King and Emperor

“It's bigger than ours,” came a gloomy voice. Some friendly memory helped Shef to recognize it.

“Anything's bigger than yours, Odda,” he replied. “What are you waiting for, Osmod? Pull the bolt.”

As he saw Osmod turn, with a certain fear, to the bolt, Shef himself turned his back, ran up the stone steps to the parapet of the left-hand tower. Behind him he heard a squeak of protesting metal being drawn. Then a long scraping noise which ended in a great crash. He looked round just in time to see the sling release and the boulder that two mighty men had strained to lift fly into the sky like a pebble.

As it soared out on its long arc Shef followed it, ignoring the groans of protesting timber, the shouts and yells from the crew. The top of its arc, there, must be the midway point. He was sure it was on line for “War-Wolf.” But the range?

Shef let the breath escape in a long sigh. He knew already it was going to be over, even well over. His shot had been far worse than the enemy's. The thump and cloud of dust had come down well over. How well over? He put down the far-seer with its cloudy lenses, strained his one eye to get a sure view. There were too many things in the way. At a guess he would say forty yards over. Consider. How many men, stretched head to foot, between what he could see of “War-Wolf” and the already settling dust-cloud. Shef counted, nodding his head unconsciously to each imaginary six feet. Maybe not forty yards. More like thirty-five. Under rather than over. Say thirty-four.

Now how far was it from “War-Wolf” to the gate? The guard captain Malachi was standing by him, saying nothing but looking anxious.

“Think carefully. You must have walked that road many times. How far is it from the gate to their machine? Think of it in double paces.”

A long pause. “I would say one hundred and forty.” And twenty, already paced out, from the center-line of his own machine to this side of the gate. A hundred and sixty, times five and a half feet, was the range he meant to shoot. That sum, plus thirty-four, times three, was what he had shot. He had to reduce the fifteen-hundred-pound throw weight in proportion to the reduced distance to get a hit with a boulder of the same weight. Two days ago he would have thrown his hands up, declared the sum impossible. Now…

Shef sprinted down the steps again to where his sand table waited. Osmod met him with a face of woe. “The machine. It's falling apart. The weight's too big for it. Needs side-braces, like what they've got…”

Shef pushed him aside. “Wedge everything back as best you can, use nails if you have to. It has to hold together for one more shot. Tell the men to unload, winch up, put in ten hundred pounds. Then wait.”

He bent to his table, lines already drawn for the first of his sums. One hundred and sixty, times five, add on eighty—that was easy. Write “880” in the sand. Thirty-four, times three, add it on, write “982” in the sand.

Now, divide fifteen into 982 to find out how much distance to each hundred-pound bag. And then, divide that figure into the 880. Shef struggled on, absorbed. His own men watched him curiously. Solomon and Malachi exchanged glances. Either of them, they suspected, could have carried out the operation faster, as could any trader in the market. But then a market-trader would not have known what it was that the king of the barbarians was trying to do. He might be near-illiterate. But he had made the machine. The flares, the kites, the crossbows. Best to trust to what the Arabs would call his iqbal. The odor of success.

Shef straightened. He could not do quantities less than one, had had to double his numbers both sides to get a fair approximation, but he knew the answer.

“Ten hundred-pound bags in? Right, add three more. Open a fourth. Take half out. Exactly half.”

Shef bent over the open bag. There should be fifty pounds in it. According to his figures he should now take out seven more. What difference could that possibly make to a boulder of the size they were throwing? Grimly he scrabbled out what seemed to him to be seven pounds of dirt, the same weight as two days' rations. He twisted the bag closed, stepped up the ladder, hurled it in on top of the pile.

“Ready to throw again? Have you checked the line?”

A shout from the parapet, where Thorvin had gone to watch. “ ‘War-Wolf’ is ready! I can see the long arm raised!”

Shef looked at Osmod. There was no crash of metal here, no trumpets blaring and war-cries rising, but this was where the battle would be decided. All “War-Wolf” had to do was drop its range six feet. Unless they smashed it with this shot, the next act they would take would be to run for the harbor. To face the floating fort, the noon-day calm, and the Greek fire. In an hour they would all be burnt corpses floating in the sea.

Osmod shrugged like a farm-hand asked about the haymaking. “I checked her for line again. I can't say nothing about what happened to the timbers. You heard them start to come apart.”

Shef took a deep breath, looked at the counterweight, the frame, the sling with its carefully-chipped boulder. It felt wrong. The figures said it was right.

“Stand by to shoot. Get back, everybody. All right, Osmod. Shoot!”

As he pulled back the bolt Shef was already in mid-leap for the steps and the parapet. Behind him he heard the scrape, the crash, and this time a chorus of yells of alarm as the hastily-wedged timber frame slowly, inexorably, sprang apart. The boulder was still in the air, still rising, as he reached his vantage-point. As he focused on his target he saw it, too, suddenly move. The great wooden counterweight-chamber dropped instantaneously behind the mantlets, he saw the long arm rise, the inconceivably powerful lash of the sling, like a giant's arm coming round. And then there were two boulders in the sky. One falling, one rising. For an instant he thought they would strike each other. Then all he could see out on the plain was dust. And out of the dust, the enemy's missile still climbing.

Erkenbert's weak eyes had not let him see the flight of his first missile. He had a Lanzenbruder standing beside him to act as his observer, but the man had said only, “Very close, just over the top, drop it just a cat's hair, herra, and we are through!” Encouraging, but hard to count a cat's hair.

Erkenbert did his best. One thing he knew was that his throw-weight would not change, not now that he had the system in place for hauling the counterweight up again by main force. As the men struggled with it, heaving at unyielding ropes, he reflected on his problem. It was three hundred yards from machine to gate, more or less. He needed to shoot just a trifle less. So use the next boulder up in his graduated pile. But would that then fall short? What was the difference? If a stone of some two hundred pounds were to be thrown three hundred yards by the weight he had, whatever that weight was, how heavy a stone would be needed to travel just two hundred and ninety-five? Erkenbert knew how to find the answer. He needed to multiply three hundred by two hundred, and divide the answer by two hundred and ninety-five.

But to Erkenbert, product of the great and famous school of Latin learning at York, the school that in its time had produced such men as Alcuin the deacon, the minister of Charlemagne, preserver of manuscripts, poet, editor and commentator on the Bible, the problem did not present itself like that. To him, three hundred was CCC, two hundred CC. III times II was VI, C by C—but there common sense would have to step in, not calculation, and give an answer as XM. Erkenbert had plenty of common sense, he could soon, if not immediately, deduce that CCC multiplied by CC must be VIXM. But VIXM—six-ten-thousand—was more like a word or a phrase than a number. What VIXM divided by CCXCV might be—that, hardly the wisest man could tell, and even he not on a battlefield.

Erkenbert considered, ordered forward the next size of boulder up from the one he had just hurled. According to the number painted on its side, it should be perhaps five, perhaps ten pounds heavier than the last one—more or less, like the three hundred yards Erkenbert had estimated for the range. Arithmeticus though he was, absolute precision in numbers was no part of his world-view, except perhaps for calculating rents, the symbolism of Bible numbers, and the date of Easter. And “War-Wolf” had never before faced a reply. The stone that had crashed into the ground forty yards away had angered Erkenbert with its proof of hostile and inventive minds resisting him, and his Emperor, and their Savior's will. Its wild miss had cheered him as well: what better could one expect from illiterates imitating their betters, without so much as a copy of Vegetius to instruct them? Nor would they have had the ingenuity to match his roller and his ropes. Why were the laborers taking so long to haul the weight back into place? He waved forward the Lanzenbruder to flog the idle levies on.

One of the men heaving at a rope, his feet slipping in the soft dust, dared to snarl a comment in the ear of the man next to him.

“I'm a sailor, I am. We shift our lateeno-yards over the mast all the time, just like this. But what we use is