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V

It seemed to Falkayn that he had been riding through his whole life. Whatever might have happened before was a dream, a vapor somewhere in his emptied skull, unreal . . . reality was the ache in every cell of him, saddle sores, hunger, tongue gone wooden with thirst and eyelids sandpapery with sleeplessness, the fear of death battered out of him and nothing left but a sort of stupid animal determination to reach Gilrigor Castle, he couldn't always remember why.

He had made stops during the night, of course. A fastiga was tougher than a mule and swifter than a horse, but it must rest occasionally. Falkayn himself hadn't dared sleep, though, and saddled up again as soon as possible. Now his beasts were lurching along the road like drunks.

He turned his head—the neckbones creaked—and looked behind. His pursuers had been in sight ever since the first predawn paling of the sky made them visible. When was that—a century ago?—no, must be less than an hour, the sun wasn't aloft yet, though the blackness overhead had turned plum color and the Sisters were sunken below Kasunia's wall. There were four or five of them—hard to be sure in this twilight—only two kilometers behind him and closing the gap. Their spears made points of brightness among the shadows.

So close?

The knowledge rammed home. Energy spurted from some ultimate source, cleared his mind and whetted his senses. He felt the dawn wind on his cheeks, heard it sough in the wiry brush along the roadside and around the staggering hoofbeats of his mount, saw how the snow peaks in the west were reddening as they caught the first sunrays; he yanked the little transceiver from his pocket and slapped the switch over. "Hello!"

"Davy!" yelled Schuster's voice. "What's happened? You okay?"

"So far," Falkayn stammered. "N-not for long, I'm afraid."

"We been trying for hours to raise you."

He'd called the ship while he fled, to relate the circumstances, and contact was maintained until—"Guess I, I got so tired I just put the box away for a minute and then forgot about it. My animals are about to keel over. And . . . the Sanctuary boys are overhauling me."

"Any chance you can reach the castle before they get in bowshot?"

Falkayn bit his lip. "I doubt it. Can't be very far to go, a few kilometers, but—What can I do? Try to make a run for it on foot?"

"No, you'd be ridden down, shot in the back. I'd say make a stand."

"One of those bows, God, they've got almost the range of my gun, and they can attack me from every side at once. There's no cover here. Not even a clump of trees in sight."

"I know an old frontier stunt. Shoot your animals and use them for barricades."

"That won't protect me long."

"It may not have to. If you're as near the castle as you say, Ivanhoan eyes ought to spot flashes in the air from your shots. Anyhow, it's the only thing I can suggest."

"V-v-v—" Falkayn snapped his teeth together and held them that way for a second. "Very well."

Schuster's own voice turned uneven. "I wish to God I could be there to help you, Davy."

"I wouldn't mind if you were," Falkayn surprised himself by answering. Now that was more like how a man facing terrible odds ought to talk! "Uh, I'll have to pocket this radio again, but I'll leave the switch open. Maybe you can hear. Root for me, will you?"

He reined in and sprang to the ground. His fastigas stood passive, trembling in their exhaustion. Not without guilt feelings, he led the pack carrier around until it stood nose to tail with the mount. Quickly, then, he set his blaster to narrow beam and drilled their brains.

They collapsed awkwardly, like jointed dolls; a kind of sigh went from the loaded one, as if it were finally being allowed to sleep, but its eyes remained open and horribly fixed. Falkayn wrestled with the legs and necks, trying to make a wall that would completely surround him. Scant success . . . Panting, he looked eastward. His enemies had seen what he was about and broken into a trot, scattering right and left across the downs before they stopped to tether their spare animals. Five of them, all right.

The sun's disc peered over the ridges. Wait, the more contrast, the more visible an energy flash will be. Falkayn fired several times straight upward.

An arrow thunked into fastiga flesh. The boy went on his stomach and shot back. He missed the retreating rider. Crouching, he glared around the horizon. Another Larsan was drawing a bow at him, less than half a kilometer distant. He sighted carefully and squeezed trigger. The gun pointed a long blue-white finger. An instant later it said crack! and the Larsan dropped his bow and clutched at his left arm. Two other arrows came nastily near. Falkayn shot back, without hitting, but it did force the archers out of their own range for a little while, which was something.

He hadn't many charges left in the magazine, though. If the Consecrates' hired blades kept up their present tactics, compelling him to expend his ammunition—But did they know how little he had? No matter. They obviously were not going to quit before they finished their job. Unless he was lucky enough to drop them all, David Falkayn was probably done. He discovered he was accepting that fact soberly, not making much fuss about it one way or another, hoping mainly that he would be able to take some of them on hell road with him. Rough on Mother and Dad, though, he thought. Rough on Marty Schuster, too. He'll have to tell them, if he lives.

Two guards pounded down a grassy slope toward him, side by side. Their manes streamed in the air. When they were nearly in gunshot, they separated. Falkayn fired at one, who leaned so low simultaneously that the bolt missed. The other got off an arrow on a high trajectory. Falkayn shot at him, too, but he was already withdrawing on the gallop. The arrow smote, centimeters from Falkayn's right leg where he sprawled.

Nice dodge, he thought with the curious dispassion that had come upon him. I wonder if they've met my kind of defensive maneuver before, or are just making a good response to something new? Wouldn't be surprised if that last was the case. They're brainy fellows, these Ivanhoans. While we, with our proud civilization, we can't respond to so simple a thing as a local taboo on wheels.

Shucks, it should be possible to analyze the problem

Two others were galloping close from the right. Falkayn narrowed his blaster beam as far as he could, to get maximum range, and shot with great care. He struck first one fastiga, then another: minor wounds, but painful. Both animals reared. The riders got them under control again and wheeled away. Falkayn turned about in time to fire at the other two, but not in time to forestall their arrows. Misses on both sides.

and figure out precisely what a wheel does, and then work out some other dodge that'll do the same thing.

Where was the fifth Larsan, the one who'd gotten winged? Wait . . . his fastiga stood riderless some distance off. But where was he? These bully boys weren't the type to call it a day just because of a disabled arm.

I got good grades in math and analytics. My discussants told me so. Now why can't I dredge something I learned back then, up into memory, and use it? I could solve the problem for an exam, I'll bet.

Most likely the wounded one was snaking through the taller bushes, trying to get so close that he could pounce and stab.

Of course, this isn't exactly an examination room. Analytical thinking doesn't come natural, most especially not when your life's involved, and it's very, very odd that I should begin on it at this precise moment. Maybe my subconscious smells an answer.

The four riders had gotten together for a conference. They looked like toys at this distance, near the top of a high ridge paralleling the road and sloping down to its edge. Falkayn couldn't hear anything but wind. The sun, fully risen now, made rippling violet shadows in the gray grass. The air was still cold; his breath smoked.

Let's see. A wheel is essentially a lever. But we've already decided that the other forms of lever aren't usable. Wait! A screw? No, how'd you apply it? If any such thing were practical for us, Romulo Pasqual would've thought of it by now.

How about cutting the wheel in slices, mounted separately? No, I remember suggesting that to Rebo, and he said it wouldn't do, because the whole ensemble viewed from the side would still have a circular outline.

The riders had evidently agreed on a plan. They unstrung their bows and fastened them carefully under the saddle girths. Then they started toward him, single file.

What else does a wheel do, besides supply mechanical advantage? Ideally, it touches the ground at only one point, and so minimizes friction. Is there some other shape which'll do the same? Sure, any number of 'em. But what good is an elliptical wheel?

Hey, couldn't you have a trick mounting, like an eccentric arm on an axle that was also elliptical, so the load would ride steady? M-m-m, no, I doubt if it's feasible, especially over roads as dreadful as this one, and nothing but muscle power available for traction. The system would soon be jolted to pieces.

The leading Sanctuary guard broke into a headlong gallop. Falkayn took aim and waited puzzledly for him to come in range of a beam wide enough to be surely lethal. The transceiver made muffled squawkings in Falkayn's pocket, but he hadn't the time for chatter.

Same objection, complexity, inefficiency, and fragility, applies to whatever else comes to mind, like say a treadmill-powered caterpillar system. Perhaps Romulo can flange something up. But there ought to be a foolproof, easy answer.

Crouched against the neck of his fastiga, the leading guard was nearly in range. Yes, now in range! Falkayn fired. The blast took the animal full in the chest. It cartwheeled several meters more downhill, under its own momentum, before falling. Its rider had left the saddle at the moment it was struck, before the beam could seek him out. He hit the ground with acrobatic agility, rolled over, and disappeared in the brush.

By the time Falkayn saw what was intended, he had already shot the second. It crashed into the barrier of the first. The third rushed near, frightened but under control.

"Oh, no, you don't," the human rasped. "I'm not going to build your wall for you!" He let the other two pound by. As they slued about, exposing their riders to him, he had the bleak pleasure of killing an enemy. The fourth escaped out of range, jumped to earth, and ran toward the dead animals, leading his own but careful to stay on its far side.

Falkayn's bolts raked the slope, but he couldn't see his targets in the overgrowth and it was too moist in this spring season to catch fire. The third Larsan got to the barrier and slashed his fastiga's throat. It struggled, but hands reached from below to hold it there while it died.

So three warriors had made the course. Now they were ensconced behind a wall of their own, too thick for him to burn through, high enough for them to kneel behind and send arrows that would arch down onto him. Of course, their aim wouldn't be good—

The shafts began to rise. Falkayn made himself as small as possible and tried to burrow under one of his own slain fastigas.

Something which . . . which rolls, and holds its load steady, but isn't circular

The arrows fell. Their points went hard into dirt and inert flesh. After some time of barrage, a leonine head lifted above the other barrier to see what had happened. Falkayn, sensing a pause in the assault, rose to one knee and snapped a shot.

He ought to have hit, with a broad beam at such close range. But he didn't. The bolt struck the barricade and greasy smoke puffed outward. The Larsan dove for cover.

What made Falkayn's hand jerk was suddenly seeing the answer.

He snatched out the radio. "Hello!" he yelped. "Listen, I know what we can do!"

"Anything, Davy," said Schuster like a prayer.

"Not for me. I mean to get you fellows out of here—"

The arrows hailed anew. Anguish ripped in Falkayn's left calf where he crouched. He stared at the shaft that skewered it, not really comprehending for a moment.

"Davy? You there?" Schuster cried across a thousand kilometers.

Falkayn swallowed hard. The wound didn't hurt too much, he decided. And the enemy had ceased fire again. They must be running low on ammo, too. The road was strewn with arrows.

"Listen carefully," he said to the box. It had fallen to the ground, and blood from his leg was trickling toward it. A dim part of him was interested to note that human blood in this light didn't have its usual brilliance but looked blackish red. The rate of flow indicated that no major vessel had been cut. "You know what a constant-width polygon is?" he asked.

A Larsan ventured another peek. When Falkayn didn't shoot, he rose to his feet for an instant and waved before dropping back to shelter. Falkayn was too busy to wonder what that meant.

"You hurt, Davy?" Schuster pleaded. "You don't sound so good. They still after you?"

"Shut up," Falkayn said. "I haven't much time. Listen. A figure of constant width is one that if you put it between two parallel lines, so they're tangent to it on opposite sides, and then revolve it, well, the lines stay tangent clear around the circumference. In other words, the width of the figure is the same along every line drawn from side to side through the middle. A circle is a member of that class, obviously. But—"

The Larsan whose left arm had been scorched to disability sprang from a clump of bushes along the road. There was a knife in his right hand. Falkayn caught the gleam in the corner of an eye, twisted about, and snatched for his blaster where it lay on the ground. The knife arm chopped through an arc. Falkayn shrieked as his own hand was pinned to earth.

"Davy!" Schuster cried.

Falkayn picked up the blaster with his left. The muzzle wavered back and forth. He shot and missed. The guard cleared the barrier at a jump, drawing his sword as he sprang. The blade swept around. Probably he had closed his eyes at the moment the gun went off, for he struck with accuracy. The weapon spun clear of Falkayn's lacerated grasp.

The human yanked out the knife that pinned him, surged to his feet, and attacked left-handed. His voice rose to a shout: "A circle's not the only one! You take an equi—"

His rush had brought him under the Larsan's guard. He stabbed, but the point slithered off the breastplate. The native shoved. Falkayn lurched backward. The guard poised his rapier.

"Equilateral triangle," Falkayn sobbed. "You draw arcs—"

A horn sounded. The guard recoiled with a snarl. On the hillside, an archer rose and sent a last arrow at Falkayn. But the human's hurt leg had given way. He went to his knees, and the shaft whirred where he had been.

Another arrow, from another direction, took the sword-wielder through the breast. He uttered a rather ghastly rattling cough and fell on top of a fastiga. The surviving Sanctuary agents pointed frantically at the circles on their cuirasses. But arrows stormed from the riders who galloped out of the west, and the episode was over.

Rebo Legnor's-Child drew rein at the head of his household warriors and sprang from the saddle in time for Falkayn to crumple into his arms.

 

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