The Sand-Reckoner

by Gillian Bradshaw

  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 t
hat 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?