"The wrong answer to your present geodetic research may well get you a.s.sa.s.sinated."

"By Ptolemy?"

"I don't read pharaoh... I see a woman... young, beautiful, dedicated."

"So you know about Ne-tiy. Placed in my house by the Horus-priest, Hor-ent-yotf."

"Everyone knows. The female cobra within the flower basket. Why don't you get rid of her?"

"Nonsense. He'd find someone else. Meanwhile, she's where I can keep an eye on her."

Marcar shrugged. "That's up to you, of course. But the risk to your life is not the only matter of significance. There's another thing."

"Oh?"

"You will have a visitor. A most remarkable visitor, from a place far away. I am tempted to say he is a G.o.d, but I know how you feel about the G.o.ds. Like you, Eratosthenes, he faces a great trouble. But you can help him, and he can help you."

The mathematician chuckled. "Now that, friend from the marshes, is a prediction. Years away, of course. It's always safe to predict things that happen ten years from now.''

Marcar smiled. "According to the signs, he arrives on the first day of the New Year.''

"There you go again. Which New Year? The New Year when Sirius is first seen in the dawn skies, announcing that the Nile will begin its rise? In fact, tomorrow, in the hour before sunrise? Or do you mean the New Year of the current Egyptian calendar, the first day of Thoth, which is actually two hundred days away? I remind you that the Egyptian calendar is based on 365 days, not 365 and a quarter, as shown by the stars, and that it loses one full year every 1,460 years. The last time the calendar was right was 1,171 years ago. It won't be right again until 289 years from now. So-which New Year, most n.o.ble charlatan?''

Marcar's eyes gleamed. "Your sign is Cancer. And how-ever you calculate it, O great geometer,Cancer begins at midnight tonight, and announces the first day of the summer solstice. In the dark morning skies Sirius will indeed be seen, heralding the New Year, and the awakening of Hapi, which you Greeks call the Nile, with great festivities beginning in all towns and villages the entire length of the river, and continuing for twenty-one days, with carousing, merriment, and consumption of seas of barley beer.''

Eratosthenes laughed heartily. "I take it, most astute as-trologer, that buried in that Rhea-flood of rhetoric is an a.s.sertion that my relevant New Year is within the small hours of tomorrow morning, beginning with Sirius ascendant?"

"Thou seeest all, wise Eratosthenes."

"I see that you are a fraud, more colossal than any pyramid atGizeh."

"My lord overwhelms me with his flattery." He leaned forward. "Now that your stomach is weak with laughter and your defenses breached, may we talk of your sun-project?"

"It's a bit premature."

"In any case, presumably you have by now determined the shape of the Earth? Perhaps you could tell an old friend?"

"My report goes first to Ptolemy. You know that.'"

"Of course, of course. Nevertheless, what harm is a hint... in strictest confidence?"

The mapmaker grinned. "I hear the odds are disc, two to one; cylinder, even; three to one against a square; and ten to one against a sphere." He rose to leave. "Later, Marcar. Later. I promise."

"If you live," whispered the astrologer.

The visitor stopped. He turned around slowly. "Have you drawn the horoscope of Hor-ent-yotf?'' It was a stab in the dark, a flash-of what? Psychic insight? Stupidity?

Marcar peered at him most strangely. Finally he said, "Why do you ask?"

"Never mind. Really none of my affair." But he knew. The astrologer had lifted the veil on the sinister Egyptian, and he had not understood what he had seen. It was pointless to press the seer further. One thing was certain: the fates of Eratosthenes and Hor-ent-yotf were inextricably interwoven, like designs into a funerary shroud.

He bowed and left.

6. The Shadow And so home again, away from smells and noises and dirty streets. Eratosthenes nodded to the gatekeeper and walked up the palm-lined entrance toward the central gardens. He paused under the colonnade and looked out toward the focus of the courtyard. There, as he had ordered, the scribe Bes-lek sat cross-legged in front of the shadow cast by the man-high gnomon, and he was chanting.

Bes-lek had selected his own chant, a hymn, really, something addressed to Horus the sun G.o.d, a recital not too long, not too short. As the Greek watched, the clerk finished his mumbled litany, dipped his reed pen into the little pot of charcoal ink, and made a tiny dot at the tip of the gnomon shadow on the circular stone flagging. Then he commenced again. "Horus, giver of light, son of Osiris and Isis, shine down upon us in thy journey across the sky..." It was in Egyptian, and between the foreignness of the language and the garbled maundering, the sense was largely lost on the librarian.

Eratosthenes walked up the gravel path toward the chanter. Bes looked up and saw him coming, but his droning mumble did not waver. The geometer looked down at the white flag-ging with critical eye.

Bes sat just outside a concave curve of dots. He had begun about an hour before noon, and now it was about an hour after noon. The dots showed longer shad-ows at the beginning, growing shorter as noon approached, then growing longer again as midday was pa.s.sed. The dot closest to the gnomon basewould be the one for noon. That was the one to measure. "Bes," he said, "my faithful friend, I can see from the marks that you have made a fine record of the G.o.d's overhead course. The matter is complete, except for measuring the noon angle. Get up now, stretch your legs, and then help me with the angle rod."

"Aye, thank you master." The little man groaned with great eloquence as he struggled to his feet.

"Such strain, such care. My poor joints. I shall ache for days. For the pain, perhaps my lord could allot two extra puncheons of fine barley beer."

"Two?"

"One for my wife. The dear creature a.s.sumes all my pains. And considering that the festivities begin tonight."

"Two, then. Tell the steward. But first, hold the angle rod. Put the point on that inner dot, the one closest to the gnomon. Yes, that's it. Steady, while I rest the upper edge on the top of the gnomon. Fine, fine. A good angle. Now, let me take the precise measurement on the protractor arc. Yes. Seven degrees, twelve minutes, I'll take the rod."

"Is it done, master?"

"One more measurement. I need to know the distance of the dot to the base of the gnomon." He placed the rod at the base of the gnomon and alongside the noon dot. "Hm. Check me here, Bes. What number do you read?"

The scrivener squinted. "It is one and a quarter units, and yet it is a generous quarter.''

"We'll call it one and a quarter." He doesn't ask why, thought Eratosthenes. He doesn't wonder. He doesn't care. Not one hoot of the owl of Athena in Hades. He gets his daily bread, with an occasional extra ration of beer. He has his G.o.ds and his feast-days, and he's happy. A true son of the Nile. Well, why not? It seems to work for him. He said, "Tell the guard of the kitchen I said to give you three puncheons of good brown khes, suitable for Ptolemy's own table. One for you, one for your wife, and one to lay on the altar of Horus, the hawk-G.o.d of the sun, who has favored us today."

Bes bowed low. "The master overwhelms me."

He's not even being sarcastic, thought Eratosthenes. "Go," he said.

And now back to the calculations. The gnomon was ten units high. The leg measurement was one and a quarter. The tangent of the sun angle was therefore one hundred and twenty-five thousandths. What was the angle? It ought to check out pretty close to seven degrees, twelve minutes. He had trigonometric tables in the Library that would give the value. Check. Confirm. Recheck. Pile up the data. It's the only safe way.

Why was he doing this? Who cared whether the earth was a globe? Who cared what size that globe might be? Not Ptol-emy Philadelphus, his lord and master, the pharaoh-G.o.d, who had brought him here to run the great Library. In fact, Ptolemy had made veiled references to temple pressures. Hor-ent-yotf, the high priest of Horus, was complaining that these studies were demeaning to the hawk-deity and might even fore-shadow a revival of monotheism, as attempted by Ikhnaton a thousand years ago. That misguided pharaoh had proclaimed, "There is but one G.o.d, and he is Aton, the sun. Pull down all other temples." The crazed pharaoh had been slain and his name obliterated from all monuments. Over the years the tombs of all his descendants, direct and collateral, had been searched out and desecrated.

All except one, mused the geometer. The boy pharaoh, who married the third daughter of the heretic.

The youth had been a.s.sa.s.sinated, of course, and then properly and secretly buried, along with suitable treasures, in a hillside in the necropolis at Thebes. However, before the Aton-haters could find the grave, the tomb of the fourth Rameses was dug in the cliffside just above, and the boy-king's grave was buried under the quarry chips. Eratosthenes had seen the maps and read the reports, and then he had hidden them away.And why was he thinking of the tomb of Tut-ankh-amun? Because it was knowledge that might save his life.

He pa.s.sed on into the building and walked through silent halls into the mathematics room. Here he found the scroll of trig tables and ran his finger down the tangent columns. The angle whose tan is one hundred twenty-five thousandths. Here we are. Seven degrees, seven and one-half minutes. I was looking for seven degrees, twelve minutes. Well, not bad. Within experimental error? And how good are these tables? Some day soon, redo the whole thing. Suppose I take the average. Call it seven degrees, ten minutes, or almost exactly 1/50 of a circle. Base line, Syene to Alexandria, 5,000 stadia.

So if the Earth is a sphere, 5,000 stadia is 1/50 of its circ.u.mference, which is, therefore, 250,000 stadia.

Two hundred and fifty thousand stadia.

That's what the numbers said. But was it really so? Such immensity was inconceivable.

He rubbed his chin in perplexity as he walked over to the big table where his map was spread out.

His greatest work. Ptolemy himself had praised it and had accorded the ultimate flattery of reproducing the map in mosaic in the floor of his study. Copyists were turning out duplicates at the rate of one every two weeks, and probably making all sorts of errors in their haste. For which he, the author, would be blamed, of course.

He bent over the sheet.

It had been a magnificent effort, drawn mostly from docu-ments in the library: travelers' reports (especially Herodo-tus'); terse military accounts; letters; local descriptions; sea captains' logs; census and tax reports. To the west, it showed the Pillars of Hercules; and even beyond that, Ca.s.siterides, the tin-islands discovered by Himilco the Phoenician. To the east, Persia, conquered by Alexander, and on to India and the Ganges River. And beyond that a mythic land, Seres, where a fine fabric called silk was woven. Then the legend isles of c.i.p.angu (which he didn't even show). But the whole known world, from west to east, was at most 75,000 stadia-less than one-third of the sphere he had just calculated.

And yet he knew his numbers were right.

There was more to the world than he or anyone else had dreamed.

Was the rest simply water? Vast, barren seas? Or, on that other invisible hemisphere, were there balancing land ma.s.ses, with peoples and cities and strange G.o.ds? His heart began to pound. He knew it was futile to speculate like this, but he couldn't help it. Some day...

7. The Light Khor sniffed the cabin air. Was it going stale? Yes, the CO2 was definitely building. Which meant the absorbers were very nearly saturated. Why hadn't the alarm sounded? And then he noticed. The purifier bell was ringing. And the proper red light was flashing. Swamped by his other troubles, he just hadn't noticed. Alkali. Did he have any more? No. He re-membered shaking out the last flecks of sodium carbonate from the container. He had tossed the empty box into the disposal.

Was there any chance of finding alkali down there on that watery little planet?

Conserve. Conserve. Breathe slowly, slowly. Khor, you luckless zoologist. Whatever possessed Queva to give you her sleep key? Not very smart of her.

Well, now, Planet III, just what sort of world are you? Is there intelligent life down there, waiting to hand me emer-gency tape, a barrel of oil (meeting hydraulic spec K-109, of course), and a basket of alkali? And (who knows) maybe they'll hand me a featherless biped as I leave.

How silly can I get?He watched the 3-D shaper carve out a fist-sized copy of the planet sphere: blue for oceans, brown for continents, white for polar ice. He pulled the ball out of the lathe and studied it. Very, very interesting.

How big? No way to tell. All he got was shape and surface. No matter. Maybe he was going to live after all. There had to be something down there. He put the ball in a fold of his s.p.a.ce-jacket.

Back now to the screen.

Looking visually. Night-side. But no city lights? No civili-zation? Take her around again. Another orbit. Try north-south. Nothing? Not yet. Night side again. Maybe I'm too high. Lower... lower still.

Watch out! Water! Slow down. I'm over some kind of sea. Hey-a light! A big one! It's a light house!

Better switch on my running lights... what's the convention? Alternating red... green... white... blue.

Plus a forward search beam. By Zaff, I see buildings. Spread out... a city. Saved!

Where to put down?

8. Arrival Eratosthenes wrapped his woolen cloak tighter about him as he stared out to sea. It was the last hour of evening and the first of night. Dark sea was indistinguishable from dark sky. The constant north wind pushed back the dubious perfumes of the delta and the royal harbor, to his rear. He inhaled deeply the crisp salt air blowing in from the reefs.

He stood on the balcony of the great light house, on the Isle of Pharos, that long spit of limestone protecting Alexan-dria from the encroaching Great Green. He was so high, and the air so pure, that he didn't even have to use mosquito ointment.

Ah, Pharos-isle of strange and diverse fortunes! Menelaus, bound homeward from the Trojan War, blown ash.o.r.e and becalmed by angry Zeus, nearly starved here, with disdainful Helen. So Homer sang.

How long ago? Eight centuries, perhaps nine. But then eighty-two years ago the great Alexan-der came.

"A fine island," he said. "It will shelter a new city, over there on the delta." He paced it out, where to put everything. Everything but the final essential building: his tomb. The first Ptolemy had built that and then had brought the body back.

"Eratosthenes." he said to himself, "you're dodging the issue. You're thinking about everything except the problem." Ah, yes. So he had confirmed (in his own mind at least) that the Earth was a sphere, with a circ.u.mference of 250,000 stadia. But it was too much. A globe that size! Incredible. Or was it? There was, of course, a rough check, available to anyone. You didn't have to go to Syene. You didn't have to look down a well at high noon, on the day of the solstice. There was another way. Just an approximation, of course.

He walked a slow circuit of the balcony, pondering vaguely the beauty of the night sea and the twinkling lamps of the city. It was lonely here, and he could think. No one to bother him. The lighthouse keepers knew him as the curator of the great Library, and let him come and go as he pleased. Far below in the courtyard Ne-tiy waited patiently with the chariot.

To the north nothing was visible except the stars and the light shaft thrusting out horizontally from the great concave mirror at the top of the tower. He had come here to think about that light beam. It was supposed to be visible out to sea for 160 stadia. To him, that was one more proof that the Earth was spherical. The light was visible out to sea to the point where the Earth's curvature shut it off. He reviewed the problem in his mind. He saw the diagram again. Circles. Tangents. The height of the Pharos tower, taken with the seaward visibility. That would give an angle-call it alpha- with the horizon. That angle alpha would be identical to the angle-call it beta-at the center of the Earth subtending the 160-stadia chord of the light shaft. The lighthouse was two-thirds of a stadion high. The sine of the angle alpha was therefore two-thirds divided by 160, or 417 hundred thou-sandths. Next, the angle whose sine was 417 hundred thou-sandths was about 14'/3 minutes, or about 1/1500 part of a circle, and finally, 1500 times 160 gave you 240,000 stadia. Close enough to the Syene measurement of 250,000. So he couldn't betoo far wrong. He had done the numerical work already. He knew the result before he came out here tonight. But he still found it hard to believe. The Earth couldn't possibly be that big. Or could it? Had he made an error somewhere? Maybe several errors? Actually, the measure-ments using the lighthouse were not easy to make. Sighting the Pharos light had to be done at sea from a pitching, bobbing boat.

Subtractions had to be made for the height of the perch at the mast top.

He clenched his jaw. He had to believe his numbers. He had to believe his rough check. And he had to believe the only conceivable conclusion that his calculations offered. The Earth was indeed a huge sphere, in circ.u.mference 240,000 to 250,000 stadia, more or less.

The question now was, should he so report to Ptolemy, and possibly get himself discharged from his post at the Library. Or worse?

He was due at the palace by midnight. He would have to decide within hours.

He had just turned back, to descend the outer stairway, when something in the dark northern skies caught his eye. Lights, moving, flashing. And different colors. Red... green... white... blue... flashing, on and off. And then that terrific shaft of white light... brighter even than Pharos... coining straight at him!

He threw his arm up over his eyes. There was a roar overhead. The tower shook. And then the thing was gone... no, not entirely. There it was, over the Library quarter... hovering now, stabbing its blinding light beam down. He raced around to the side of the light tower.

What in the name of Zeus!

Was it now over his house, the great manse entrusted to him by Ptolemy Philadelphus? He stared in horrified amazement.

By the wine bags of Dionysus, the thing was... descend-ing into his fenced park.

For a moment he was paralyzed. And then he recovered and started down the stairs. Outside, he awoke the dozing charioteer. "Ne-tiy! Home! Home!"

9. Encounter Khor read the preliminary data in the a.n.a.lyzer. Oxygen, nitrogen, air density, viscosity, temperature...

Nothing ob-viously toxic. Gravity a little low. No matter. Everything within acceptable limits. He turned off the lights and got out. Fortunately for the ship (not to mention his unwitting host), he had come down in a clearing. There were trees and hedges on all sides. Tiny little things, but they would provide shelter.

He had landed within some sort of private estate, and very likely he could complete his repairs without the bother of curious and/or hostile crowds. And what did they look like? If they built cities, they must have hands, and legs to get about, and certainly they were able to communicate with each other.

Probably very handy little fellows.

He walked on the cropped turf back to the rear of the ship. Yes, there was the hole. He played the light on it and around it. The outer plate had laminated over nicely. Only the inte-rior would need attention. Well, get with it. Start knocking on doors. "Could I borrow a few hundred xil of adhesive tape?

And a load of high-spec hydraulic fluid (you supply the container). Plus a var of sodium carbonate. Just enough to get me to a star some nine light cycles away."

And that raised another problem. What language did these creatures speak? Better get the telepathic head-band. He crawled back up the hatchway and returned with it. Suppose they're unfriendly? Should I bring a weapon? No, I've got to look absolutely peaceful.

His ear tympani vibrated faintly. Noises. Wheels churning in loose gravel. Cries, addressed, he thought, to a draft animal of some sort. Two different voices? They had seen his ship come down, and they had driven here to confront the trespa.s.ser.

Fair enough. He unfolded the long veil, starting at his head, over the teleband, and quickly draped hisentire body from head down to talons. (No use alarming them right at the outset!) Then he propped up his portable beam between rocks in the clearing so that it would shine on him.

He listened to the cautious steps on the fine pebbles, closer, closer.

And there they were, two of them, standing just outside the light circle.

By the pinions of Pinar! Featherless bipeds!

One seemed calm, the other fearful and fidgety. The calm one stepped out into the light.