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agreed Gwenlyn.

"And there are limits to their talents?"[39]

"Naturally!"

Morgan broke in, amused. "Gwenlyn insists that I have the talent of finding and using talents."

"A mild talent, Father," said Gwenlyn. "Not enough to make you revolting. Butโ€”"

A door opened. A tweedy man with a small mustache stood in the doorway.

"I believe I'm wanted?" he said offhandedly.

Morgan introduced him. His name was Logan. He was the lightning calculator, the mathematical talent of Talents, Incorporated. Bors shook his hand. The tweedy man sat down. He drew out a pipe and began to fill it with conscious exactitude. He looked remarkably like a professor of mathematics who modestly pretended to be just another commuter. He dressed the part: slightly untidy hair; bulldog pipe; casual, expensive sports shoes.

"I understand," he said negligently, "that you want some calculations made."

"I'm told I do," said Bors, harassedly. "But I don't know what they are."

"Then how can I make them?" asked Logan with lifted eyebrows.

"Naturally," said Morgan, "you'll find out the kind of calculations he needs, that he can't get anywhere else. That'll be the kind he needs from you."

"Hm," said Logan. He blew a smoke-ring, thoughtfully. "Where do you use calculations in space-travel?"

"Everywhere," said Bors. "But we've computers for it. And they're quite adequate."

Logan shrugged. "Then what do you need me for?"

"You tell me!" said Bors, nettled. "Certainly we don't need calculations for space-travel. We've no long journey in mind. We're simply going to go out and do some fighting when the Mekinese fleet gets here."

Logan blew another smoke-ring.

"What calculations do you use in space-fighting?"

"Courses and distances," said Bors. He could see no sense[40] in this, but he went on. "Allowing for acceleration and deceleration in setting our missiles on targets. Allowing for the motion of the targets. Again we have computers for this. In practice they're too good! If we send a missile at a Mekinese ship, they set a computer on it, and it computes a course for a counter-missile which explodes and destroys our missile when it's within a certain distance of it."

"Then your missile doesn't hit," said Logan.

"All too often, it doesn't," admitted Bors.

"Then their missiles don't hit either."

"If they send a hundred missiles at us, they're cancelled out if we send a hundred to destroy them. Unfortunately, if they send more than we can counter, we get wiped out."

Bors found his throat going dry. This, of course, was what he'd desperately been denying to himself. It was the fundamental reason for a total lack of hope. The history of warfare is the history of rivalry between attack and defense. In the matter of missiles in space, there was a stalemate. One missile fired in attack could always be destroyed by another fired in defense. It was an arithmetic balance. But it meant that three ships could always destroy two, and four ships three. In the space-fight ahead, there would be at least ten Mekinese ships to every one from Kandar. The sally of Kandar's fleet would not be a rush into battle, but an advance into annihilation. "What we need," said Bors desperately, "is a means to compute courses for our missiles so they'll hit, and that the enemy can't counter-computeโ€”so that his missiles can't compute how to change course in order to cancel ours out."

He was astonished as the words left his mouth. This was what was needed, of course. But then he realized that it couldn't be done.

Logan blew a smoke-ring.

"Mechanical computers," he said, "have limits. They're designed to calculate a trajectory with constant acceleration or no acceleration. But that's all."

Bors frowned. "What else could there be?"[41]

"Changing acceleration," said Logan condescendingly. "A mechanical computer can't compute that. But I can."

Bors continued to frown. One part of his mind assured him that the statement that mechanical computers could not calculate trajectories of missiles with changing acceleration was incorrect. But the rest of his mind tried to imagine such a trajectory. He couldn't. In practice, men do not have to handle the results of variable acceleration as cumulative effects.

"I think," said Bors carefully, "that if you can do thatโ€”"

Logan blew a smoke-ring more perfect than any that had gone before.

"I'll calculate some tables," he said modestly. "You can use them on your computer-results. Then if you arrange your missiles to change their acceleration as they go, the Mekinese missiles can't intercept them."

He waved his hand with the grand air of someone assuring a grammar-grade pupil that multiplication tables were quite reliable and could be used with confidence. But his eyes fixed themselves on Bors's face. As the Captain realized the implications of his statement, the eyes of the Mathematical Talent of Talents, Incorporated shone with gratified vanity.

"We'll go out in a couple of tin cans," said Bors fiercely, "and try this out with dummy warheads!"

Gwenlyn said quickly, "Marvelous! Marvelous, Logan!"

"It's nothing," said Logan modestly.

But it was a very great deal. Bors, impatient to try it out, nevertheless realized that Logan hadn't made the suggestion out of a brilliant perception of a solution to a problem in ballistics, but because he thought in terms of mathematical processes. He didn't think of a new missile operation, but a new kind of computation. And he reveled in the fact that he had showed off his brilliance.

In the ground-car on the way to the fleet, Bors said helplessly to Gwenlyn, "I'm not the right man to be the liaison with you people. But this might make us a pretty costly conquest for Mekin! With luck, we may trade them ship for[42] ship! They won't miss the ships they lose, but it'll be a lot of satisfaction to us!"

"You expect to be killed," Gwenlyn said flatly.

"My uncle," explained Bors, "considers that he should have gotten killed when Mekin took over Tralee. It would have set a good example. Since we didn't do it for Tralee, we'll do it for Kandar. The king's going along too. After all, that's one of the things kings are for."

"To get killed?"

"When necessary," Bors told her. "Kandar shouldn't surrender even though there will be at least ten Mekinese to one Kandarian."

She smiled at him, very oddly.

"I suspect," she said, "that not everybody on the fleet will be killed. I'm sure of it. In fact, as my father would say, that's Talents, Incorporated information!"

Bors frowned worriedly.

The fleet of Mekin continued in overdrive, heading for Kandar. Each second it traversed a distance equal to the span of a solar system, out to its remotest planet. A heartbeat that would begin where a pulsing Cepheid, had it been possible to see, would have seemed at its greatest brilliance, and would end where the light from that same giant star seemed dimmed almost to extinction. Of course no such observation could be made from any ship in overdrive. Each one of the many, many ugly war-machines was sealed in its own cocoon of overdrive-stressed space. Even in the armed transports that carried officials and bureaucrats and experienced police organizers to set up a puppet government on Kandar, there was not the faintest hint of anything that happened outside the individual ship. But, what might be termed the position of the fleet, changed with remarkable swiftness. It traveled light-hours between breaths. Light-days between sentences. Light-months and light-years....

But it would not arrive on Kandar for a long while yet. Not for three whole days.

[43]

Chapter 4

The small fighting ship lifted swiftly from the surface of Kandar. As it rose, the sky turned dark and the sun's brilliant disk, far too bright to be looked at with unshielded eyes, became a blazing furnace that could roast unshielded flesh. Stars appeared, shining myriads despite the sun, with every one vivid against a background of black. The planet's surface became a half-ball, of which a part lay in darkness.

"Co-o-ntact!" said a voice through many speakers placed throughout the fighting ship's hull.

There was the rushing sound of compartment doors closing. Then a cushioned silence everywhere, save for the faint, standby scratching sounds that loudspeakers always emit.

Screens lighted. A speck moved among the stars.

"Prepare counter-missiles," said the voice. "Proximity and track. Fire only as missiles appear."

The moving speck flamed and was again only a moving speck. It ejected something which hurtled toward the ship just up from Kandar.

"Intercept one away!" said a confident voice.

The last-launched missile fled toward the first moving speck, diminishing as it went. It swung suddenly, off course.

"Fire two!" snapped somebody somewhere.

Another object hurtled away toward the stars.

"Fire three! Fire four!"

Far away, something came plunging toward the ship. It did not travel in a straight line. It curved. It was not reasonable for a missile to travel in a curved line. The interceptor missiles had to detect it, swing to intercept, to accelerate furiously. The first interceptor missed. Worse, it had lost its target. It went wandering vaguely among the stars and was gone.[44]

The second missed. The voice in the speaker seemed to crack.

"Fire all missiles! They're turning too late! Pull 'em up ahead of the damned thing!"

The deadly contrivances plunged away and further away into emptiness. The third interceptor missed. The fourth. Tiny specks moved gracefully on the radar screen. There was something coming toward the ship that had risen from Kandar. The tracer-trails of missiles appeared against the stars. They made very pretty parabolas. That was all. The thing that was coming left a tracer-trail too. It curved preposterously. The just-risen ship furiously flung missiles at it. It did not dodge. But none of the tracer-trails intersected its own. All of them passed to its rear.

For the fraction of a second it was visible as an object instead of a speck. That object swelled.

It went by. Bors's voice, relayed, said,

"Coup! You're out of action. Right?"

The skipper of the ship just up from Kandar said grudgingly, "Hell, yes! We threw fifteen missiles at it, and missed with every one! This is magic! Can we all have this before the Mekinese get here?"

"I hope so," said Bors's voice. "We're trying hard, anyhow. Will you report to ground?"

"Right," said the speakers in the ship which had just fired fifteen missiles without a hit or interception. "Off."

And then the compartment doors opened again and the normal sounds of a small fighting ship in space began again.

An hour later, aground, Bors said impatiently, "Half a dozen ships have checked out with me. I sent a single dummy-warhead missile at each one. They knew I was trying something new. They tried interceptors. Not one worked. Worse, my missiles drew the interceptors off-course so they lost their original aim on the Isis. Missiles set for variable acceleration not only can't be intercepted but they draw interceptors off-course and are super-interceptors themselves. I fired one dummy warhead at each target-ship. I got six hits with six[45] missiles. They fired an average of twelve missiles against each of mine. They got no intercepts or hits with seventy-two tries! This appears to me a very gratifying development for the situation we're in."

The bearded man who'd plumped for negotiation, earlier, now spoke indignantly in the War Council.

"Why wasn't this revealed earlier? We could have made a demonstration and Mekin would have been wary of issuing an ultimatum! Why was this concealed until it was too late to use in negotiations with them?"

"It wasn't available until today," Bors answered. "It was tried, and it worked."

An admiral said slowly, "As I understand it, this is a proposal of theโ€”hmโ€”Talents, Incorporated people."

"No," said Bors. "We got the idea but couldn't do the math. Talents, Incorporated did the computations to make the missiles hit."

"Why? Why let them do the math? There may be a counter to this device. Perhaps Talents, Incorporated, was sent to us to get us to adopt this freakish trick."

"Talents, Incorporated," said Bors, "enabled us to smash a submerged Mekinese cruiser. In giving us the necessary information, Talents, Incorporated kept the Mekinese from wiping out our space-fleet. Talents, Incorporatedโ€” Oh, the devil!"

The admiral gazed about him.

"Thisโ€”device," he said precisely, "is not a tried and standard weapon. On the other hand, the sally of our fleet is not war. Because of our civilian population we cannot make war on Mekin! The defiance of our fleet will be a gesture onlyโ€”a splendid gesture, but no more. It should be a dignified gesture. It would be most inappropriate for our fleet to take to space, ostensibly to say that it prefers death to surrender, and for it then to unveil a new and eccentric device which would say that the fleet was foolish enough to hope that a gadget would save it from dying and Kandar from conquest. The fleet action should be fought with scorn of odds. It should end its existence in a manner worthy of its traditions!"[46]

Bors exploded, "Damnitโ€”"

King Humphrey held up his hand and said fretfully, "As I remember it, Admiral, you have been assigned to hold together the defense forcesโ€”those who either did not insist on going with the fleet, or for whom there was no roomโ€”who have to be surrendered.

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