The Sand-Reckoner

6

To most of the city, the following day was the Day King Hieron Returned- but to Archimedes, the king and his army were merely an annoying interruption on the Day We Moved the Welcomer.

Only one workman- Elymos- assisted him with the catapult; Eudaimon insisted that the rest remain in the workshop to help on another arrow-shooter. Straton was still in charge of transporting the machine, however, and Archimedes was very glad of his assistance before the day was done. It took the heavy ox-drawn wagon more than two hours to reach the Hexapylon, and when they arrived at the fort they found that there was no crane to move the one-talenter to the enclosed platform on the tower selected for it.

This platform was the first floor of one of the fort's outer towers- large catapults were normally placed on the lower floors of towers, leaving the upper stories to the lighter machines. A stone stairway ran up past the platform, which stood open to the fort's interior yard, but it was not possible for three men to maneuver a thirty-foot stock up the stairs. Straton cajoled the fort garrison into lending some rope and pulleys, and Archimedes rigged up hoists, but it was still the middle of the afternoon before the pieces of catapult were all lying on their platform, and then they needed to be fitted together. King Hieron and his army appeared before the gates while this was being done. All the fort garrison went off to cheer the king as he rode past, and Straton joined them- quite unnecessarily, thought Archimedes, as he struggled to rearrange his hoists so that the catapult stock could be refitted to its stand. Straton, he told himself angrily, should have remained to haul on ropes when he was told to.

But when the king had gone, Straton said he must return the wagon and oxen to the Ortygia, and departed as well, leaving Archimedes and Elymos to continue the struggle alone. It was dark before the catapult finally stood intact in its place. Archimedes was staggering with exhaustion by that time, and his hands were blistered from the rope to the point where he couldn't feel any one particular ache. When the job at last was done, he examined his blisters, then looked at Elymos, who was, if anything, even more blistered and exhausted than he was himself. "If you don't want to walk all the way back to the Ortygia," he told the slave, "you can sleep at my house tonight."

"That's very kind of you, sir," said Elymos gloomily, "but Epimeles told me to stay here tonight."

"Here?" asked Archimedes in surprise, glancing about the bare room. The catapult was under cover, but nobody would describe its location as comfortable. The yard side of the platform stoodopen and the floor was rough planking. In one corner stood a pile of forty-pound shot, left over from the platform's previous catapult.

"That's right," agreed the slave mournfully. Epimeles had ordered him not to let the catapult out of his sight, and to make his bed beneath it.

"But- why?" asked Archimedes, totally mystified.

Elymos just shrugged and spat out the artillery port. Epimeles had also told him not to worry Archimedes. "We don't want that lad's mind distracted," he'd said. "We don't want him spoiling his chances. He'll win the crown now if he just runs easy down to the finish line; if he starts thinking he has to put on a spurt, maybe he'll trip over his own feet."

"Maybe," added Elymos hopefully, "you could ask the captain of the fort to give me a mat and a blanket and a bit of supper?"

"Very well," said Archimedes, bewildered. "I'll see that you get some wine, too, if you like."

"Thank you, sir!" said Elymos, eyes gleaming.

Archimedes decided during the long walk home that it was actually very sensible of Elymos to stay at the Hexapylon overnight. The Achradina wasn't quite as far as the Ortygia, but it was still a long way, and by the time he arrived home it was very late. Marcus, yawning, let him in, but the rest of the family had been asleep for hours. No, Elymos was quite right to get some sleep at once, with the catapult.

But despite his exhaustion, Archimedes had trouble falling asleep. He tossed in the heat, blistered hands aching, mind running swiftly through things that could go wrong with his catapult. When he did at last slide into an uneasy sleep, it was to dream of an army attacking the Hexapylon, equipped with battering rams and siege towers. He knew that if the enemy reached the walls, they would get in and kill everyone; he knew that if he could fire the catapult he could keep them back- but the catapult kept coming apart in his hands. In desperation he slammed at it- and the impact of his blistered hand against the bed woke him again fully.

He groaned, rolled onto his back, and lay staring up at the darkness. His hands throbbed. After a minute he got up, went downstairs, and poured some water into a bucket so that he could soak his blisters. Above the courtyard, the Milky Way hung shimmering. The stars had wheeled far around toward morning. Archimedes sat against the wall, soaking his hands in the bucket, and watched the stars. Infinitely far away, eternally lovely. All the earth was incomparably small, and Syracuse a speckle upon a mote of dust. He closed his eyes, imagining the illimitable sphere of the universe, and the image of the catapult faded at last.

Archimedes was still asleep the next morning when there was a staccato knocking at the house door. Marcus, who was in the courtyard, opened the door and found two men in full armor. One was Straton, polished almost out of recognition; the other a wiry man in the crimson cloak and scarlet-crested helmet of an officer, wearing a beautiful bronze breastplate decorated with glittering silver medallions. "This is the house of Archimedes son of Phidias?" asked the officer.

Marcus nodded, his face dropping into its mask.

"I need a quick word with him," said the officer.

Philyra came down the stairs into the courtyard in her tunic with her hair loose, realized that there was a strange man at the door, and backed into the stairway with a squeak. The officer grinned at her in an appreciative way Marcus very much disliked. "The gentleman wants a word with your brother, mistress," he announced, stressing the title to make it plain that this was the daughter of the house, not a slave girl. Philyra nodded and shot back up the stairs.

She burst into her brother's room, shouting, "Medion! Medion, an officer has come for you!" Archimedes picked his head up, then groaned and pulled the sheet over his head.

Philyra hauled it off and threw him the first tunic that came to hand, and presently he stumbled down the stairs to the courtyard, barefoot and unshaven. Dionysios son of Chairephon had been admitted to the courtyard and was chatting to Arata, while Straton stood at attention by the street door. When Archimedes appeared, the captain raised his eyebrows.

"Get dressed," he commanded.

"I, uh," said Archimedes, running a hand through his tangles. He was never at his best first thing in the morning, and he'd been too tired for supper the night before- and, come to think of it, too busy for lunch before that. "I, uh- are we going to do the catapult trial this morning?"

"The king is reviewing the forts along the wall this morning," said Dionysios shortly. "He has specifically asked to witness the trials of your catapult. I don't know when exactly he'll reach the Hexapylon, but I'm off to join his escort now. So- get dressed. If he shows up and you're not there, you're out of a job." He gave the company a nod and set off. Straton shot Archimedes a grin, and followed at a smart march.

Archimedes scratched his head again, then sighed. Philyra once more vanished upstairs, then returned with his good cloak. "Let me at least eat first!" he protested, gazing at the garment with loathing and wishing that Philyra had thought to weave of it of linen.

"Medion!" exclaimed Philyra angrily. "That was the captain of the Ortygia garrison, telling you the king wants you to hurry!" "I believe in the equality of all citizens in law!" said Archimedes proudly.

"I believe in this household having an income!" Philyra hurled back.

Arata clicked her tongue approvingly: support for democracy was fine in theory, but money was good in practice, and you needed to bow to authority for that. "You can take some food with you," she told her son soothingly. "I'll pack a basket, and Marcus can carry it."

Archimedes, trailing Marcus, reached the Hexapylon before the middle of the morning. The king was not there: he'd begun his tour of inspection at the south end of the city, and nobody knew when he'd reach the Hexapylon. The fort's garrison were still busy polishing and tidying. Morosely, Archimedes went to the catapult platform where he'd erected the Welcomer.

Elymos was still lying underneath the great machine, but he sat up when they came in. He was pale and queasy: he had been generously provided with wine the previous night, and was suffering the consequences. Archimedes nodded at him vaguely, and began checking that the catapult strings were correctly tuned.

Marcus set down the basket of food and gazed at the catapult. He had never seen one so large. After a moment, he ran his hand along the rough oak of the stock, then went to the end of the slide and sighted along it out the aperture, one hand on the lax trigger. He imagined sixty-pound shot flying, and shivered.

"It's a beauty, isn't it?" Elymos asked him.

Marcus said nothing. "Beauty" was not the word that leaped to his mind at the sight of the Welcomer. He glanced over at his master, who had now opened the shutter on the artillery port and was gazing out. It was hard to associate anyone so vague and soft-hearted with anything so powerful and deadly. He felt for a moment physically sick in the self-contradiction of his own desires. He had wanted this machine to be an outstanding success, for the sake of the household, for the sake of Syracuse. But he did not want it used on Romans.

Archimedes pulled off his new cloak and dropped it across the sill of the artillery port. "Marcus, where's the food?" he asked plaintively.

They sat together by the open artillery port and ate the bread and figs Arata had packed for them. Elymos sat with them, but did not want food.

The morning sun flooded the landscape below them. The view was stunning. The founders of Syracuse had enclosed the harbor area alone, but this had left them vulnerable to any invader who could command the heights of Epipolae, above them to the west, so as the city grew mighty she had rebuilt the walls to run along those heights, miles from the heart of the city, commanding the landscape from all sides. The fortifications had not only been kept in good repair, but had also been renovated almost continuously to keep up with developments in warfare. The initial open ram-parts were covered over with a steeply pitched roof to protect the defenders from catapult fire, while bronze-shuttered artillery ports had been added to the guard towers and to the wall itself. From the tower of the Hexapylon Marcus and Archimedes could see the north road winding off across the fertile landscape through field and vineyard, while Mount Etna loomed, snowcapped and smoking, in the far distance. When he'd finished his meal, Archimedes gazed at the volcano, wondering what made it erupt and whether its fiery nature had anything to do with its shape, which was certainly an obtuse-angled cone. Sections of obtuse-angled cones did have some extremely interesting properties. He looked around for something to sketch with.

When King Hieron finally arrived at the tower of the Hexapylon and climbed the steps to the tower, it was to find a young man in a worn tunic scratching on the floorboards with a bread knife. Two slaves who had been seated on the end of the enormous catapult beyond him jumped to their feet and stood at attention as soon as the king's head appeared up the stairway, but the young man scratched on obliviously.

The king climbed the last few steps and emerged onto the catapult platform. His entourage followed him: four staff officers; his secretary; Dionysios; the captain of the Hexapylon; Eudaimon, the catapult maker; Kallippos, his chief engineer; and six guardsmen, including Straton. Archimedes took no notice of any of them. He sat back on his heels and chewed on the hilt of the bread knife, frowning at his sketches.

Marcus eyed the king nervously, then took a step forward and despairingly hissed, "Archimedes!"

"Unnh?" Archimedes asked around the bread knife.

The king stepped closer and gazed down at the scratches: twin curves sliced from a broad double cone. "Hyperbolae," he observed.

Archimedes gave a grunt of agreement and took the knife hilt out of his mouth. "I wish I had my compasses," he said. "And a ruler."

"Here's a ruler, anyway," said the king.

Archimedes glanced from the drawing to the feet before him- then, suddenly taking in the gold-studded purple-laced sandals, looked up, leaped up, and went crimson.

The king smiled. He was a plump man, a full head shorter than Archimedes, and he had a pleasant face, round and good-natured, with curly black hair and sharp eyes dark as his sister's. He looked more like the host of a country inn than a Sicilian tyrant, despite his purple cloak and tunic and the purple band of the diadem across his forehead. He was younger than Archimedes had expected, too; not much above thirty-five. "I presume you're Archimedes son of Phidias?" he said.

"Uh, yes," stammered Archimedes, trying to remember what he'd done with his cloak. "Uh- good health, O King!"

"Good health! I knew your father," said King Hieron. "Studied with him for a couple of months, in fact, when I was young. I was sorry to hear that he's ill. What's wrong with him?"

Still scarlet with embarrassment, Archimedes stammered out a brief account of his father's illness. Hieron listened attentively, then asked Archimedes to convey his hopes for the sick man's recovery. "And tell him I've always wished I could have studied with him longer," he added. "But that's not what we're supposed to be doing today. This is the one-talenter you made for me, is it?" Hieron strolled across to the catapult. "Herakles, what a huge machine! What's this wheel for?"

"That's to help it pivot, lord," said Archimedes, and demonstrated.

Hieron's chief engineer, Kallippos, a tall hawk-nosed man of about forty, at once bore down upon the catapult and elbowed his king out of the way. He examined the system of pulleys and windlasses closely. "Is this Alexandrian?" he demanded.

"Um, no," said Archimedes uncomfortably, "I, uh, just developed that myself. It works, though."

Kallippos made a noise through his teeth, half hiss and half whistle, and looked disbelieving. Hieron gently moved his engineer out of the way again and took over the windlasses himself. He sighted along the stock through the aperture, aimed the catapult at an empty field to the north of the road, then reached for the third windlass to elevate it.

"That doesn't work so well," Archimedes told him, embarrassed again. "I'm going to try something different on the next one."

Hieron raised his eyebrows, then turned the windlass. It was very stiff, and Kallippos had to help him, but between them they tilted the great catapult slowly back to its maximum elevation. "It works," said Hieron. "What were you going to do that was different?"

Archimedes explained an idea he'd had about a screw fixed to a wheel beneath the catapult. Kallippos made his hissing noise again and looked even more disbelieving. Screws had previously been used solely for holding things together.

Hieron's smile broadened. "I'll look forward to seeing that," he said. "But we'd better see how this one shoots before you start building the next one. I have to see it work before you can be paid, isn't that the arrangement?" He nodded to the fort captain, who nodded to the soldiers. One-talent ammunition had been brought up that morning, and now a sixty-pound stone was rolled over, and the catapult string was winched back with its fearsome groan, so that the missile could be set in its place.

Archimedes blinked: that groan had differed from the one the machine had made in the workshop- lower, more dissonant. "Wait!" he exclaimed. He went to one side of the catapult and struck the solid mass of twisted hair that formed its strings: they made a hollow sound. He ducked under the uptilted nose and struck the strings on the other side. Another hollow sound- but a deeper one.

"It's gone out of tune!" he cried in horrified disbelief. The strings had been fine that morning.

There was a displeased stir throughout the king's entourage. The catapult's drawstring was allowed to slip back so that the tension on the strings could be readjusted. Archimedes scrambled onto the stock, ran up the slide to the peritrete, and worked the bronze guard cap off the top of the set of strings which had produced the lower sound. Catapult strings were always twisted on a crosspiece which was then fixed into a bracket with wedges; the gear all looked fine, but when the two sets of strings were struck again, the difference in pitch was even more marked. Somebody handed up the heavy winding gear- windlass and crank- and Archimedes fitted it to the crosspiece without looking to see who. Hooking a leg around the frame to brace himself, he twisted the strings, secured them, then nodded to Elymos to strike the strings on the other side. Again, the deep note; he struck his own strings again- and they were still too low, and what was worse, the note slid downward as he listened to it: something was slipping. He frowned and checked the wedges: they were fine. He struck the strings again, and the note slipped even further.

He looked around for the king, and saw that Hieron was standing immediately beneath him: it had been he who had handed up the winding gear. Archimedes went red again. It was bad enough that his catapult should fail to work properly; worse that it should fail in front of the king; worst of all that the king should be a man who actually knew something about catapults. "I'm sorry, lord," he said miserably. "I think something's gone wrong with the lower fixture. The tension's slipping. I–I'm going to have to take the strings off and look, and then restring it."

Somebody sniggered. Archimedes glanced around, and realized that it had been Eudaimon.

Hieron merely looked commiserating. "Very well," he said. "Do that."

"I-it will t-take about an hour," stammered Archimedes, utterly mortified.

"No matter," said the king cheerfully. "I was planning to stop for some lunch anyway. Restring it, and we'll have the trial after I've eaten."

"Lord!" exclaimed Eudaimon, shocked and astonished. "The catapult doesn't work. Surely you're not going to waste any more time on it?"

Hieron fixed him with a bright smile. "Son of Kallikles, I'm not so ignorant of catapults as that!" he exclaimed. "Any catapult can go out of tune. We don't know yet whether this one works or not. After all, it's not as though we'd fired it and seen it hurl crooked, is it? Which, of course, it would have done if it had been fired while it was out of tune. Isn't it lucky that young Archimedes here has such a good ear for pitch? Most people wouldn't have noticed that there was a problem until it was too late. That would have been doubly unfortunate here, because he would have been dismissed, wouldn't he? Oh, but perhaps that event would have pleased you."

Eudaimon, for some reason Archimedes could not understand, went very pale. Elymos had gone pale as well. Archimedes himself was still red, too ashamed and embarrassed to worry about them. He began pulling out the wedges to get at the strings.

"I'll help," Eudaimon offered suddenly.

"No," said Hieron, still smiling. "I think not. Kallippos, you stay and help: tell me if you find anything. Eudaimon, you come with me, and explain to me why we have so many arrow-shooters and so few stone-hurlers on the walls." He snapped his fingers, and he and his entourage descended the stairs again, the fort captain hurrying ahead to arrange their meal.

Kallippos watched them go, rather grimly, then turned to Archimedes. "Tell him if I find anything!" he exclaimed. "What am I supposed to find?"

Archimedes was up to his elbows in catapult strings. "Mmpff?" he said.

Kallippos looked at him, saw that it was pointless to say anything, and set to work helping to unstring the catapult.

When the mass of brown and black hair was drawn out of the bore, a piece of metal about as long as a hand tumbled from the strands and clinked against the floorboards. Kallippos picked it up: it was a razor.

"Zeus!" muttered the chief engineer. He checked through the tangle of tresses and found the place where the razor had nestled. Some of the strings must have been cut as soon as the razor was thrust in among them, but most had started to go when the drawn bowstring pulled them against the razor's edge. It had been a subtle trap, meant to be undetectable until it was too late.

Archimedes stared at the razor for a moment- then looked at Marcus with a mixture of disbelief and accusation. He could think of no one else who would want to disable a Syracusan catapult. But Marcus was staring at the razor too, in outrage.

The stunned silence was broken by a wail. Elymos flung himself at Archimedes' feet. "Oh, sir!" he cried. "He must have done it last night! He must have just come in and shoved it in quick, while I was sleeping. It wouldn't have made no noise, and I was so tired I wouldn't wake."

Marcus' face suddenly darkened. "Tired! You were drunk, sack-arse! You wouldn't have noticed if someone had taken a god-hated ax to the machine!"

Elymos whimpered. "I was tired! We'd been working all day to get it set up, and there wasn't no crane. Please, sir"- turning back to Archimedes- "you tell Epimeles I did what he said, I kept near it, I slept right under it all night- but you know how tired I was."

"I don't understand," said Archimedes helplessly. "Are you saying Epimeles expected someone to sabotage my catapult?"

"I don't know anything!" cried Elymos frantically, realizing he'd said too much. If there was a judicial investigation of the incident, he could expect to be tortured- the law rarely trusted the testimony of slaves without torturing them first. "I just did what Epimeles said, sir, that's all!"

Archimedes stared, stunned. He thought of what would have happened if the catapult had failed. The strings alone would have cost him thirty drachmae and the wood… Epirot oak, imported, three drachmae a yard… and then there was the bronze, and the iron. He imagined going home and having to tell his family not only that he was unemployed, but that all his savings had been wiped out, just when the city perhaps faced a siege. "Delian Apollo!" he exclaimed, and sat down heavily on the catapult stock.

"I will show this to the king," said Kallippos, hefting the razor. "And you, fellow"- to Elymos- "you come with me."

Elymos gave another wail, and crawled forward to clutch Archimedes' knees in supplication. "Please, sir!" he begged. "Don't let them beat me!"

Archimedes recovered himself a little with a jump. "Let him alone!" he said.

Kallippos glared at him. Archimedes blinked back, then took a deep breath and said, "We still don't know if this catapult works, and if it doesn't, there's no point in worrying about the razor, is there? And if we're to test the catapult, I need this man's help to restring it."

Kallippos glared a moment longer.

"It's up to the king to say if he wants to talk to Elymos," Archimedes insisted.

Kallippos snorted, but he nodded. He stalked off down the stairs, the razor held gingerly between thumb and middle finger.

Elymos gave a long shuddering sigh of relief. Before he could say anything, however, Marcus strode over and clouted him on the side of the head so hard he knocked him over.

"Among my people," said Marcus in a low fierce voice, "a sentry who falls asleep on watch is beaten to death by the men whose lives he put in danger. You deserve to be beaten senseless! We were going to have pay for this brute ourselves if it didn't work!"

"Marcus!" protested Archimedes. "Leave him alone! We need to string the catapult." He got to his feet and began checking through the oily hair to see how much of it was salvageable.

When the king and his entourage reappeared about half an hour later, they found the catapult restrung, and Archimedes tuning it.

King Hieron looked as bright and interested as he had before, but Eudaimon was not with him. No one made any comment on the catapultist's absence, and no one said anything about the razor. Archimedes finished winding the strings and checked that the two arms of the catapult were at the same tension, and then the great machine was once more aimed and elevated. The string was drawn back, and the missile heaved carefully into place. Everyone stood well clear of the immense arms, which had folded back until they were almost parallel to the slide. Hieron sighted once more along the stock, then eased loose the trigger.

The Welcomer gave a deep bay- a sound made up of the hollow cry of the strings, the roar as the stone rushed along the slide, and the overwhelming crack as the arms hit the heel plates. The missile was gone too fast to follow, but when the watchers ran to the artillery port, they saw the stone falling black and heavy, far out in the chosen field. Hieron laughed and punched his palm with a fist. "Zeus!" he cried. "It's got the range of a machine half its size!" He circled a hand in the air to the others, and the catapult was reloaded. "Closer this time!" the king commanded, and the catapult was depressed, then fired again.

"Beautiful!" said the king. "Now, left a bit- right a bit- fire! Oh, beautiful!"

When the catapult had been fired about a dozen times, the watchers all stood back and grinned at one another. The captain of the Hexapylon was grinning nearly as hard as Archimedes. "Welcomer, you called it?" he said, stroking the machine's trigger. "By all the gods, after a welcome from this hero, the enemy will turn around and run!"

"I think we can all agree that this catapult has been seen to work," said Hieron contentedly.

Archimedes licked his lips eagerly. Now the money- and what was more important to reassure his family, the offer of a salaried position as a royal engineer.

But Hieron's next words were: "Can you build one bigger than this?"

"Oh!" Archimedes was surprised, but pleasantly so. He'd enjoyed making the Welcomer, but duplicating it would be much less interesting, even with the addition of a screw elevator. "Yes, of course. Um- how big?"

Hieron gave him a benevolent smile. "How big a machine could you build?"

"Well, I, uh…" He glanced around the catapult platform. "I mean, it's really a case of where you want it to go. I don't, uh, think you could fit anything bigger than a hundred-pounder on a platform like this."

There was an abrupt silence. Then Kallippos made his disbelieving hiss.

"Of course, if you, uh, put it on the ground," Archimedes continued awkwardly, "you could make a bigger one. I don't think you'd, uh, run into problems with the limits of the materials until you were over three talents. A three-talenter, though, would be a very big machine. It would take up a lot of supplies and you'd need, well, cranes and things"- he waved a hand vaguely in the air- "to load it, and it would be very hard to move it once you'd set it up."

"Could it be aimed, like this one?" asked Hieron quietly.

Archimedes blinked. "Well- might need tackle blocks. But you can move anything, with enough rope."

Kallippos shook his head. "Lord!" he protested to the king. "Nobody has ever built anything bigger than a two-talenter. Not even for Demetrios the Besieger or Ptolemy of Egypt."

"Hush!" said Hieron, still smiling genially at Archimedes. "Let me be sure I understand you. Are you saying there's no limit to the size of catapult you can build?"

"There are no limits in ideal mechanics," said Archimedes. "If you build something correctly and it doesn't work, that will be because your materials are too weak, not because the principles are wrong. It's like levers and pulleys. It is theoretically possible to move any given weight, however large, with any given effort, however small."

"So you say!" exclaimed Kallippos, now openly angry and indignant. "But I've never seen anyone moving a house with levers and pulleys!"

"With a place to stand, I could move the earth!" declared Archimedes.

"This is Syracuse, not Alexandria!" snapped Kallippos. "Earth, not Cloudcuckooland!"

"I could move a house, anyway!" Archimedes told him defiantly. "Or- or a ship."

Hieron was beaming now. "Would you say that's impossible, too?" he asked his chief engineer.

Kallippos divided one glare equally between Archimedes and the king, and nodded.

Hieron turned to Archimedes. "But you say you could do it?"

"Yes," Archimedes replied without thinking. "With enough rope."

"Then do it," ordered the king. "I want to see it. Do me a demonstration of ideal mechanics. I authorize you to use any ship, any of the royal workshops you like, and all the rope you want. Butcatapults." He slapped the Welcomer. "Get Eudaimon to copy this, if he can- by the way, he's under your orders now. He's taking the rest of today off, but he should be back in the workshop tomorrow. If he isn't, or if he gives you any trouble, inform me. Correct any mistakes he makes, but otherwise let him supervise the actual labor; I want you to concentrate on a hundred-pounder. Three hundred-pounders, in fact, but I hope that Eudaimon will be able to copy those as well, once you've built the first of them. When you've finished the first one, you can start thinking about that three-talenter. No, make it a two-talenter- we don't have time for cranes. Don't postpone your demonstration to work on it, though. I do want to see you move a ship single-handed."

Archimedes blinked stupidly. He felt flattened. He had no idea what to say.

"Oh," added the king, "and my sister tells me that you're a very fine aulist. Perhaps you'd care to come to dinner at my house tomorrow, and bring your instruments?"

Archimedes felt his face going hot again. He opened his mouth, closed it when no sound came out, then tried again. "Uh, yes," he gasped, "thank you, O King."

"Excellent!" said Hieron. "Well, then, you'd better go see about your demonstration and the catapults- and I must go review the other forts. Do give your father my best wishes. Does he have a good doctor?"

"I–I," stammered Archimedes, "I think so."

"If you like, I'll send my own doctor around to have a look at him." He snapped his fingers at his secretary. "Remind me to do that. Well, then, I wish you joy!"

King Hieron turned and began to descend the steps. Marcus hurried over to Archimedes. "Sir!" he hissed in his master's ear. "The money!"

"Lord!" shouted Archimedes, and Hieron turned back with a look of mild inquiry. "Uh, Lord, I… I was supposed to be paid when the catapult was seen to work, and there was… that is, I thought there would be a salaried job."

"Ah," said Hieron. "A job. Do you mind if we leave the question of your job aside for the time being? I'm not at all sure what would be appropriate."

"You said Eudaimon was under my orders," Archimedes said faintly. "Won't he- I mean, he has a salaried position- doesn't he?"

"Indeed he does," said the king. His dark eyes flicked momentarily to Elymos, and he added, "And you, slave, can tell your foreman that much as I appreciate his taste in catapults, it was very stupid of him to expect me to sack a catapult engineer when I'm expecting a siege. Eudaimon stays as long as he obeys orders from Archimedes- which I think you'll find he's now willing to do. I wish you joy!" He turned and went on down the steps without looking back. His entourage, with various looks of speculation, curiosity, and doubt, gathered itself up and followed him. Kallippos was the last to go; he hesitated for a long minute at the top of the stairs, looking at Archimedes with a strange expression. It was no longer a glare, but something quite indefinable: anger was still there, but also pity, and perhaps even admiration.

He said nothing, however, and when the others had descended, he at last looked away and followed them.

Archimedes sat down heavily on the floor beside his catapult. "Am I a royal engineer or not?" he asked no one in particular.

"He hasn't paid you a copper," said Marcus sourly. "I'd say you're not."

"But he ordered more catapults," said Archimedes wonderingly, "and a demonstration. And he asked me to dinner." To dinner, and a bit of music. Would Delia be at the dinner? No: respectable women didn't go to dinner parties with men. But perhaps he would see her? He might even get another chance to play music with her. Delicious thought!

He smiled up at the two slaves, and found that they were both staring at him as though he were a dangerous dog. He blinked.

"I'd like it better if he'd paid you," said Marcus bluntly. "You're owed fifty drachmae, and he hasn't agreed on a price for any of the rest. Sir, you-"

"Can you really move a ship single-handed?" interrupted Elymos.

Archimedes suddenly beamed. He had always wanted to see how much weight one man could shift with an unlimited supply of rope, but nobody had ever before offered him the rope. He jumped to his feet, consumed with eagerness. "Elymos," he ordered, "you go back to the workshop and tell them the Welcomer passed. Tell them to get out the wood for another one-talenter, in the same amounts as before, and tell them that I'll be ordering the wood for a hundred-pounder tomorrow. Marcus, you go home and give them the news."

"Where are you going?" Marcus demanded suspiciously.

"Down to the docks, to see about my demonstration!" And he ran off down the steps, bright-eyed and smiling.

Marcus groaned. "Demonstrations of ideal mechanics!" he said in disgust. "Dinners and music!" He kicked the catapult stand. "What am I supposed to tell them at home? He's agreed to work for nothing!"

"Epimeles isn't going to like this," moaned Elymos. "He thought that once they fired the Welcomer, Eudaimon would go. And Eudaimon must know that!"

"It was Eudaimon who put that razor in the strings?" asked Marcus.

Elymos nodded. There seemed no point in lying about it now, to another slave.

"So that my master wouldn't get his job?"

Elymos nodded again. He was not surprised that Marcus had guessed this. His own life centered on the workshop, and he tended to assume that everyone knew about things- like Eudaimon's incompetence- which were important there.

Marcus stood still a moment, thinking. It was clear to him now that the king had expected the attempt at sabotage: he had hinted as much, and Eudaimon at least had understood. When Eudaimon offered to help restring the catapult, Hieron had refused him any opportunity to conceal the evidence of his crime; instead, the king had posted Eudaimon's superior as a witness. But as soon as the razor reached Hieron, it and Eudaimon had both disappeared, and the only result of the incident seemed to be that the king now expected Eudaimon to obey Archimedes without argument.

The only conclusion was that the king had enough evidence to charge Eudaimon with treason, but was using it to blackmail him instead. Why? And why hadn't the king given a job to Archimedes? Marcus began to chew on his lip. Hieron had a reputation for cunning, for unexpected twists of policy and unforeseen alliances. He had risen to power through the army, and yet had never used violence to get his way. He had never needed to: Syracuse had given him everything he wanted, though afterward she had sometimes found herself confusedly wondering why. Marcus had a sudden suspicion that he had just witnessed two demonstrations of supreme ability that day: one of technical competence, by Archimedes, and the other of manipulation, by Hieron. He had no idea what Hieron's manipulations were supposed to achieve, but he felt uneasily certain that they weren't finished yet and that his master was in the middle of them. Why?

There was a sound of footsteps on the stairs, and Straton hurried up, holding a letter. He glanced round the catapult platform, then looked irritably at Marcus. "Where's your master?" he demanded.

"Gone into the city to see about arranging a demonstration of ideal mechanics," said Marcus bitterly.

"He should have waited for the authorization for it!" said Straton, flapping the letter. "Where's he off to? The naval docks? Herakles! Does he really think he can move a ship single-handed?"

"Yes," replied Marcus. "You want to bet he can't?"

Straton looked at him, tapping the letter uncertainly against his hand.

"You owe me a stater," said Marcus deliberately. "You want to try to win it back?"

Straton sucked his teeth. "I don't owe you anything! The bet was that your master would be offered the job of whoever was in charge of whatever he was set to do. Eudaimon still has his job."

Elymos gaped at them.

"You're quibbling," said Marcus. "Eudaimon was in charge of catapults. Now Archimedes is in charge of catapults- isn't he?"

Straton shrugged uneasily. "King Hieron hasn't said."

"No," agreed Marcus sourly. "King Hieron hasn't even said whether he's going to pay my master the fifty drachmae that are owing to him. But the whole sense of our bet was that my master's war machines would be better than anyone else's. Now you know that's true- so pay up!"

Straton cast an embarrassed glance at the Welcomer. For all his ignorance of catapults, he was aware that this one was exceptional. He sighed, and fumbled in his purse.

"Of course," said Marcus, with deceptive casualness, "if you like you can add another stater to your stake, and bet that Archimedes can't move a ship single-handed."

Straton frowned, hesitating, staring at Marcus. Then he shook his head. "I'm not betting against your master again," he declared. Then suddenly he grinned and flipped Marcus the Egyptian stater. "Here," he said. "Take it and good luck. I know how to get it back! I'm going to lay Philonides odds of three to one that your master shifts that ship, and I don't doubt for a minute he'll take 'em!" He slung his spear over his shoulder and hurried off with the letter, still grinning.

Marcus scowled as he put the stater in his own purse. He had expected to enjoy winning that bet, but the image of the of the king's bright smile hung in his mind and soured the pleasure. Jobs were one thing: you knew what you were expected to give and what you could expect to receive. What Hieron was offering was undefined, and who knew what he might want in return for it?

"You bet that soldier that your master would be offered the job of any engineer he was set under?" asked Elymos, into the heavy silence.

"That's right," said Marcus shortly.

"Kallippos is good," said Elymos doubtfully.

Marcus shot him a look of irritation. "As good as Archimedes?"

Elymos looked at the Welcomer. Then he shook his head. "I suppose not," he said wonderingly.

For some reason, Marcus was even more irritated, and suddenly eager to get home. He glanced around the catapult platform once more, and noticed Archimedes' cloak lying abandoned in a crumpled heap under the artillery port. He went to pick it up, then paused and gazed out at the road north.

The king expected a siege. "It was very stupid of him to expect me to sack a catapult engineer," he had said, "when I'm expecting a siege." Soon, perhaps, a Roman army would be encamped there, in that field before him where goats browsed now. Marcus shut his eyes and imagined the camp: the neat squares pitched within an entrenchment, the campfires smoking, the sound of voices speaking in Latin. There was a bitter surge in the back of his throat. He had heard no Latin spoken for thirteen years now. Soon the Romans and their allies would be here: his own people. They had come to Sicily in a bad cause, and they threatened the city which had become some kind of home to him, the people he had come to care about. If they conquered, he would probably die. But they were his people still. He glanced up unhappily at the menacing shape of the catapult beside him, and reflected that if he were really loyal to his own, he would cut Archimedes' throat.