"When did you last have a bath?" asked Philyra, wrinkling her nose.
"You can't bathe on ships," he replied defensively.
Philyra sighed. "Well, you'll have to go to the bathhouse in the New Town as soon as you've had breakfast. You look perfectly disreputable! Do you have any clean clothes?"
He cleared his throat unhappily and didn't answer. "I didn't realize Papa was so ill," he said instead. "How long…"
"Since October," she said coolly. "He wrote to you then, but I guess you didn't get the letter until after the winter."
Ships did not sail on the Mediterranean between October and April; even if Archimedes had received his father's letter in late autumn, there would have been no way for him to come home until the sea-lanes opened again. But the thought of Phidias lying ill all winter while Archimedes enjoyed himself in Alexandria appalled him.
"I didn't get it until the end of April," he said miserably. "And even then I thought I had time to tie up all my business in Alexandria. All he said in it was 'A war's started and I'm not well.' I thought it just meant he wanted me home to help teach his students until he was better."
"He thought he would recover," said Philyra, and suddenly her eyes filled with tears. "He had a fever with jaundice, but Mama had it too, and she got better. We thought he was getting better, too. Only he wasn't, and this spring…"
Archimedes reached out and touched her shoulder, and she lost her no-nonsense composure, dropped her bundle, flung herself into his arms, and wept. "It's been horrible!" she cried passionately. "He gets worse and worse, and there's nothing we can do!"
"I'm sorry," he said helplessly. "I wish I'd been here."
"He wanted you," sobbed Philyra. "He kept sending Chrestos down to the harbor to see if there were any ships from Alexandria, and sometimes there would be, but you were never on them. And sometimes he'd say you must be dead, that your ship had sunk or that you'd died in Alexandria, and he'd weep for you and tell us all to go into mourning. That was the worst of all. Why didn't you come back last year?"
"I'm sorry!" he said again wretchedly, tears rising to his own eyes. "Philyra, I swear I would have if I'd known."
"I know," she said, swallowing her sobs. "I know." She patted him on the back, as though he were the one who had broken down, then drew away, wiping her eyes. Nothing could be done about death, and she was determined to bear the grief with all the dignity she could command. She picked up her bundle again and spread it out on the bed: it turned out to be a new cloak, woven of fine yellow wool, and a linen tunic with a yellow spiral pattern down the sides. "I made these for you last year," said Philyra. "You don't have any clean clothes, do you?"
"I don't think so," he admitted, tracing the pattern with one slow finger. It was a series of double spirals, all centered on a line from shoulder to knee; from each central point a line circled outward one turn, then twisted about and ran into the center of the succeeding spiral. An interesting pattern. A line constructed tangent to both spiral A and spiral B would…
Philyra firmly removed his hand from the pattern; he looked up and blinked at her in surprise. "It's to wear," she told him. "Not to do geometry on."
"Oh," he said. "Yes." After a moment, he remembered that the clothes were a present and added, "Thank you. I like them very much."
She shook her head in mock despair. "Ai, Medion! You haven't changed at all!"
He wasn't sure what to make of that, and she smiled again at his bewilderment and brushed back a stray lock of his dirty hair. "Now," she went on, businesslike and hopeful, "do you have any money? We've been running out. We had to sell some blankets and pots to pay the doctor."
Archimedes shrugged. Most of the water-snail's earnings had vanished in Alexandria. But there was a little left, and a little more from the odds and ends he'd sold on leaving the city. "I have a bit," he said. "About a hundred drachmae, I think- Marcus knows exactly."
"A hundred drachmae!" she exclaimed eagerly. "That's good! I was afraid we'd have to go around to Papa's old pupils at once, and beg them to take up mathematics again. But a hundred drachmae will buy us a couple of months' grace."
Archimedes cleared his throat and shifted nervously. "I'm not going to teach," he declared.
She stared at him in exasperation. "Medion, you can't make a living from geometry!"
"I know that!" he protested. "I'm going to get a job as an army engineer." He launched into the arguments he had carefully prepared beforehand. "With a war on, the city must need catapults, and the tyrant must be willing to pay for them. There's more money in machines than in teaching. And I'm good with machines, you know I am. That irrigation device I built last summer earned more in two months than Papa ever earned in a year. Besides, shouldn't I help defend the city if I can? I'm going to see somebody about it this evening."
At this she smiled, encouragingly rather than with conviction. She had heard about the water-snail from his letters home, but she rather doubted that it was as successful as he claimed, and as for catapultswell, the king already had engineers who could build them, so why would he want somebody new and completely untried? Even if he did, it seemed unlikely that anyone would get rich from it. Her brother had made lots of machines as they grew up together, and many of them hadn't worked at all. Machine-making didn't seem to her as reliable a source of income as teaching mathematics. Still, she liked his machines. As a small girl she had sat quietly watching as he built them, and listened to his explanations with solemn attention. As far as she was concerned, her brother's constructions were the most wonderful of toys, whether they worked or not. She would be very pleased if he could make a living from them. It was worth a try, anyway- and the household now had a hundred drachmae and a couple of months before the money ran out.
Archimedes saw that she had accepted his plan, and felt a twinge of dread, as though another gate had closed in the walls which surrounded him. He had decided in a rare moment of practical planning that there were three things he was good at- pure mathematics, mechanics, and playing the flute. To earn a living he must put one or another of those skills to use. Music was something personal, something he did for himself and his friends; it seemed profane to play to order. As for pure mathematics, as Philyra had pointed out, he couldn't make a living simply from doing geometry, and as for teaching it, he'd occasionally been called in to help his father in the past, and he was uncomfortably aware that he was bad at it. The students never understood things which seemed to him glaringly obvious, and his impatient explanations only confused them. So machine-making it would have to be.
He was dreading it. Building a new machine was fun- he liked seeing the need set out as neatly as a geometrical proposition, and devising an apparatus that would satisfy it; enjoyed the complete absorption in the task, the complex coordination between his hands and his mind, and the unarguable solid reality of the finished solution. But once a machine had been built, to make another of the same type, and then another and another and another- it was boring. No, worse: it was a stifling prison where the soul's wings atrophied and died. Pure mathematics was light and air and delicious freedom, and he loved it more than anything on earth. But he was not a nobleman, and couldn't afford to devote himself to pure mathematics without a thought for sordid considerations of gain. He had a family to support. The invisible world could no longer be his homeland, but only a place he visited when he had the time.
He would have no company on his visits to it, either; none. He would be alone- as his father had been, these three years past. With a spasm of fresh pain, he supposed that Fate was just.
Then he remembered the war. In Alexandria it had been hard to believe in it; here in Syracuse it loomed larger, far more threatening. Lines from an old song wandered through his mind:
Let none of humankind ever once say what chance tomorrow will bring, nor, seeing a happy man, that contentment will stay for, swift as a dragonfly's wing swifter again comes change.
"You get dressed," ordered Philyra, patting his hand.
"I'll go talk to Marcus about getting your other things washed."
Marcus was taking a bath when Philyra found him. Private houses did not generally have bathrooms, and bathhouses in that age were for citizens only: Marcus was washing in the courtyard with a sponge and a bucket. It was not uncommon for even the free men of a household to walk about naked indoors, and a slave's nudity was nothing to worry about, but Philyra hung back awkwardly, waiting at the foot of the stairs until Marcus had finished. She felt uncomfortable about him. She too was aware that one of the household slaves would probably be sold, and she was hoping that one would be Marcus. She had always sided with Sosibia in the household feud, and regarded Marcus as an awkward barbarian. Besides, after a three-year absence he felt like a stranger. She could contemplate selling him; she couldn't bear the thought of inflicting that fate on any of the others. She noticed now that though Marcus had a shocking bruise on his left side, and though he was just as flea-bitten as her brother, he looked sleek and fit. That would mean a good price, but still her lips narrowed with disapproval. Marcus had been sent to Alexandria to look after Archimedes, but had returned glowing with health, while his master's ribs were like a washboard.
An inconvenient fair-mindedness, however, reminded her that Archimedes had always been thin, and Marcus sturdy. And when Archimedes was doing geometry he would forget to eat unless you set his food on top of the abacus- and sometimes even then he'd simply move it out of the way and carry on calculating. It was probably unfair to blame Marcus too much for the state his master had come home in.
Marcus poured the remains of the bucket of water over his head, shook himself, and picked up his tunic. Philyra pushed herself out of the doorway into the sunny courtyard. "Marcus!" she said sharply. "Where's my brother's luggage?"
Marcus jumped and pulled his tunic hastily over his head before replying. He felt as awkward with Philyra as she with him. She'd been a schoolgirl when he'd left the house; now she was a young woman. "There," he said, indicating the chest in the corner of the yard. "But I wouldn't open it, mistress."
"Why not?" she demanded. "I can't believe the things in it are clean! It's going to be a good drying day." Indeed, the air was already hot: anything washed now would be dry well before the evening.
He shrugged. "It has presents in it," he said. "One of them is for you." His eyes lingered momentarily on the front of her tunic. She became aware of how it was clinging, and hitched it up, reddening.
"But I just told him I was going to see to his things!" she protested. "And he didn't say anything about presents."
Marcus snorted. "Would you expect him to think of a thing like that?"
No, she wouldn't. Archimedes probably remembered the presents, and must know that they were in the same chest as the clothes. But he would not put the two things together, and know that it would spoil her surprise if she opened the chest. She made an exasperated noise, Marcus grinned, and something swung into balance between them: they were both members of the same household, both aware of the tastes and foibles of the same small collection of people.
"There's no hurry, is there?" he asked.
There was not, not really. She just wanted everything to be settled: her brother indisputably home, in his own room as he should be, with the chest reduced from traveling chest to clothes chest. She walked over to the luggage and glared at it resentfully. "What's in the basket?" she asked.
"The famous water-snail," replied Marcus, grinning again. "We can unpack that, if you like." He went over to the chest and began to untie the rope.
"Won't he want to show it to me himself?" she asked doubtfully.
"No," replied Marcus, undoing another knot. Suddenly he wanted very much to show her the water-snail, to impress her. "We made thirty-two of the things in Egypt, and he's sick of the sight of them. But it's an amazing machine. Here, let me show you!" He drew the rope off the basket, hauling the coils under the chest. Philyra leaned against the courtyard wall with her arms crossed, trying to look uninterested, though in fact she was acutely curious. Marcus was sharply aware of the way her stance cast one thin hip into linen-hung relief. Too thin, he told himself- like her father and her brotherbut somehow prettier than such an angular girl should be. Perhaps it was the brightness of her eyes. Not that it had any bearing on him: he was as much her brother's property as the machine he was unpacking. Still, where was the harm in showing a pretty girl a machine?
He untied the knot that secured the basket's lid, opened the basket, and lifted out from a nest of straw a wooden cylinder. It was about a cubit long- the distance from a man's elbow to his fingertipsand the outside was made of planks bound, barrel-like, with iron hoops. The interior held a complicated structure smeared with pitch. A stand was fixed to the cylinder's core with a pin, so that the whole thing could turn like a wheel.
"The Egyptians usually lift water with a machine called a water-drum," said Marcus, turning the cylinder in his hands. "A sort of wheel with eight buckets around the rim. A full-sized one moves a lot of water, but it's heavy to turn- it needs a couple of men to shift it. Your brother started off with one of them, and finished up with this. The real machines we built were bigger, of course- they stood about as tall as a man- but otherwise they were exactly like this. As you can see, this still has eight inlets"- he showed her the eight openings in the cylinder's base- "but they're not buckets. They're tubes." He stuck a finger into one, and she saw that it was indeed a kind of tube, and that it ran up around the core at an angle. "They coil right around the cylinder several times and come out here, at the top." He slapped the top edge of the cylinder, which was identical to the bottom. "Each one is a bit like a snail shell, which is why it's called a snail. They're made of strips of willow, stuck onto the core with pitch and closed over with planks. I don't know how he fixed on the angle they spiral at, but it's very important: a lot of the people who tried to copy it got it wrong, and then it didn't work. Now, what you do to work it…" Marcus glanced about, fixed on a large amphora of water sitting in the corner of the courtyard, and hurried over to it, holding the water-snail. He set the machine down, fetched the bucket he'd used for his bath, and poured some water from the amphora into the bucket. Then he set the bucket in a dip in the courtyard, balancing it with some loose stones so that it stood at an angle on its side, and placed a laundry footboard before it to make a platform. "It has to sit at an angle," he explained to Philyra. "The exact angle is important, too- that's another thing people who copied it used to get wrong. This one is right if the stand's straight." He set the foot of the water-snail in the water of the bucket and the head on the platform. "Now all you have to do is turn it." He gestured for her to oblige.
Philyra hitched the hem of her tunic away from her feet and crouched down beside him. She put one hand on the wooden cylinder and began to turn it slowly; it revolved easily on its stand. Water ran into the tubes at the foot of the snail. She kept turning, and presently water ran out of snail's head. She kept turning the machine gently, watching it: water ran in, ran down the tubes, and…
"It's running uphill!" she exclaimed, shocked. She took her hand off the machine as though it had burned her.
Marcus grinned. "Quick!" he said. "It takes most people a bit longer to realize that. Some need to have it pointed out to them. But it doesn't- not exactly. Watch more closely."
Philyra turned the machine again. Water ran into a tube; as the tube went up, the water ran down, into the spiral, and then along it as it turned on. She laughed delightedly.
Marcus grinned back at her. "It runs downhill all the way up," he said.
"Sometimes," said Philyra, "I think my brother is a mistake of Nature. He shouldn't have been born a human being at all; he should have been an attendant spirit in the workshops of the gods. I suppose a full-sized one of these is very much easier to turn than a water-drum?"
" 'Course it is," agreed Marcus. "You don't need two men; you don't even need one. A child can operate it- because all you have to turn is the snail itself: th
e water just runs downhill." He sat back on his heels and gazed lovingly at the machine. "We had people queueing up to buy it," he told her. "We could have made a fortune!"
"I thought you did!" Philyra said in surprise. "More in two months than my father earns in a year, my brother said."
Marcus shook his head sadly. "Eighteen hundred eighty drachmae. Enough to pay our debts and live well in Alexandria for a year. But we had orders for another thirty of the machines- at eighty drachmae apiece! — and every expectation of more again. He preferred to do geometry."
Philyra stared at the water-snail and swallowed. She could not imagine eighteen hundred and eighty drachmae all together in one lump; still less could she imagine spending such a sum. The rent from the family's small farm was three hundred drachmae a year- less, now that the vineyard had been sold- and Phidias' teaching had brought in perhaps as much again. The water-snail had earned not just more than her father's salary but three times the household's entire annual income- and Archimedes had spent it all, except for a hundred drachmae.
Marcus understood her sudden silence and wished he'd kept his mouth shut. He shifted uncomfortably. "Alexandria's expensive," he said defensively. "And there was the debt, and the fare back." There'd been a woman, too, who had accounted for quite a lot of the money, but he had no intention of mentioning her to Archimedes' sister. "Your brother wasn't as extravagant as it seems," he finished instead- which was certainly true, given Alexandrian prices, to say nothing of the woman's. "Besides, there's a hundred and sixty drachmae left."
The Sand-Reckoner Page 4