The Sand-Reckoner

4

Archimedes stood staring at the regent stupidly, his mouth still open. The girl, however, was unalarmed. "Good health, Father!" she exclaimed, smiling at Leptines. "This gentleman plays the aulos. He was telling me a way to play the intermediate notes."

The regent was not appeased. He was a tall man, grim-faced and gray-haired. He stopped beside the fountain and gave Archimedes a scathing look.

Archimedes went crimson. He realized afterward that he probably should have been frightened, but at the time he was just excruciatingly embarrassed. Of all the idiotic ways to lose a job! "I, uh, I didn't know who was playing," he stammered defensively. "I didn't even realize it was a woman. I just, uh, heard the music, and I thought I'd share a trick with a fellow aulist. I didn't mean any disrespect, sir."

The regent appeared somewhat mollified at this, but he still asked icily, "Do you normally wander about the private parts of other men's houses uninvited, young man?"

"We're not in a private part of the house, Father!" exclaimed the girl. "We're in the garden."

"Delia, that's enough!" said Leptines severely. "Go to your rooms!"

Delia, thought Archimedes, stupidly pleased, even in the middle of everything, to have learned her name. He could not have asked it: it was almost as improper to ask a young lady's name as it was to talk to her unsupervised. Delia. "The Delian" was one of the titles of Apollo, the god most closely associated with mathematics. It seemed a good omen that the girl was named for his own patron divinity.

Delia did not go to her rooms; instead she wriggled more firmly into her place on the rim of the fountain. "I will not go if you're going to pretend I was doing something improper!" she snapped.

Archimedes was somewhat taken aback by this defiance, and more surprised still when Leptines merely rolled his eyes in exasperation and turned away from her. Girls were supposed to be obedient, and the heads of household were supposed to punish them if they weren't. But, of course, Leptines was not the head of Delia's household. Though she was calling him "Father," that was only courtesy: the regent was in fact merely her half brother's father-in-law, and it was her half brother who held the real authority.

"I wasn't doing anything wrong!" Delia insisted. "I was just sitting in the garden trying something tricky on the flute, and this young man- Archimedes, was it? — came up and gave me a tip on how to do it better. Herakles! Where's the impropriety in that?"

The regent looked even more exasperated at this, so Archimedes said, "I am sorry, sir. I, uh, I realize now it was improper of me to have intruded here uninvited, and I, uh, sincerely apologize for doing so. But, as I said, I had no idea who was playing, and at the time it seemed natural to share a trick with a fellow aulist."

"Very well," said the regent stiffly. "I accept your apology."

And that, surprisingly, seemed to be the end of the matter. Dionysios caught Archimedes' eye and raised his eyebrows: Archimedes was uncertain whether the look was congratulatory or sympathetic. But he decided that it could not have been the captain who had called his name in that disapproving fashion; it must have been the exalted doorkeeper. He glanced at the doorkeeper, who still looked deeply disapproving, then at the fourth member of the party. This was a man of perhaps fifty, of average height, with graying brown hair and a deeply seamed face. He was dressed in a dusty cloak worn over a workman's apron, and he was scowling at Archimedes more ferociously than any of the others.

"Archimedes son of Phidias," said Leptines, still very stiffly, "I understand that you came here this morning looking to serve the city as an engineer."

"Yes, sir," agreed Archimedes earnestly. "Captain Dionysios said you wanted someone to build some stone-hurlers. I'm sorry if-"

"And I understand," Leptines interrupted, "that you claim to be able to build a one-talent catapult, although you have never, in fact, built any war machine at all."

Delia looked surprised; Archimedes was aware of it, and shot an apologetic glance toward her before replying, "Uh, that's right. You, uh, don't have to have actually built one so long as you understand the mechanical principles."

"Conceited rubbish!" exclaimed the workman, scowling still harder. "Experience is the most valuable part of mechanics. You have to develop a sense of how to do things, a wisdom in your hands. That comes only from making machines."

Archimedes looked at the workman again, and the workman glared back. The others were now watching the two of them, the regent and his doorkeeper like judges, Dionysios with an air of expectancy, and Delia as though she were intently following a play.

"Sir," said Archimedes respectfully, wondering who the workman was- he hoped not Eudaimon, the man in charge of providing the city with catapults, though he rather feared just that. "Sir, it's true that you have to have made machines to be able to make machines. I wouldn't quarrel with you on that. But you can't possibly mean to say that before you can make a particular type of machine you have to have made it already!" Delia grinned, and he was encouraged to continue. "I've made lots of machines. I know what works and what doesn't. As for catapults, I've seen them and studied them and I'm perfectly sure I can make them. I wouldn't be here otherwise. Didn't Captain Dionysios say that you don't have to pay me until you've seen the first catapult work?"

"Waste of wood, strings, and workshop time!" snarled the workman. He turned to Leptines. "Sir, you should throw this arrogant young fool out!"

"I would throw him out," said Leptines impatiently, "if you could promise to produce the catapults the king wants. But since you have failed to, and since he says he can, I am bound to let him try."

The workman's jaw set with indignation. So, thought Archimedes unhappily, the man was Eudaimon- and he plainly viewed Archimedes' appointment as an insult and a threat. The new job wasn't looking very secure.

But the regent turned back to Archimedes and said, "I am willing to authorize you to use the royal workshop to build a one-talent catapult. However, in view of your lack of experience, I am going to insist that if your machine doesn't work, not only will you not be paid for it, but I will require you to reimburse the workshop for the materials you have used."

"That's not fair!" Delia broke in indignantly. "The materials could be reused by somebody else!"

"Delia, be quiet!" commanded the regent.

"No!" she said angrily. "You're being unfair to him because he talked to me. You can't expect me to sit quiet for that!"

She cast a concerned glance toward Archimedes. He did not know what to feel in response: it was pleasing that she was worried about him, but humiliating that she so clearly expected him to fail. He pulled himself up straight, tossed his stained cloak back, and declared boldly, "Please don't be concerned, lady! My machine will work, so I don't mind agreeing to pay for the materials if it doesn't."

Eudaimon laughed harshly. "I hope you have money!" he told Archimedes. "Do you have any idea how much wood and string a one-talenter will need?"

"Yes, I do," said Archimedes triumphantly. He took his sheet of calculations from his purse again, unfolded it, and offered it to the regent. "Here are the estimates."

Leptines stared at the papyrus with surprise, not touching it. Eudaimon, however, glared harder than ever, then snatched the sheet. "What is this nonsense?" he demanded, scanning it. "There's no way you could know what the diameter of the bore of a one-talenter should be! There isn't such a machine in the city!"

"The Alexandrians have come up with a formula," said Archimedes with satisfaction. "You probably wouldn't know it, because it's still new, but they did a lot of trials on it and it works. You take the weight to be thrown, multiply it by a hundred, take the cube root, add a tenth, and you get the diameter of the bore in finger-breadths."

Eudaimon sneered. "And what in the name of all the gods is a cube root?" he asked.

Archimedes blinked, too astonished to speak. The solution to the Delian problem, he thought, the keystone of architecture, the secret of dimension, the plaything of the gods. How could someone who was supposed to build catapults not know what a cube root was?

Eudaimon gave him a look of stark contempt. Then, deliberately, he crumpled up the sheet of papyrus, pretended to wipe his backside with it, and dropped it on the ground.

Archimedes gave a cry of outrage and jumped to rescue his calculations, but Eudaimon set his foot on the papyrus, and he was left tugging at the edge which stuck out from under the imprisoning sandal. "You think that you can make catapults because you know mathematics?" the chief catapult engineer demanded.

Archimedes, kneeling at his feet, still tugging at the crushed sheet, glared up at him. "Yes, by Zeus!" he exclaimed hotly. "In fact, I'd say it's perfectly evident that a man who doesn't know mathematics can't make catapults. You don't, and can't, or I wouldn't be here!"

Eudaimon, infuriated, kicked at him. The gesture was meant more as a threat than with any real intention of hitting him- but as soon as the foot shifted Archimedes lunged for his calculations, and the kick caught him squarely in the right eye. There was an explosion of red and green which seemed to lance up into his brain, and he collapsed, stunned. He clasped at his face with both hands and rolled back and forth on the ground, gasping with pain. Then he became fuzzily aware of people clustering around him and someone trying to pull his hands away from his face.

He had the papyrus in one fist, and he resisted.

"Come on!" said a man's voice- Captain Dionysios, he realized. "Let me see your eye."

At that Archimedes lowered his hands- though he kept firm hold of the papyrus- and Dionysios examined the injury gently. "Try to open your eye," he said. "Can you see?"

Archimedes blinked at him: the captain's face swam, clear on one side, blurred and reddened on the other. He groaned and put a hand over the blur. "Not clearly," he said. "You look red."

Dionysios sat back on his heels. "You're lucky. You could have lost the eye. No permanent harm done, though." He slapped Archimedes' shoulder and stood up.

Archimedes pulled himself up to a sitting position against the side of the fountain and nursed his eye again; it hurt. "By Apollo!" he muttered. He found Eudaimon with his good eye, standing back and looking embarrassed, and gave him a glare.

Delia suddenly bent over him. Without a word she slipped the crumpled papyrus out of his fingers and gave him a wet lump of leather instead. The cool wetness against his burning face was indescribably comforting. "Thank you!" he told her gratefully.

She noticed, however, that his good eye followed her a moment, and returned to the others only when he saw that she was not doing anything with his calculations.

The men began upon the incident's aftermath- Leptines rebuking Eudaimon; Eudaimon protesting that it had been an accident; Dionysios suggesting that he take his protege out, and the protege himself trying to get back to the subject of making catapults. Delia stood back and allowed them to get on with it. She uncrumpled the cracked piece of papyrus and looked at it. Itheld a drawing of a catapult, labeled with measurements, done in a precise and careful hand. She turned the sheet over: on the other side, in the same careful hand, were less intelligible sketches- cylinders, curved lines cut by straight ones, pairs of letters joined by squiggles or arrows- and some of the same numbers that had adorned the catapult. She frowned, then looked back at the young man propped up against the side of the fountain. Until that moment she had not really noticed him. She had been interested in what he told her about the intermediate notes on the aulos and excited by the water-aulos; she'd been pleased because he'd continued to speak to her naturally even after he'd discovered who her brother was; she'd been concerned that she might have got him into trouble. But she hadn't had any interest in who he was. Now she felt as though she'd stubbed her toe on a rock, and looked down to find that it was part of a buried city. He had guarded these incomprehensible squiggles more jealously than his own eyes, and she wondered what kind of mind would order its priorities so strangely.

Dionysios helped Archimedes to his feet; Leptines asked him if he was all right; Archimedes swore that he was. There was more discussion of catapult-making, and finally a price was set for the finished catapult if it worked- fifty drachmae. When this point had been resolved, Delia stepped forward and handed Archimedes his sheet of calculations. Archimedes bowed unsteadily, still pressing the wad of wet leather to his eye, wished the company joy, and wobbled off toward the door. Captain Dionysios followed him, caught his arm, and helped him out.

Delia waited. Leptines turned to her- then gave a sigh of resigned exasperation and strode off without saying anything. She had never been obedient, and he had long before given up trying to discipline her. Eudaimon bowed and stalked off in the opposite direction. The exalted doorkeeper waited until regent and engineer were gone, then crossed his arms and looked at Delia with his usual disapproving expression. "You want something," he said.

Delia felt herself flushing. The doorkeeper's name was Agathon, and he was a shrewd, sour man who missed nothing. He was a slave, but he had served her brother, Hieron, long before Hieron was a king, and his loyalty had won him an influence free men could only envy. Delia disliked his habit of guessing that she was going to ask him something before she asked it, but, like Hieron himself, she tolerated it because Agathon always knew more about what was happening in the city than anyone else in the house, including the king.

"Yes," she admitted. "That young man who was here- I want to know more about him."

Agathon's disapproval grew heavy enough to press olives. "A fine thing to ask!" he exclaimed. "The king's sister wants to know more about some brash young flute player!"

Delia made an impatient gesture. "Herakles, Agathon, not like that!"

"You, mistress, have no business being interested in wine-stained engineers!"

Delia sighed. "If Hieron were here, he'd be interested," she said.

Agathon's disapproving look lightened a little, and his eyes narrowed. "Eh?"

"Two things," said Delia, picking up her auloi and resting her chin on them. "First: he's confidently offered to make a bigger catapult than any machine in the city, even though he's never made a catapult before. You don't think that would interest Hieron?"

"Mmm," said Agathon, and waggled the fingers of one hand a little to show doubt. "There's no shortage of ignorant and conceited young men."

"Maybe- but before you and Father came up, he was talking about catapults as confidently as he talked about auloi- and he knew auloi, Agathon: even you have to admit I couldn't be fooled on that."

"Boasting," said Agathon shortly. "Like many another man faced with a pretty girl. Second interesting thing about Archimedes son of Phidias?"

"He loved those calculations better than his eyes."

Agathon gave a sudden snort of laughter. "True son of his father, there. Phidias is supposed to have claimed that Euclid's Elements is a greater book than Homer's Iliad, and to have sacrificed to the gods in gratitude for some mathematical observation of the stars."

"You know something about him?"

"Most of Syracuse has heard of Phidias the Astronomer. Bit of an eccentric, bit of a reputation, see? Teaches, too: only man in the city who teaches advanced mathematics. The master studied with him for a little, oh, must be fifteen, twenty years ago now."

Delia stared. To Agathon, "the master" was always and exclusively Hieron. "I didn't know that!" she exclaimed.

"Why should you?" asked Agathon. "Long time ago, before he bought me, even. But the master's said a couple of times he wished he'd had more time to study mathematics with Phidias. He only had a couple of months, see? Then your father stopped paying the fees, and the master went into the army. I doubt Phidias even remembers him."

Delia nodded: she'd long known the story of how her father had paid for his bastard's education, but only until the boy was seventeen. Hieron had then been a year too young to join the army, but he'd been thrust into it anyway, and left to make his own way in the world- with spectacular results. "So why does Hieron regret not having studied longer?" she asked. "Was Phidias a very good teacher?"

"Don't think so," said Agathon. "No, it's that mathematics is useful to kings. War engines, surveying, building, navigation…" Agathon trailed off, staring at Delia, then lost his disapproving look completely and uncrossed his arms. "Very well!" he exclaimed. "You're right: he'd be interested in Archimedes son of Phidias. If that fellow's confidence is well founded, he's valuable."

Delia nodded.

"I'll see what I can find out," said Agathon. Then he looked at Delia again and asked, "And?"

He'd done it again. Delia sighed. "How much would you trust Eudaimon?" she asked.

"Ah," said Agathon, face relaxing to something as close to geniality as it was ever likely to attain. "You mean, do I think he's going to try to sabotage your dusty musician's one-talent catapult?"

Delia didn't answer for a moment. To suggest that Eudaimon would deliberately disable a machine which was potentially of great value to the defense of the threatened city was to accuse him of treason. "I don't know him very well," she said at last, humbly. "Father's been cursing him ever since Hieron went away, he's obviously furious to have a rival, and I don't like him- that's all."

Agathon shrugged. "He's a man that's worked all his life and never been much good at what he works at. He's the worst of the master's engineers, which is why he's here and not at Messana. He's bitter and he's tired, he's getting old, and he's clinging to his position by his fingernails. He doesn't want some Alexandrian-educated mathematical flute player traipsing in and showing him up- that much is certain. And I think he'll convince himself that that catapult would fail anyway, but still want to make sure it does. Yes, I think if he gets the opportunity to sabotage that catapult, he'll take it. You want me to ensure he doesn't get that opportunity."

"Isn't that what Hieron would want you to do?" she asked innocently.

Agathon gave another snort of laughter. "You and the master!" he said affectionately. "I don't know where it comes from. Can't be from your mothers, because you don't share 'em, but it can't be from your father, because he was a fool."

Delia smiled and got to her feet. "Can you do it?" she asked eagerly. "Without actually accusing Eudaimon of anything, I mean."

"Oh, yes!" said Agathon comfortably. "Few words in the ear of the foreman at the workshop. He knows who I am. He'll keep an eye on the catapult and Eudaimon both, and report anything suspicious. You want me to have a word with the regent as well?"

Delia nodded. "But," she added nervously, "don't tell him I…"

"…have any interest in wine-stained players of the aulos. No."

"It would be misunderstood," said Delia, blushing.

"I hope so," said Agathon, with a return of the disapproving look. "I certainly hope that what he understood would be mistaken."

Dionysios son of Chairephon helped Archimedes from the king's house as far as the temple of Athena on the main road. There he stopped. "I'm headed for the barracks," he said, gesturing to the left, "but I think you'd better go home and lie down for a bit," gesturing right, toward the Achradina. "Eudaimon caught you pretty hard."

"He's a bugger-arsed idiot!" said Archimedes, with deep feeling. "By Apollo! Builds catapults and doesn't even know what a cube root is! Who's the real engineer for Syracuse?"

"Kallippos," said Dionysios at once. "A gentleman of good family and better skill. But he's with the king at Messana. The king thought Eudaimon could manage what there was to do here in the city, but there was more to be done than we realized. Wait here- I'll call your friend Straton and tell him to help you home."

Archimedes shook his head- cautiously, because his eye hurt if he moved it suddenly- and began turning his lump of wet leather to find a cool spot in it. "I'd rather go to the workshop and order my wood," he said. The leather suddenly unfolded and revealed itself as a long wide strap. Archimedes blinked at it: it was a shape he knew well. "Oh," he said blankly. "She's spoiled her cheek strap." Then he realized that he now had an excuse to see her again- to give her a new cheek strapand despite the ache in his eye, he beamed. He folded the leather carefully and set it tenderly back in place.

"Do you really play the aulos?" asked Dionysios curiously.

"Of course I do!" said Archimedes, surprised. "You don't think the king's sister would have spoken to me for two seconds otherwise, do you?"

"I hoped not," replied Dionysios, relieved that his new associate realized when a girl was out of reach. "And, my friend, you should not have spoken to her at all. When I saw you chatting with her there in the garden, I not only expected you to be sent off at once, but I thought I was likely to be in trouble myself for inviting you there in the first place. Nai by Zeus, you were lucky you confined yourself to flutes! Well, if you're really going to the workshop, I can show you the way: it's right next to the barracks."

The royal catapult workshop was a big dirt-floored barn near the tip of the Ortygia promontory, secured by the same enclosing wall as the barracks of the Ortygia garrison. It was full of beams and presses and saws, and a forge jutted from one wall. The sides were stacked high with timber and iron, bronze and copper, oily boxes of sinew and of women's hair- the last the most favored material for stringing a catapult, a source of sorrow to slave girls and useful income to poor women. About a dozen people were busily at work about the room, some clustered around an arrow-firing catapult which stood half assembled in the center of the building, others making catapult bolts and heel plates. There was a smell of sawdust, glue, charcoal, and hot metal. Archimedes stopped in the doorway and took a deep breath of the scent, then smiled: it was a good smell, the smell of making. He wished Dionysios joy and strode forward eagerly to find the foreman and place his own order for wood.

Marcus spent most of that day digging out the latrines- a job too heavy for young Chrestos to manage easily on his own, and thus one which had been postponed since the beginning of the summer. In the Sicilian heat the delay had made the job even fouler than it would have been ordinarily, but he set about it stoically, and carted the night soil off on a borrowed donkey.

At evening, when he returned from dumping the last load, he found his master in the sickroom, just arrived back, cloakless, with an aulist's cheek strap tied over one eye, but enormously cheerful. A knot of unease that had been situated somewhere between his shoulders unraveled. He was only too keenly aware of what would happen to the household slaves if the young master failed to get a job.

Archimedes was happily telling the assembled family about the royal catapult workshop when Marcus came silently to the door. "They weren't very helpful this morning. They just pointed me at the stores and left me to my own devices. I thought that was fine- you should see the stores! Top-quality Epirot oak in any thickness you like, and a dozen sorts of glue! But about noon the king's doorkeeper came in to check that I had everything I needed, and after that they realized I was official. After that they set about doing anything I asked. It's amazing how much it speeds things up. I thought it was going to take me a month to make this catapult, and I was cursing the pay. But with this sort of help I can do it in a week."

"But how much is the pay?" asked Philyra anxiously. Marcus looked at her approvingly: it was what he was very anxious to know himself, but hadn't quite dared to ask, in front of his owners and still stinking of latrines.

"Fifty drachmae," said her brother, with satisfaction.

"Fifty!" cried Philyra, her eyes lighting. "Medion, fifty in a month would be good pay; fifty in a week…!"

Archimedes nodded, grinning. He had not thought fifty a month good pay, but he supposed he'd been spoiled by the water-snails.

"You don't have to pay for the supplies out of that?" asked Arata anxiously.

Her son nodded. "I don't need to pay for the supplies unless the machine doesn't work. And you don't need to worry about that, Mama: I know what I'm doing."

Marcus frowned, suddenly anxious again, and Philyra caught some restless movement he made and glanced over. Their eyes met, and each recognized in the other the same anxiety: how much did the supplies for a one-talenter cost? This worry, however, was almost immediately eclipsed. "What happened to your eye?" asked Arata, and Archimedes told them about Eudaimon, then, obedient to their urging, took off the cheek strap.

The area around the eye had by this time turned blue-purple and swollen up, and, even worse, the white of the eye itself had turned red, and a veil of blood hung across the light brown iris. "Medion!" cried Philyra in horror. "You ought to sue him for assault!"

Archimedes just shrugged. "I'm going to stay away from him as much as I can," he said.

"Absolutely right," said his mother approvingly. "He's senior to you, and you don't want trouble." She frowned, sniffed, and glanced around at Marcus. "Oh, it's you," she said. "Go and wash."

Marcus bobbed his head and retreated back into the courtyard. He was engaged in cleaning himself when Philyra came out of the old workroom, still frowning. She paused when she noticed him, then came over resolutely. Marcus at once pulled his dripping tunic back on, embarrassed to be naked in front of the young mistress.

"How much do the supplies for a one-talent catapult cost?" asked Philyra.

"I don't know," Marcus admitted. "The strings would be the worst of it. They sell prepared hair by the drachma weight, and for a one-talenter you must have to buy it by the pound."

Philyra was silent for a moment. "He can build it- can't he?" she asked at last.

"He's good," said Marcus flatly. "He can."

Philyra studied him a moment, then let out a long unsteady breath. "I don't know anyone else who makes machines."

He nodded; naturally she had no way of judging her brother's skill. "In Alexandria," he informed her, "the best engineer in the city offered him a partnership. He wouldn't take it, of course- it wasn't geometry- but he could have had it if he'd wanted. He's exceptional. This fellow Eudaimon's absolutely right to be worried. Mistress, the only worries I have are about what happens if something outside your brother's control goes wrong."

She let out another long breath, looking at him closely, trying to determine how far she would trust his word. Then she smiled, relaxing. "Medion left his cloak at the workshop."

"At least we know where he left it," said Marcus. "In Alexandria I was always having to run all over the Museum looking for it."

She giggled. The sweet soft sound seemed to bubble a moment in his heart. "Fifty drachmae a week!" she repeated reverently, smiling over it. "We could buy back the vineyard! And I…"

She stopped herself. The vineyard sold to pay for her brother's Alexandrian education should have been her dowry, but she had always tried very hard not to acknowledge that painful fact. Her father, she knew, had hoped to save a new dowry for her from his earnings, but his savings had all been eaten away during his illness. She was of an age to marry, she had school friends who were married already, but with no dowry she was unlikely to find a bridegroom. That was a humiliation she tried not to think about, and not the sort of thing a young lady should confide to a household slave. She scowled at Marcus, who was waiting, his face open and alive, for her to finish her sentence.

Marcus abruptly understood how that sentence would have ended, and busied himself by bending down for his bucket of dirty water. Of course. He had silently disapproved of the vineyard sale precisely because it had seemed to him to cheat the daughter of the house of an essential in order to pay for a luxury for the son. But now he found that he was in no hurry to see Philyra dowried and married off. He would miss her. No need to worry yet, though. It would take some time to amass a dowry for her, even at the rate of fifty drachmae a week. And with the war…

He was determined not to think about the war. "If you'll excuse me, mistress," he muttered, and went to tip the water over the scraggle of pot herbs by the door. Philyra watched him a moment in surprise, taken aback by the way he had pulled off a sore subject unprompted. She had not thought he had either the sensitivity or the wit.

The following morning Archimedes set off early for the catapult workshop. Philyra, setting out to do the shopping about midmorning, found only Marcus in the courtyard: Agatha, who normally accompanied her, was helping her mother in the kitchen, and the boy Chrestos had exercised his talent at making himself scarce when he was needed. She looked at Marcus a moment, thoughtfully, then clapped her hands to summon him over and handed him the basket.

Walking behind her along the narrow street in the morning sun, looking at her straight back, respectably swathed in a white woolen cloak, Marcus found his steps light with an unaccustomed happiness. Philyra was starting to trust him a little. He prayed silently that the gods would offer him the opportunity to prove his honesty. He kept his eyes firmly shut to the reason he wanted her good opinion: there was nothing to be had there, except pain. Getting that good opinion, winning her trust and liking- that was a pleasure no one could deny him.

They went first to the baker's, and then to the greengrocer's shop around the corner. The groceress, a thin shrewish woman named Praxinoa, looked at them warily. Philyra bought some leeks and some olives, and paid for the goods with one of her brother's Egyptian silver pieces. The groceress studied the money a moment before putting it in her box and taking out the change. "How's your brother settling in?" she asked Philyra, with an eagerness that surprised the girl.

"Very well," Philyra told her; then, eager for the neighbors to appreciate the family's improved status, went on, "He's found work already. He's building catapults for the king."

"Catapults, is it?" asked the groceress. "Huh." She glanced around, then leaned closer to her customer and said in a low voice, "Perhaps that explains it, then. I had a fellow in here just before you came, asking about your brother."

"What?" asked Philyra, startled and alarmed. "Who?"

"I don't know who," said Praxinoa, with relish. "Never seen him before. He wasn't anybody from the neighborhood. He was smartly dressed, though. Official, I thought. Must be because of those catapults. They're strategic, aren't they?" Her eyes glittered, hungry for scandal.

"Yes," said Philyra, trying to sound resolute, though her heart had speeded up. In Syracuse, official interest could be very, very dangerous. "They probably ask about everyone who works in the catapult workshop."

"They do in Alexandria," put in Marcus dismissively. "Saw it there, too."

Praxinoa subsided, disappointed. "Learned about catapults in Alexandria, did he?"

Outside the shop again, Philyra looked at Marcus angrily. "You think it really was somebody from the king, because of the catapults?"

"I can't think of anything else it would be," Marcus told her.

Anger gave way to anxiety- and embarrassment at asking advice from a household slave. "Did people come and ask about him in Alexandria too?"

Marcus shrugged. "No. But in Alexandria he wasn't allowed in the royal workshops. King Ptolemy thinks a lot of his catapults, and never allows foreigners anywhere near 'em. Archimedes looked at some machines on the wall with his engineer friend, that was all. But catapults are strategic. I don't think this is anything to worry about."

Philyra nodded, but she was still frowning as they walked on. Phidias had never attracted any disquieting official interest. Of course, Phidias had never earned fifty drachmae in a week, either. Things were changing. She wished she felt more confident that all the changes would be for the good.

Archimedes was obliviously enjoying the workshop. In the past he had always made his machines himself, assisted frequently by Marcus and occasionally by an unskilled slave lent for a particular task: there had always been a great deal of sawing, hammering, and blistered hands in between the interesting parts of machine-making. Now he only needed to say "I want a beam this big to be joined to that beam with tenons," or "I need an iron heel plate this shape to fit that aperture," and within an hour, there it would be. It removed the drudgery from machine-making and left only the agreeable inventive side.

He wore a linen patch over his eye for his first few days in the workshop, tying it on with Delia's cheekstrap. He had already resolved to give the king's sister her new cheek strap when he went to the house to announce the catapult's completion; in the meantime, it gave him a secret thrill each time he tied on the old one. He did not tell his family where he'd acquired the little leather strap, however. He thought they would disapprove.

He followed his own advice and tried to stay out of Eudaimon's way. It was impossible to do this entirely, of course. They were sharing the same workshop and the services of the same carpenters. But Eudaimon seemed as happy to avoid speaking to Archimedes as Archimedes was to avoid speaking to him, and for some days all proceeded peacefully. Archimedes made a trip to the nearer forts on the city wall, looking for a catapult whose dimensions he could copy. He eventually fixed on a fifteen-pounder with a particularly vigorous and accurate throw, and corrected the estimated dimensions of his own machine accordingly. The fact that his original was much smaller than his copy raised a few problems, which he enjoyed solving. The one-talenter would have an eighteen-foot arm span and be nearly thirty feet long; it was too heavy and too powerful to aim or draw by conventional methods, and he had to devise systems of pulleys and winches for it. That was fun.

Eudaimon paid no attention to what his rival was doing until Archimedes had been working on the catapult for four days and was ready to balance the stock on the stand. Then the chief catapult engineer came up and watched in silence as the beam- thick enough for a ship's mainmast, and still only partially finished- was suspended above its tripodal stand by a system of ropes and lowered carefully. When Archimedes signaled the workmen to stop lowering and secure their ropes, however, Eudaimon stiffened. With the beam dangling just above the pin, Archimedes began to thread about it the first of his aiming devices.

"What's that?" asked Eudaimon harshly.

Archimedes glanced at him- a process that involved turning his whole body, since his eye was still bandaged- then went on threading his pulleys. "It's to help it pivot," he said.

"There's nothing like that on the fifty-pounders at the Euryalus fort!" snapped Eudaimon. He sounded affronted by it.

"Isn't there?" said Archimedes, mildly surprised. "How do they pivot, then?"

"Didn't you look?" said Eudaimon.

Archimedes shook his head. Biting his tongue with concentration, he threaded a rope around a pulley set into the stand, looped it through the attachment on the stock, and fixed it back on the stand, to a windlass. Only when he'd made it fast did he realize that Eudaimon hadn't answered his question, and look back.

Eudaimon was still standing behind him, staring at him with a mixture of shock and outrage. "What's the matter?" asked Archimedes.

"You didn't look at the fifty-pounders in the Euryalus?" asked the chief catapult engineer.

"No," said Archimedes. "It's a long walk out there, and I found a machine I liked much closer."

"But they're the closest in size to what you're trying to build!"

"Yes," said Archimedes, "but I'd still have to scale them up, and it's just as easy to scale up a fifteen-pounder. How do they pivot?"

There was a silence. Then the workshop foreman, Epimeles- a big, slow, soft-spoken man in his forties- said, "They don't. To aim them you have get a few strong lads to move the stand."

"Well, that's stupid!" observed Archimedes. He began threading his second pulley. There would be one on either side of the catapult. The operator would turn a windlass on the side required and use a third windlass to adjust the elevation.

He paid no attention when one of the workmen sniggered, but looked up sharply at the sound of a blow and a cry of pain. He was just in time to see Eudaimon striding off and one of the workman clutching his ear. Archimedes dropped his rope and dashed after the chief. Eudaimon stopped abruptly and spun about, his seamed face black with anger.

"You had no business hitting that man!" Archimedes told him furiously.

"I will not be laughed at in my own workshop by my own slaves!" Eudaimon shouted back.

"They're not your own slaves, they're the city's. You had no business hitting him! And anyway, what was it to you? It's not as though you'd made those fifty-pounders!"

"I'm in charge here!" declared Eudaimon. "I can have that fellow flogged if I like. Maybe I do like. Elymos! Come here!"

The man he had struck stepped back in alarm, and the other workmen stared at the chief in horror.

"You don't dare!" cried Archimedes in outrage. "I won't let you!" He turned to the foreman. "You run up the road and tell the regent about this!"

"Do you think Leptines wants to be bothered with a squabble in the workshop?" said Eudaimon.

"He will if he has any decency!" replied Archimedes. "He's in charge, and nobody should allow people to go about flogging people when they haven't done anything wrong!"

"I will tell the regent," said the foreman decisively, and turned to go.

The foreman was as much a slave as the rest of the workmen, but he was a valuable, experienced, and trusted slave, and his word carried some weight even in the king's house. Eudaimon started in alarm and ordered, "Stop!"

Epimeles turned back and looked at Eudaimon levelly. "Sir," he said, "you and… this gentleman are both authorized to use the workshop. If you say Elymos is to be punished, and he says he is not, surely it's for our master to tell us which one of you to obey?"

"I am in charge!" grated Eudaimon.

"In that case the regent will tell us to obey you and flog Elymos," said the foreman quietly.

There was another silence, and then Eudaimon said, "I never gave any such order." He glared at them all. "You all know that! I never gave any such order." He turned on his heel and walked off.

The foreman let out his breath slowly. Elymos gave a whistle of relief and sat down, and his friends thumped him on the shoulder. Archimedes thought of thumping the slave's shoulder too, but refrained: he was aware that the threat of flogging had been made only because of him.

"Are you all right?" he asked instead, coming over.

Elymos nodded and grinned up at him. "Thank you, sir," he said. "I'll remember how you stood up for me."

"You shouldn't have laughed," Epimeles told him sternly, coming over as well.

Elymos ducked his head appeasingly: Eudaimon might order floggings, but Epimeles was the person who was really in charge of the workshop. "Couldn't help it! It was funny!" protested Elymos.

"But it wasn't even his fault that those fifty-pounders can't pivot," said Archimedes. "He didn't build them."

At this Elymos laughed again, more loudly this time. "That makes it even funnier!"

Some of the other workmen laughed as well. Archimedes stared, perplexed, and they nudged one another and giggled among themselves. Archimedes realized that the laughter was directed at himself, and flushed. He went back to his catapult and began rethreading the ropes in hurt silence. People had always laughed, were always laughing, at him. He got lost in his geometry and didn't notice things, or he got excited about things they didn't understand, and they laughed. Even slaves he had defended were laughing at him.

Elymos leaped up and followed him. "Oh, sir, don't be offended!" he said. "It's just a workshop joke, that's all."

"Well, I don't get it!" said Archimedes angrily.

The slave sniggered again, then, at a sharp glance, looked solemn. "Sir, I couldn't explain it. Not to you. Jokes are never funny if you explain them. But please don't be offended, sir. It's just a…a slaves' joke, that's all." He hurriedly took the third rope and tried to thread it around a pulley.

"Not that one!" Archimedes told him hastily. "That goes on top. No- no, leave it! Go fetch me the chalk, if you want to be helpful!"

The foreman, Epimeles, watched for a little while as the massive beam was set down upon the joint pin in its stand. Archimedes had calculated the approximate area of equilibrium and ordered a series of holes drilled along it. The stock was found to balance best upon the middle one: Epimeles smiled. He watched for a minute longer as the huge machine pivoted left and right in response to the windlassesthen sighed and reluctantly left the building. He had a long walk before him.

It was dusk when Epimeles got back to the Ortygia, but he did not go directly to the barracks next to the workshops, where he and the other workmen lived. Instead he went to the king's house and knocked upon the door.

Agathon opened it- that was his job, after all- and regarded the workshop foreman with displeasure. "Your business?" he demanded.

"Came to show you something," replied Epimeles calmly.

Agathon snorted and invited him in.

The doorkeeper had a lodge beside the door, a small but comfortable room with a couch and a carpet and a stone water cooler against the interior wall. Epimeles sat down on the end of the couch with a sigh of relief and began rubbing his calves. "Walked up to the Euryalus and back this afternoon," he commented. "I could do with a cup of wine."

Agathon looked even more disapproving than usual, but took a jar from beside the wall, poured some into two cups, and added some water, fresh and chill from the stone. "Why should I be interested that you were up at the Euryalus?" he asked, sipping.

Epimeles drank most of his wine off at once, then set the cup down. "Because I went up there for that engineer you told us tolook after," he said. "I found this." He opened the small sack he'd been carrying and brought out a coil of fine cord. It was divided into sections by a series of regular knots, which had been dyed red or black.

Agathon inspected it straight-faced, then said, "There's something peculiar about a fort having a measuring line, is there?"

Epimeles pulled a second measuring line out of the sack. It was seemingly identical to the first, but older, fraying a little and discolored. He stretched the two cords out side by side, and it was immediately apparent that they weren't identical after all: the new cord's divisions were shorter than the old one's. "This one's mine," said Epimeles, touching the old cord. "It's accurate."

Agathon looked at the two cords expressionlessly.

"You know that when you're building a catapult, the essential thing is to make all the parts stand in exactly the right proportion to the diameter of the bore?" coaxed Epimeles. "You get a catapult that works, and you measure it, and then you either reproduce it exactly or scale it up or down."

"I believe I'd heard that," said Agathon. He did not, in fact, know very much about catapults, but he had no intention of admitting it- and he understood enough to grasp the implication of the cord. "You're suggesting that Eudaimon left this"- he touched the new measuring cord- "at the Euryalus, so that anyone who took measurements of the machines there would get the wrong figures, and any catapult built in imitation wouldn't work?"

Epimeles nodded. "See," he said, "the two fifty-pounders up at the Euryalus are the biggest catapults in the city at the moment. Eudaimon assumed that Archimedes would measure them, then guess at the increases necessary to make them throw the extra ten pounds: it's the way he'd have gone about designing a one-talenter himself. This afternoon it came out that Archimedes couldn't be bothered to walk up to the Euryalus and took his measurements from some little fifteen-pounder close by. Eudaimon was…" The foreman hesitated, picking his words, then said, "… outraged, shocked, and disappointed. When I saw that, I thought I'd go up to the Euryalus and see what he'd been up to- and sure enough, I found this, in the storeroom where the gear's kept. The lads at the fort all agree that it was just where their old one was, but that it's new, and they don't know how it got there. But they remember Eudaimon coming up there in the afternoon four days ago."

"I see," said Agathon grimly.

It wasn't evidence to convict a man of treason: they both knew that. But it could be an underminer, a question mark, a stone in the shoe. It could hurt Eudaimon.

Epimeles shifted the cord toward the doorkeeper. "I thought you should look after it."

Agathon nodded thoughtfully and picked up the false measuring cord. He began winding it about his hand. "I'm surprised you went all the way up to the Euryalus to look for it," he said. The fortress lay at the extreme point of the city wall, six miles from the Ortygia.

At that Epimeles grinned. "I would have gone twice as far if it'd help get your lad put in charge of catapults. It will, won't it?"

Agathon looked up in surprise.

"Well, you know he's good!" said Epimeles, surprised at the question on his face. "You told us to look after him and make sure nobody interfered with his one-talenter, and we realized why pretty quickly. He's so good he doesn't even realize how good he is. That one-talenter- you know what he's done with it? The little fifteen-pounder he copied can be pivoted, of course, so he thought up a system with windlasses so that his will pivot as well. When I told him that the fifty-pounders at the Euryalus don't pivot, he just looked surprised and said, 'Well, that's stupid!' "

Epimeles laughed. Agathon looked at him sourly and asked, "Is it?"

"People will say so now, won't they? But nobody ever used to expect anything bigger than a forty-pounder to pivot. Archimedes has just invented an entirely new system for aiming big machines- and he doesn't even realize! It was easier for him to design it than it was to walk up to the Euryalus and have a look at how other people did it. Some of the lads laughed about that, and he didn't even understand why. Zeus! I almost feel sorry for Eudaimon. He's never built a catapult that wasn't copied piece by piece from another catapult, and when he can't get definitive measurements- and on the big machines, each one is a bit different- he guesses and he struggles and he runs all over the city trying to find out what the right figure is. Archimedes sits down and scribbles for half an hour and has the perfect number there in his hand. Zeus!" he said again. "Eudaimon's like some little local athletics teacher who trains hard every year and toils to come third or fourth in the city games- and he's trying to race against a fellow who could take the crown at Olympia and barely raise a sweat. He's not good enough to compete in the same event. He's not even good enough to realize that!"

"So he cheats," said Agathon sourly.

" 'Course he does," agreed Epimeles. "Mind you, he would against any opponent, and I can't entirely blame him. When he loses this job, where will he go? He's got family, too, depending on him."

"You're almost sorry for him?"

The foreman looked down. "No," he said, quietly, "I am sorry for him. But I don't want him in charge. Nobody likes building catapults that are feeble, or kick over, or can't shoot straight. That one-talenter, now- that will be a real Zeus, a hurler of thunderbolts. You can feel it when you look at it. It sort of pulls the whole workshop in around it like a whirlpool and it makes my hair stand up to touch it." He paused, then added, "And don't worry. Nobody's going to hurt that machine now. The lads and I will see to that."

"Has Archimedes asked you to guard it?"

Epimeles looked offended. "You think we need him to ask us? A divine thing like that? That catapult is our work as well! But no, he hasn't asked us. I don't think he's even noticed that he's putting Eudaimon out of a job, and it's never occurred to him that Eudaimon would ruin the catapult to hurt him. He doesn't notice Eudaimon much. He doesn't notice people much anyway, and when it's a person he doesn't like he notices him even less. He's pleasant enough when he does notice, though, and he treats the lads decently. I'll have no trouble working with him." He grinned at the prospect, and finished his cup of wine. "Will you show that"- he gestured at the measuring cord- "to the regent?"

Agathon sucked his teeth thoughtfully for a minute, then shook his head. He had a low opinion of Leptines. "I'll wait for the master to come home," he said. "He'll be very interested."