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minions already knew; each of which fitted itself into its long-assigned place. Every planet of Civilization had sent its every vessel capable of putting out a screen or of throwing a beam, but so immense was the number of warships in Grand Fleet that this increment, great as it intrinsically was, made no perceptible difference in its size.

On Rally Day Grand Fleet lay poised near Earth. As soon as he had introduced Samms to the intensely interested listeners at the Rally, Roderick Kinnison disappeared. Actually, he drove a bug to a distant corner of the spaceport and left the Earth in a light cruiser, but to all intents and purposes, so engrossed was everyone in what Samms was saying, Kinnison simply vanished. Samms was already in the Boise; the Port Admiral went out to his old flagship, the Chicago. Nor, in case any observer of the Enemy should be trying to keep track of him, could his course be traced. Cleveland and Northrop and Rularion and all they needed of the vast resources of the Patrol saw to that.

Neither Samms nor Kinnison had any business being with Grand Fleet in person, of course, and both knew it; but everyone knew why they were there and were glad that the two top Lensmen had decided to live or die with their Fleet. If Grand Fleet won, they would probably live; if Grand Fleet lost they would certainly die—if not in the pyrotechnic dissolution of their ships, then in a matter of days upon the ground. With the Fleet their presence would contribute markedly to morale. It was a chance very much worth taking.

Nor were Clayton and Schweikert together, or even near each other. Samms, Kinnison, and the two admirals were as far away from each other as they could get and still remain in Grand Fleet's fighting cylinder.

Cylinder? Yes. The Patrol's Board of Strategy, assuming that the enemy would attack in conventional cone formation and knowing that one cone could defeat another only after a long and costly engagement, had long since spent months and months at war-games in their tactical tanks, in search of a better formation. They had found it. Theoretically, a cylinder of proper composition could defeat, with negligible loss and in a very short time, the best cones they were able to devise. The drawback was that the ships composing a theoretically efficient cylinder would have to be highly specialized and vastly greater in number than any one power had ever been able to put into the ether. However, with all the resources of Bennett devoted to construction, this difficulty would not be insuperable.

This, of course, brought up the question of what would happen if cylinder met cylinder—if the Black strategists should also have arrived at the same solution—and this question remained unanswered. Or, rather, there were too many answers, no two of which agreed; like those to the classical one of what would happen if an irresistible force should strike an immovable object. There would be a lot of intensely interesting by-products!

Even Rularion of Jove did not come up with a definite solution. Nor did Bergenholm; who, although a comparatively obscure young Lensman-scientist and not a member of the Galactic Council, was frequently called into consultation because of his unique ability to arrive at correct conclusions via some obscurely short-circuiting process of thought.

"Well," Port Admiral Kinnison had concluded, finally, "If they've got one, too, we'll just have to shorten ours up, widen it out, and pray."

"Clayton to Port Admiral Kinnison," came a communication through channels. "Have you any additional orders or instructions?"

"Kinnison to Admiral Clayton. None," the Port Admiral replied, as formally, then went on via Lens: "No comment or criticism to make, Alex. You fellows have done a job so far and you'll keep on doing one. How much detection have you got out?"

"Twelve detets—three globes of diesels. If we sit here and do nothing the boys will get edgy and go stale, so if you and Virge agree we'll give 'em some practice. Lord knows they need it, and it'll keep 'em on their toes. But about the Blacks—they may be figuring on delaying any action until we've had time to crack from boredom. What's your idea on that?"

"I've been worried about the same thing. Practice will help, but whether enough or not I don't know. What do you think, Virge? Will they hold it up deliberately or strike fast?"

"Fast," the First Lensman replied, promptly and definitely. "As soon as they possibly can, for several reasons. They don't know our real strength, any more than we know theirs. They undoubtedly believe, however, the same as we do, that they are more efficient than we are and have the larger force. By their own need of practice they will know ours. They do not attach nearly as much importance to morale as we do; by the very nature of their regime they can't. Also, our open challenge will tend very definitely to force their hands, since face-saving is even more important to them than it is to us. They will strike as soon as they can and as hard as they can."

Grand Fleet maneuvers were begun, but in a day or so the alarms came blasting in. The enemy had been detected; coming in, as the previous Black Fleet had come, from the direction of Coma Berenices. Calculating machines clicked and whirred; orders were flashed, and a brief string of numbers; ships by the hundreds and the thousands flashed into their assigned positions.

Or, more precisely, almost into them. Most of the navigators and pilots had not had enough practice yet to hit their assigned positions exactly on the first try, since a radical change in axial direction was involved, but they did pretty well; a few minutes of juggling and jockeying were enough. Clayton and Schweikert used a little caustic language—via Lens and to their fellow Lensmen only, of course—but Samms and Kinnison were well enough pleased. The time of formation had been very satisfactorily short and the cone was smooth, symmetrical, and of beautifully uniform density.

The preliminary formation was a cone, not a cylinder. It was not a conventional Cone of Battle in that it was not of standard composition, was too big, and had altogether too many ships for its size. It was, however, of the conventional shape, and it was believed that by the time the enemy could perceive any significant differences it would be too late for him to do anything about it. The cylinder would be forming about that time, anyway, and it was almost believed—at least it was strongly hoped—that the enemy would not have the time or the knowledge or the equipment to do anything about that, either.

Kinnison grinned to himself as his mind, en rapport with Clayton's, watched the enemy's Cone of Battle enlarge upon the Admiral's conning plate. It was big, and powerful; the Galactic Patrol's publicly-known forces would have stood exactly the chance of the proverbial snowball in the nether regions. It was not, however, the Port Admiral thought, big enough to form an efficient cylinder, or to handle the Patrol's real force in any fashion—and unless they shifted within the next second or two it would be too late for the enemy to do anything at all.

As though by magic about ninety-five percent of the Patrol's tremendous cone changed into a tightly-packed double cylinder. This maneuver was much simpler than the previous one, and had been practiced to perfection. The mouth of the cone closed in and lengthened; the closed end opened out and shortened. Tractors and pressors leaped from ship to ship, binding the whole myriad of hitherto discrete units into a single structure as solid, even comparatively as to size, as a cantilever bridge. And instead of remaining quiescent, waiting to be attacked, the cylinder flashed forward, inertialess, at maximum blast.

Throughout the years the violence, intensity, and sheer brute power of offensive weapons had increased steadily. Defensive armament had kept step. One fundamental fact, however, had not changed throughout the ages and has not changed yet. Three or more units of given power have always been able to conquer one unit of the same power, if engagement could be forced and no assistance could be given; and two units could practically always do so. Fundamentally, therefore, strategy always has been and still is the development of new artifices and techniques by virtue of which two or more of our units may attack one of theirs; the while affording the minimum of opportunity for them to retaliate in kind.

The Patrol's Grand Fleet flashed forward, almost exactly along the axis of the Black cone; right where the enemy wanted it—or so he thought. Straight into the yawning mouth, erupting now a blast of flame beside which the wildest imaginings of Inferno must pale into insignificance; straight along that raging axis toward the apex, at the terrific speed of the two directly opposed velocities of flight. But, to the complete consternation of the Black High Command, nothing much happened. For, as has been pointed out, that cylinder was not of even approximately normal composition. In fact, there was not a normal war-vessel in it. The outer skin and both ends of the cylinder were purely defensive. Those vessels, packed so closely that their repellor fields actually touched, were all screen; none of them had a beam hot enough to light a match. Conversely, the inner layer, or "Liner", was composed of vessels that were practically all offense. They had to be protected at every point—but how they could ladle it out!

The leading and trailing edges of the formation—the ends of the gigantic pipe, so to speak—would of course bear the brunt of the Black attack, and it was this factor that had given the Patrol's strategists the most serious concern. Wherefore the first ten and the last six double rings of ships were special indeed. They were all screen—nothing else. They were drones, operated by remote control, carrying no living thing. If the Patrol losses could be held to eight double rings of ships at the first pass and four at the second—theoretical computations indicated losses of six and two—Samms and his fellows would be well content.

All of the Patrol ships had, of course, the standard equipment of so-called "violet", "green", and "red" fields, as well as duodecaplylatomate and ordinary atomic bombs, dirigible torpedoes and transporters, slicers, polycyclic drills, and so on; but in this battle the principal reliance was to be placed upon the sheer, brutal, overwhelming power of what had been called the "macro beam"—now simply the "beam". Furthermore, in the incredibly incandescent frenzy of the chosen field of action—the cylinder was to attack the cone at its very strongest part—no conceivable material projectile could have lasted a single microsecond after leaving the screens of force of its parent vessel. It could have flown fast enough; ultra-beam trackers could have steered it rapidly enough and accurately enough; but before it could have traveled a foot, even at ultra-light speed, it would have ceased utterly to be. It would have been resolved into its sub-atomic constituent particles and waves. Nothing material could exist, except instantaneously, in the field of force filling the axis of the Black's Cone of Battle; a field beside which the exact center of a multi-billion-volt flash of lightning would constitute a dead area.

That field, however, encountered no material object. The Patrol's "screeners", packed so closely as to have a four hundred percent overlap, had been designed to withstand precisely that inconceivable environment. Practically all of them withstood it. And in a fraction of a second the hollow forward end of the cylinder engulfed, pipe-wise, the entire apex of the enemy's war-cone, and the hitherto idle "sluggers" of the cylinder's liner went to work.

Each of those vessels had one heavy pressor beam, each having the same push as every other, directed inward, toward the cylinder's axis, and backward at an angle of fifteen degrees from the perpendicular line between ship and axis. Therefore, wherever any Black ship entered the Patrol's cylinder or however, it was driven to and held at the axis and forced backward along that axis. None of them, however, got very far. They were perforce in single file; one ship opposing at least one solid ring of giant sluggers who did not have to concern themselves with defense, but could pour every iota of their tremendous resources into offensive beams. Thus the odds were not merely two or three to one; but never less than eighty, and very frequently over two hundred to one.

Under the impact of those unimaginable torrents of force the screens of the engulfed vessels flashed once, practically instantaneously through the spectrum, and went down. Whether they had two or three or four courses made no difference—in fact, even the ultra-speed analyzers of the observers could not tell. Then, a couple of microseconds later, the wall-shields—the strongest fabrics of force developed by man up to that time—also failed. Then those ravenous fields of force struck bare, unprotected metal, and every molecule,

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