"A water-aulos," repeated the girl, tasting the new word: hydraulis. "What does it sound like?"
"More like a syrinx than an aulos. Louder, though, and richer-toned- almost bell-like. It can be heard above a crowd. The Alexandrians put one in the theater. I told Ktesibios he ought to call it a water-syrinx, but he preferred his own name for it."
"You said you helped to make it?"
"Mostly I just helped Ktesibios tune the pipes. He never actually had any training in music, though he's the most astonishingly ingenious man. He's-"
"Could you build one?"
Archimedes blinked.
"Not now," said the girl quickly. "I know there's a war, and it's more important to build catapults. But afterward, if there is an afterward- could you build me a water-aulos?"
Archimedes blinked again. "I'd love to," he told her. "But they're complicated. They-"
"You couldn't?"
"I- not that. They take a long time to build. I couldn't afford to do one cheap. Ktesibios charged sixteen hundred drachmae for his."
The girl did not look at all disappointed. "My brother likes music," she said. "And he loves ingenious machines. I'm sure he'd be willing to pay sixteen hundred drachmae for a water-aulos if you could make one."
"Your brother?" asked Archimedes, with a sudden horrible feeling that he knew who this was.
"Ah," she said, and her straight black brows came down. "You didn't realize. King Hieron."
"No," he said, feeling numb, "I didn't realize." He studied her a moment: the silver belt, the fine tunic. But he could not concentrate on the expensive clothes. His eyes kept sliding back to her round face with its black curls and brilliant dark eyes, and her strong musician's hands. He added accusingly, "You don't look old enough."
"He's my half brother, actually," she said. All the animation had left her face and voice, and she sounded the bored aristocrat. "He was almost grown up when our father married my mother."
King Hieron was a bastard, the result of a wealthy Syracusan's youthful indiscretion: all Syracuse knew that. Archimedes guessed that this girl must be the rich man's legitimate daughter. She was not of his class at all. He shouldn't really be here, in the private part of the house, talking to her. Syracuse allowed women more freedom than many other Greek cities, but still, it was grossly improper for a young man to slip into any private house and chat with the owner's unmarried sister, unintroduced and unsupervised, and this girl was the daughter of a nobleman and sister of a king. But he pulled his stained cloak straight and told himself defiantly that he was a democrat. "I can build a water-aulos," he declared. "If your brother's willing to pay for it, I'd love to build you one. I prefer wind instruments to stringed ones anyway."
At this she smiled again, a long slow grin, and he knew he'd said the right thing, and grinned back. "What's your name?" she asked.
He had just opened his mouth to reply when the answer was shouted at him- "Archimedes son of Phidias!" — in a tone of shocked disapproval. He and the girl turned together, and found four men bearing down on them. One was Dionysios, one the exalted doorkeeper, one a middle-aged workman, and the fourth, from his purple cloak, had to be the regent Leptines.
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 machin
es. 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 express
ion. "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."
The Sand-Reckoner Page 8
