time. The engineer had gone home looking green. Hieron could understand how he felt; he'd felt that way himself after killing his first man. It had taken him months to get over it- as much as he ever had: he still woke up sometimes at night remembering that mercenary's face and feeling the hot stickiness of blood on his hands. Any man could lose his nerve. The cavalryman who'd galloped downhill had never recovered it. Should he go after Archimedes and try to talk him through the crisis? No. If the man were pressed to create more engines of death, the revulsion he must feel against those engines now would spill over onto the king as well. Better to leave him alone. Archimedes understood the importance of his work: his answer to the money had proved that. He would work himself around to the task if he could.

Hieron sighed. There were plenty of tasks awaiting him, too, down those stairs. But he sat for a while longer, alone at the top of the tower, looking out over his shining city.