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THE JAKANDI MODULI by Francis G Rayer

This short story first appeared in the magazine New Worlds, Issue Number 42, dated December 1955.
Editor: John Carnell. Publisher: Nova.
Country of first publication: Great Britain (England, Wales, Scotland and Northern Ireland).
This work is Copyright. All rights are reserved.


THE JAKANDI MODULI

By Francis G. Rayer

Through the years there have been plenty of stories dealing with space “warps ” although few authors have ever attempted to define one. Francis Rayer visualises in this story a number of ships being warped out of our own space-time continuum — and offers a possible suggestion of just how such an event could occur.

illustrated by QUINN

“ Warbler on course to contact talk-down,” the communicator said metallically.
Alan Spey swivelled his broad chair and flipped a switch, lighting screen 17 on the second row of cathode-ray tubes facing him. Coming in at twenty miles altitude, the Warbler was a fleck captured by the spaceport radar. He depressed the button under the screen.

“ Kelsey Central Control here. Go into high ceiling course round east radio beacon.”
He released the button and his gaze sped over the four rows of twenty-five screens, eighty of which were illuminated by travelling dots. Dark, nearly six feet, he was filling out to match his height. Stray hair hung over his forehead, swaying as he swivelled the chair at the focus of the four rows of screens. Piled high in orbits above Kelsey Central, eighty spaceships waited his command, occupying a chimney of air twenty miles in altitude and thirty in diameter at its top.

A communicator fitted to his right chair arm buzzed. He flipped it on, gaze steady on two screens where ships lowest in the chimney were upending for touchdown.
“ A message from government command office, sir.”
The girl sounded apologetic. Well she might, Alan thought. A man with eighty ships on his mind did not welcome interruptions.
“ Yes ?”
He pressed a button, issuing swift instructions to correct a course on the second level. His gaze travelled over the other screens, pausing momentarily on 17. The Warbler had gone into orbit round the east marker signal with the practised accuracy of an old hand.

“ We are asked to remind you that the Dipper II, due next, carries the Tertullian junior ambassadors,” the girl said.
“ Thanks.”

He released the communicator button. He had not forgotten. The arrival of the Tertullian ambassadors had been news for months, and he had been expecting the Dipper II to drift into the top of the stack at any moment. Due from Mars, she had been fitted for her special task. The Tertullians had landed on Mars because conditions there were more like home, he recalled, and their extra-galactic vessel had been left there.

His eyes flickered to the wall clock. Another two hours would see him through this duty period, and he was glad. In an hour his replacement would be in, ready to memorise the overall picture before taking the chair.

“ Dipper II on course to contact talk-down,” the ceiling reproducer stated.

Alan’s gaze swept along the screens, and he flipped on No. 4. The reproducer in the ceiling was on an uninterrupted single circuit from the great radio station due south of Kelsey Central. There, scores of radiomen brought in their scores of ships, with ten thousand free miles of space, he thought wryly. But once the ships were in the Kelsey Central chimney all were under the control of one man. A single brain was necessary to memorise and integrate the orbits, bringing the ships slowly down, level by level, until they could up-end and touch down. Only five men in the country could operate the Central Control panels. One was sick from an auto accident. That left four only, meaning six hours on, one taking over, and seventeen off. Alan hoped there would at least be no further accident to personnel, which would mean eight hours on, one taking over, and fifteen off.



He talked the Warbler to her second beacon, and the Dipper II into course round the east marker. A further screen flickered with its radar frequency request for touchdown. He saw her down, swept clear the channel, and lifted two ships half-way down the chimney, which were two-thousand feet under altitude. Over a score of ships were weaving upwards, level by level, through the chimney, courses shuttling among those of the ships coming down. Regular as ninepins on a vast board, others stood on the field landing disc, just down, or awaiting blast-off.

He brought the Warbler down one level, systematically checked a score of other ships, and saw that the Dipper II was going in too fast and overshooting her beacon course. A few snapped words brought her back on circuit and he smiled slightly as he thought of the Tertullian junior ambassadors. If they did not like a 4g turn then they could discipline their Captain, trained to fly the Earth ship for them ! Once in the Kelsey Central stack, an order from Control must invariably be obeyed without question, and each captain was required to know the orbit into the top level by heart.



Never had the spaceport been so busy, Alan thought as he worked ships down level by level. Radioactive contamination of exhaust gases had posed a problem, but a young engineer had solved it by the waterflushed landing disc. That was fifty years before. Now, Hillington Kelsey was old and Kelsey Central grown to dimensions undreamed of when he set up the first control post. Alan could not remember a time when there had been more than sixty ships simultaneously in the stack. The number had leapt to eighty because of the Tertullian visit. He brought Dipper II down to second level. The Warbler was already in her third level orbit, at fifteen miles altitude. His gaze flashed to other screens. Among the increased traffic was the Spacecar, full of journalists from Mars, and the Thunderstone, a ship carrying high brass from preliminary discussion with the Tertullians on Mars. Soon would come the Tertullian chief ambassador, at terminus after a journey of over four light years.

A step came behind the chair. Alan glanced up briefly. His replacement, Harry Laing, was ten years his senior, and his brows were high.
“ A lot of ships in the stack, Alan !” he said.
Alan grimaced. “ The Tertullians. Journalists, officials. A few big businesses, too, waiting to see which way the cat jumps.”
“ Anything special ?”
“ N-no. Theoretically we can handle a hundred ships.” He hoped they never would.

They were silent as he moved ships up and down in the stack. One blasted off and two landed. A new vessel came into orbit round the east marker beacon. The Warbler was coming down still, and would soon be in the middle of the chimney, a mere ten miles up. A red bulb over one screen and Harry Laing indicated it.

“ Serious ?”
“ No. The old Landflirt. I’ve lost count of the times I’ve talked her down — and warned her ! Now they’ve got a defective tube, and she’s on emergency course down through the stack.”

He watched the screens, with their weaving dots. Eighty ships on interlacing paths, courses crossing, rising and failing in a warp and weft exactly computed for maximum safety. Down through the whole wove the red dot of the Landflirt. Alan watched her, and the courses of the Warbler and Dipper II. Both were exactly on course. He brought the Warbler down a further level, and checked on the Dipper II. Her captain had retrieved his first error, and was exactly on orbit. He scanned other screens, then his eyes went back to the seventeenth on the second row. The Warbler had gone. No radar dot marked the silver screen.

A shock ran through Alan from scalp to toe. Behind, breath hissed through Harry Laing’s teeth.
Alan thumbed buttons. Flecks lit on the seventeenth screen, showing field and marker positions. The screen was working. Everything was there — except the Warbler. Even had she blown all tubes and dropped like a stone the screen would have shown her fall and destruction as she was automatically tracked by directive echoes.

“ Gone !” Laing said.
The arm unit buzzed imperatively. “ Report present position of Warbler."
Alan’s lips dried. He moved three other ships down the stack automatically, saw another signal for touch-down, and landed it. Position of Warbler unknown, he thought. It was fantastic — impossible. The position of every ship within the stack was always known !

He compromised. “ Screen has ceased to show Warbler's position.”
There was a delay. The girl’s voice was replaced by that of a man. The new tones had the snap of authority.
“ Locate Warbler and inform at once of her position !”

Alan worked controls in a panel in front of his chair. The weaving pattern showed all other ships in order, but the gap the Warbler should have occupied remained unfilled. Control to ship radio reported inability to raise her. The overall big-screen radar showed nothing. The Warbler had not merely gone, but had ceased to exist.



It was an hour past time when he left the seat and Harry Laing slipped into it. Dipper II was nearly down. The heavy traffic of ships had thinned, leaving barely fifty in the stack. Alan mopped his brow, feeling twice his twenty-five years, and closed the sound-proof door of the control room with a mixture of relief and unease.

An upright man, with peppery moustache and military bearing was waiting.
“ Mr. Spey ?” he snapped.
Alan nodded, recognising the voice. General Frazer had buzzed at five minute intervals since the initial order demanding the Warbler's position.
“ Come with me !”

Frazer turned on a heel as he gave the order, and a subaltern stepped smartly beside Alan. They strode to the lift, and thence to an office at ground level. The subaltern closed the door.

“ Dipper II was behind the Warbler," Frazer stated. “ I don’t need to remind you the Tertullian junior ambassadors were on the Dipper II. They’re raising hell on earth. They suspect treachery — assassination gone wrong ! They’ve nearly burned up the radio, threatening immediate return to Mars and Alpha Centauri !”

Alan nodded, understanding. “ They think we tried to get the Dipper II and got the Warbler by mistake ?”
“ Just so !”
Alan felt irritated. “ And you’re letting a lot of one-eyed worms shout you down, General ?”

A spark appeared in Frazer’s eyes. He grew visibly in stature, his face carved from lined stone. “Earth needs bases in the Alpha Centauri system, Mr. Spey ! Without them our development is finished !”

“ Sorry.” Alan guessed higher officials were giving Frazer a bad time. He sat on the desk. “ Look, I’ve worked the chimney stack this five years, and no ship has done that before. She didn’t blow up, or slip out of the pile. She just vanished. That the Dipper II was next was only chance. I’ve no more idea of what happened to the Warbler than you have. General.”

General Frazer sighed. “You know the Tertullian chief ambassador is on his way. This needs clearing up before he arrives, or — ”

He left the words and Alan guessed what he meant. Lack of explanation would destroy Tertullian confidence in Earth. There would be no grant of bases on Alpha Centauri system planets. Earthmen would stew in their own corner of space, deprived of stepping-stones to remote systems.



An hour later Alan had eaten, changed, and been asked to return to Frazer’s office. He drove slowly from the apartments where staff lived. The rim of the landing disc was a mile away across the wide turf safety belt. Above was the unseen stack of ships, losing altitude and tightening courses to land, or spiralling up until given the clearance order. As he turned at a junction, a silvery needle settled out of the sky on plumes of fire. Above, another ship was momentarily visible through cotton-wool clouds, curving in on lowest level orbit, ready for turn-up.

He left the auto outside the great control block, wLere myriad radar antennae pointed at the sky. Kelsey Central had never had an accident — or a disappearance, he thought as he went in.

An old man with creamy white hair sat at the side of the desk. Astonished, Alan recognised Hillington Kelsey, who shook his hand.
“ Mr. Kelsey can make no suggestion,” Frazer said flatly.
Kelsey looked apologetic and pyramided his fragile hands. “You’re too complicated for me these days. General. When will Mr. Jakandi from the computer section be here?”
“ Jerry Jakandi ?” Frazer eyed the clock. “ Within minutes. And she’s a girl.”

Alan had heard of her but they had never met. Hillington Kelsey pursed his lips. “ A girl — with that responsibility ?”
“ But the grand-daughter of Ayres Jakandi, the mathematician !” Frazer put in. “ That helps to explain.”

They waited and Alan wondered what line Frazer and Kelsey were taking. Jerry Jakandi came in smartly and smiled. The smile and her tight, dark ringlets remained in Alan’s mind. She was little over twenty, he judged, but had eyes filled with wisdom. Furthermore, he knew no wire-pulling on earth could have got her into Kelsey Central, if ability were lacking.

illustration from THE JAKANDI MODULI by Francis G Rayer “ You know of the loss, and its repercussions on the Tertullian delegation,” Frazer said, elbows on desk so that his head looked sunken. “ You have no explanation ?”

Jerry Jakandi shook her head quickly. “ None worth mentioning.” “ There is not some — some coincidence of orbits ?” Kelsey asked, leaning forward. “ Some error which would only show up when many ships were in the funnel ?”

Alan frowned, and realised this was a point he had not considered. Yet it was obviously not the explanation.
“ No. If courses had coincided we should have had a crash. There are actual ships, besides orbits computed on paper.”
“ That is so,” Kelsey admitted. “Could some pattern of other ships conceal the Warbler, or nullify the radar ?”
The dark head shook a third time. “ Impossible !”
General Frazer tapped his desk. “There has been no crash reported, and no normal radio contact with the ship.”

Kelsey was silent, clearly with no other suggestion. The girl’s eyes settled on Alan.
“ You’re Mr. Spey, who was on duty?”
“ Then I’d like to check figures with you later.”

The door opened almost explosively and a junior officer, harassed, conferred in whispers with Frazer. Alan saw anger, annoyance and irritation cross the General’s face. “ Try to get him to wait !” he snapped at last.

“Yes, sir.”
The officer departed and Frazer scraped back his chair. “ The Tertullian chief ambassador refuses to come in to be talked down !” he stated bitterly.

“ But why ?” Kelsey looked helpless.

“ Suspicion !” Frazer swore. “Afraid we’ve some secret plan to wipe him out. Everybody knows the Warbler’s gone already ! Some news syndicate has been following the Tertullians ever since they landed on Mars to change to earth ships, and they’ve seized on this as hot news. Damn ’em.” He swung suddenly and directed a finger at Jerry Jakandi. “You will plot a new course — one straight down through the stack ! A safe, simple, direct course — ”

Alan saw her mouth open, and close . . . Never in fifty years had such a request been made. Even emergency courses were far from simple and direct.

Frazer seemed to understand her hesitation, and silenced any argument before it came with a gesture of dismissal. “ This is larger than any of us. Miss Jakandi !” His tone made the words an apology. “ Earth needs bases near Alpha Centauri. It’s taken over fifteen years of negotiation to get the Tertullian ambassador this far. If he leaves without landing it’ll be the gravest tactical defeat we have ever suffered.”

Silence, then she saluted. “ It can be done. The computer can be cleared, some ships stood off. I’d like the man who will talk down the ship with me.”

Frazer indicated Alan. “ I’ll try to keep the ambassador on schedule. It will be early in Mr. Spey’s duty period.”
“ Then I’ll take him !”



The conditioned air of the computer block smelt faintly of ozone and their feet were quiet on the compo floor. Data for a course to any planet could be prepared within the hour.

“The orbits for the hundred channels you have were plotted years ago, and have never been changed,” Jerry Jakandi said as they descended in a silent lift. “Except for occasional emergency orbits, we’re engaged usually in interplanetary routes. Freighters want maximum economy, military ships minimum transit' time.” She gestured, stepping from the lift. “ What the General asked isn’t easy.”

Alan thought of the hundred possible courses down, and the hundred up. That made two hundred, not counting the various special courses, mostly for military ships. Of the possible hundred ships in the Kelsey Central Control chimney, any number might be landing, and any number taking off. That gave ten thousand possible orbit combinations. Assuming the random placement of ships in landing and take off, there were a hundred times ten thousand ultimate overall possible combinations.

His step faltered momentarily. “You have a million orbital combinations here !”
She smiled back at him. “ Only just realised that ? How many days have you had the same stack sequence ?”
He grimaced. “ Never ! I’d never realised that before. It’s always different. Like — like — ” He sought for an illustration. “ Like cube chess !”

Her laugh tinkled as she opened a silenced door. “ Cube chess is child’s play compared with the orbits of 100 ships, in every possible combination, believe me,” she said.

Alan felt inclined to agree as he followed between the rows of differential computers that could integrate a thousand variables instantly and give a solution that was no mere approximation. The control room, with its four rows of screens, was even simple by comparison. Jerry Jakandi worked with two assistants, men twice her age. Bewildered, he could only listen and watch, and try to store in memory such facts as he must know. Courses were modified. Others were temporarily abandoned on the supposition that a full hundred orbits would not be required. Down through the intricate mass of routes, which might consist of an unspecified number of ships rising, and an unspecified number landing, was plotted a simple spiral, to quick turn-over and touch down. Two hours had passed when it was completed. After, Alan took a sheaf of notes and went off to sleep. As he left the building a subaltern he recognised handed him a message.

“ Tertullian ambassador’s ship is the Allergo, and will enter Central Control stack at 1900. Frazer.”

Alan wondered whether he would sleep. Jerry Jakandi’s notes burned a hole in his pocket. When he closed his eyes her laughing face danced behind rows of computations.



Half an hour before the Allergo was due to go into orbit round the east beacon marker signal Alan took over. First glance on entering the control room had shown traffic was heavy, and craft were stacked high in the twenty mile funnel that terminated on the landing disc. A bulb glowed red at one screen.

“ The Orgemore from Venus,” the man he was to replace said briefly. “ Had trouble first with her tubes blasting off there, and I’ve just got her on an emergency orbit.”

Alan studied the screen. The Orgemore was on a steady descent spiral at the perimeter of the aerial chimney. If her tubes failed she would speed out of the stack in a straight path which would terminate in the destruction of no ship except herself. Meanwhile, her course would demand no sudden manoeuvres or unnecessary stress. It was the same emergency course on which he had nursed down the old Landflirt during his previous duty period, he saw.

He was alone when the Allergo came in on the east marker, a trifle too fast. Correcting her, he wondered why the Tertullian skippers were always too rapid. Dipper II, with its load of junior ambassadors, had been the same.

“ One-eyed worms !” he grunted.
He had never seen a Tertullian, but the news screens had seldom failed to show them for months, their topicality reaching crescendo with the arrival of the ambassadors on Mars. Tall as a man, they were fat, vermiform creatures that balanced on one end and regarded humanity pensively with a solitary eye situated in the other. Nevertheless, their ships could reach Mars from Alpha Centauri in the minimum time of five years, which bettered by six months any earth ship driven as near the speed of light as it could be forced to attain.

Minutes later the reproducer rattled into life. “ Canopus, military, coming into control.”
Alan adjusted a pick-up screen that would start at the top and follow down through the twenty miles stack. The Canopus sped in sweetly and went into orbit round the east beacon marker with the exactitude of a military flagship with admiral aboard.

Minutes ticked by, and screens winked. Every sense alert, Alan twirled the chair, pressing buttons, issuing commands, sixty ships in his hands. Very slowly an unease began to dawn in his mind. The ships were flying motes that seemed to be working into a pattern. The Allergo had overshot, and was in corrected orbit. The Canopus was true as a dart on a string. Below, the Orgemore was descending the emergency way, a mere drifter circling the complexity of ships. Thus it had been with the Dipper II, the Warbler, and the Landflirt, Alan thought. His gaze went back to the screen where the military craft sped . . . had sped. It was blank.

A released spring, his thumb opened a channel to the general radio.
“ Contact Canopus !”
“ Yes, sir.” Moments, then: “ No reply, sir.” Delay again, then: “ Report present position of Canopus, please.”
Alan licked his lips, dry. “ The Canopus is no longer visible on my screen !”

The same statement as before, he thought. Within moments the arm communicator awoke to a voice near panic. Eyes on his screens, Alan answered automatically, talking craft through the stack as he did. Yes, he knew the Canopus should not have vanished. No, it was inexplicable. Yes, he knew the Tertullian chief ambassador was adjacent in the stack and could have witnessed the disappearance of the Canopus, had he been looking.



When the bedlam ceased he felt sweat on his brow. The Allergo was descending rapidly on the path Jerry had computed, he observed. She left behind layer upon layer of ships, the limping Orgemore, and signalled for turn-up. He gave her turn-up, and she settled. Her screen went dark and he concentrated on the other ships in the stack, searching some hint of the location of the Canopus. There was none.

The arm communicator did not sound again. When he went off, nerves jagged, an odd quiet seemed to have settled on the building. He sought General Frazer’s office, and was admitted at the fourth knock. Frazer seemed to have aged.

“ The Tertullian ambassadors have gone into isolation,” he said wearily. “ The chief ambassador left his ship immediately on landing and joined his staff. They have issued no statement, and will answer no message.” A desk communicator buzzed. Frazer flipped its switch, and Alan saw his face grow pale. “Thanks.” He sat back, tired eyes on Alan. “ They have issued a statement — now. They wish to return to Mars, and Alpha Centauri, at once, and ask a take-off orbit be prepared for the ship they will occupy.”

Defeat was bitter in his eyes and Alan nibbled his lower lip. No negotiation. Therefore no bases on Alpha Centauri planets, and no expansion of humanity. Damned suspicious one-eyed worms ! he thought. Calling them that somehow gave him relief and satisfaction.

“ Can’t they be convinced it’s an accident ?” he asked.
“ We’re trying. But it’s happened twice and they’re a suspicious lot.”

An hour later Alan was in his own rooms when a message came from the Kelsey Central chief controller, stating that the injured operator was back, and that he, Alan Spey, was suspended indefinitely from duty. Alan’s face clouded and he hoped the suspension was merely to inspire confidence in the Tertullian delegation. Shortly after his private phone buzzed and General Frazer’s voice awoke from it.

“ You are free, Mr. Spey ?”
“ Yes.” Alan wondered if the suspension order had originated with Frazer.
“ Good. You are to leave for Mars at once — ”
Alan felt astonishment. “ Mars ?”

“To prepare for the return of the Tertullians to Alpha Centauri.” Defeat undertoned Frazer’s voice. “ We must assure their journey back is in every way smooth and uneventful. It is hoped they may then reconsider, and possibly allow another delegation to come to Earth sometime during the next decade. It’s a long term policy, but all we can do.” The General sighed. “ We know they tap most of our radio communications. A message saying they’re to be taken special care of on Mars may be interpreted as anything from weakness on our part, to a dangerous code signal that we’ve failed to liquidate them here and that Mars is to rectify the error. So you’re to go personally, with Miss Jakandi, and will have twenty-four hours start, if they continue to sit tight here. It is your duty to see they land on Mars in the simplest and safest fashion, that no possible hitch arises, and that the Tertullian vessel is given every aid in clearing Mars and our system without danger or hindrance.”

“ Sugaring the pill of defeat. General ?”
“ No, Mr. Spey.” The crisp note was back. “ The defeat is ours, and one we’ll need half a generation to overcome.”
The line went dead and Alan prepared to leave. As Frazer said, humanity had put up a bad show, and to speed the Tertullians’ departure would at least prove no assassination had been intended.

The Kelsey Central site was a vast expanse of concrete within the wide ring of the green belt. Alan parked, and found Jerry Jakandi waiting at the passing out offices on the concrete perimeter. She smiled, waving.

“ We’re to travel fast in a military ship !”
Alan studied her. “ Why did General Frazer pick us ?”
“ Possibly because you’ve assisted more ships in planetfall than almost anyone living.”
“ And you ?”
She smiled. “ Perhaps because I’ve got more orbits by memory than anyone he knows.”

A flat motorised truck took them across the concrete to the edge of the disc that had made Hillington Kelsey’s fortune. Heat-resistant as mica and asbestos combined, unabsorbent as glass, it was flushed with an artificial lake mere inches deep. The water gurgled ceaselessly from perimeter to centre, and down through ducts to purifiers hundreds of feet below ground.

A dozen assorted ships stood like skittles on the disc. Jerry pointed. The Thunderstone was new, longer than the other vessels, and equipped with every defence and attack device humanity could devise. Her cage awaited them.

It was seldom he saw this aspect of the complex stack of ships, Alan thought as they ascended. In the control room the ships tended to become symbols in some weird game — characters that threaded a com- plex maze on courses that must never touch.

The Thunderstone’s captain was waiting, brisk and straight as a ramrod, obviously unimpressed by his two civilian passengers, but intent on being pleasant.
“ You are Captain Ned Gilliand,” Jerry Jakandi said.
Gilliand nodded, and Alan liked him. “ We’re ready for clearance on millitary trajectory.”

Alan followed them in, wondering if they knew just what a military trajectory cost a Central Controlman in perspiration. It was a direct blast up through the stack of ships, computed with an accuracy that would make even Ned Gilliand’s short hair stand on end, if he knew.

A ship descended with a woosh from the blue, slowing on a pillar of flame as if elastic held it to the heavens, and settled amid a cloud of steam that momentarily hid it. High above in the midsummer sky Alan could catch occasional glimpses of other silvery motes swimming the chimney down.

Men hastened through the ship, amid clanging of doors and murmur of motors. Within ten seconds the movement and sound had ceased. Fifteen seconds later a signal that all personnel were cradled ran through the ship, and five seconds after Alan felt that the earth had exploded at its core and was pressing him in the back. It was minutes before they could leave the cradles and stand.

Jerry Jakandi massaged a tender spot. “ That’s the first time I’ve ever taken off in military trajectory — and the last !” she stated.

Alan felt an impression of half-inch netting was embossed for ever on a large area of his person. There were no ports here to watch the planet’s surface recede.

“ Going back to the Warbler and Canopus,” he said. “ In Frazer’s office you remarked you had no explanation — worth offering. So what was the explanation you felt not worth offering . . . ? ”

She looked at him quickly. “ A woman in my position doesn’t risk a hard-won reputation on wildcock theories.”
Alan smiled. “ I don’t hire and fire you. But I do feel interested in what you think.”

She listened to the murmur of the Thunderstone’ s tubes. “ I’ve nothing to go on except a lot of figures you’d neither be able to check or understand — and the fact that both vanished ships were on the same orbit, in similar conditions.”

“ Same orbit ?” He considered. “How’s that an explanation ?”
“ I — don’t know.”

He pondered her words as they ascended to the control deck. Ned Gilliand had a quiet efficiency speaking of long experience and ample self-confidence. Alan judged the take-off alone had been a convincing demonstration of both. He wondered what Jerry meant. Same orbits — therefore the same weaving path amid the complex pattern of ships. She was clearly deep, in thought, and once he caught a murmured phrase as she stood by his side looking down on the moon-like earth.

“ Modulus of disappearance — ”
He looked at her quickly, and saw any question would go unanswered. He tried to recall terms of student days, and knowledge that had drifted to be a mere background in his specialised training. A modulus could be many things. It was a multiplier to convert Napierian into common logarithms. He considered. Such a definition seemed unapplicable. It also indicated the relationship between physical effect and the force producing it. Perhaps that was nearer, he thought. Effect: a ship vanishes. Force producing it . . . the term was missing. When they went down he chanced a question.

“ What could be — a modulus of disappearance ?”
She smiled very faintly. “ How should I know ?”



Six hours out Gilliand sent a message into their cabin. Trip cancelled. Come up.
They ascended again to the flight deck and found Ned Gilliand looking black.

“ Thought you’d like to hear in detail,” he said. He gestured at the radio. “ General Frazer. The Tertullians have come out of isolation with the statement that they will meet earth ambassadors. They agree the accidents to the two ships, as they term them, may be only unfortunate coincidences. They note the operator then in charge has been suspended for disciplinary action,” His lips bore a momentary half smile. “ In short, there is now no need for our trip to Mars, and we’re preparing to return.”

Alan nodded understanding, not liking the bit about suspension for disciplinary action. Though probably it had sounded well in one of Frazer’s messages to the Tertullian delegation.

The ship turned over and began to reduce speed. There was a moment of weightlessness, then pressure returned. The tubes began to murmur with a renewed surge of power as the ship went into a course which would give rapid planetfall. Alan returned to their cabin after an hour spent with Gilliand, and found Jerry pensive.

“We’re on the same course the Warbler and Canopus took,” she stated.



In the control room of Kelsey Central Harry Laing watched the tubes. The ceiling reproducer awoke. “Thunderstone coming into your control.” He got her into a tight orbit round the east radio marker beacon, and turned his attention to the other screens. A freighter heavy with ore from Mars, with a defective tube, was drifting down the stack in emergency orbit. Time some of the old trading companies had a severe check, Laing thought. Another craft came in fast, overshooting the beacon orbit. He corrected the Thunderstone’s course to suit, and glanced at the clock. Another two hours to go, he noted, and felt tired. His gaze reverted to the screens — and his fingers awoke to frantic life, darting over the controls while he thumbed the communicator.

The Thunderstone’s screen was blank.




Ned Gilliand shook his head determinedly. “ We can’t change orbit just because of what you say. My superiors would — ”
The ship quivered like a struck gong. The scene below, with the tiny central dot that was the Kelsey site, disappeared. The sun vanished, leaving a faint greyness.
“ We’ve modulated out of space,” Jerry said. “ I’ve been trying to tell you !”
The radio operator looked back momentarily from his panel, his features pale. “ I’ve lost contact with Kelsey Control, sir !”

Alan experienced a mixture of triumph and dismay. This proved he had not been at fault in some inexplicable way. But it also placed them in the same difficulty as the Warbler and Canopus. He followed the operator’s urgent fingers with his gaze.

“ I suggest he see what he can contact !”

The pale greyness surrounding the ship was broken only in a dim line a few degrees broad extending axially round her. The narrow belt was rainbow hued, deep violet towards the ship’s prow fading to red invisibility in the direction of her stern. He could just distinguish individual sparks of light making up the band, sweeping always backwards and changing hue as they went. Gazing, he knew he was witnessing some queer modification of the Doppler effect. The ship was moving faster than light, giving blankness for’ad and aft. Only within a narrow band parallel to her motion did remote stars appear, shifting to the red as they came level and passed.

He felt fingers grip his arm and met Jerry’s eyes. “ You’re thinking what I’m thinking, Alan — ”
He nodded. “ Tell me about your modulus.”

“ I haven’t finally computed it, but believe I can, when we get back to headquarters.” She paused. “ If we get back, I should say. A certain complex of movement and ships apparently modulates one ship out of ordinary space into this space-time continuum. Just as a musician can modulate chords from one key to another.” She spread her fingers expressively. “ It’s happened three times. If we get back I can tape it, with the help of the computer.”

“ There are two signals in the distress band,” the radio man put in abruptly.
Ned Gilliand’s thick brows went up. “ Contact them and identify.” There was a long pause, and Alan wondered what astonished messages were burbling into the operator’s phones.
“ The Warbler and Canopus, sir !” he stated at last.

A momentary pressure on Alan’s arm told him Jerry Jakandi had almost expected it. She put her back to the queer dimness.

“ Could you have them take bearings and join us. Captain ?” Gilliand nodded. “ A good plan. Miss Jakandi, if it can be done.” Alan left them, gazing through the port and wondering if the pale light outside was the hypothetical hyperspace postulated by various mathematicians whose work he could not pretend to follow. He pitied General Frazer, wondering, also, if the Thunderstone’s disappearance had again made the Tertullians withdraw into shocked isolation.

Slowly he grew aware of two dim ghosts drifting up to match their course w'ith the Thunderstone’s. Pale steel in the faint light, they slid silently five hundred yards out, the Canopus, very long and sleek, moving slowly ahead of the smaller Warbler.

“ And to think we found this by chance,” a voice said at his side.
He noted the inner glow on the girl’s face. “ Half the great discoveries of the past arose from investigating phenomena that arose by chance,” he pointed out.

“ Perhaps,” another voice put in. He turned and found Ned Gilliand behind them. Gilliand drew in his cheeks, and his face looked very thin. “We now have three ships in what we may term hyper- space, Miss Jakandi,” he said quietly. “ What we need now is an out-of-hyperspace moduli !”. .

An odd expression came to her eyes. Watching her, Alan remembered a reproduction of a venerable man’s face he had somewhere seen, years before. It came back, now . . . Ayres Jakandi’s features, in the science section of a museum. At that moment Jerry Jakandi looked very much like her grandfather. She turned abruptly for the silence of their cabin.

“ I’ll see what I can do, Mr. Gilliand !”



illustration from THE JAKANDI MODULI by Francis G Rayer Alan retired to a hammock and was not ashamed to sleep. A gentle movement came once, telling him the Thunderstone was turning, presumably to regain the point of her entry into hyperspace. It would need dead-reckoning, but would be the part of their journey even the ship’s chief navigator could handle.

He slept, and awoke to a signal of general alert, and the knowledge that Jerry was in the adjacent suspended netting. Dark rings made bright her eyes.

“ I’ve done my bit,” she said. “It’s up to Gilliand.”
Alan felt she deserved encouragement. “ Then we’re safe ! He could thread the ship through the eye of a needle, given a course !”
A twist ended his words. The Thunderstone seemed to stand on her tail and dance. A fiendish cartwheel followed, and he clung to the net.
“ This isn’t a course — it’s insanity !”

“ There is a range of moduli,” Jerry murmured. “ The moduli required to move from one continuum to another is necessarily more difficult when the ships are so few. But it’s simpler to work on paper as there are fewer constants.”

“ I’ll say it’s simple !” Alan grated as the hammock inexplicably became entangled with his open mouth.
A curve lifted them, then the ship rang like a gong. Light blinked on . . . sunshine. The earth was thirty miles below.
Jerry Jakandi smiled. “ That chief navigator needs a medal for his dead-reckoning !”

Alan’s astonishment was unabated when he walked from the Kelsey disc, and he paused twice to look back at the silently standing Warbler, Canopus, and Thunderstone. Frazer was waiting at the edge of the decontamination area. His hair was awry, his uniform creased. He had obviously not slept for some days.

“ Ruined !” he stated, his lips closing like a trap. “ The Tertullians have gone into isolation, and demand guarantee of a safe transit back to their ship on Mars. There will be no bases for us.” He smote a folder grasped in one hand. “ They consider us unreliable and unpredictable, and our ships uncertain and dangerous ! They refuse to have any further communication with us, and would as soon grant us bases as cede Alpha Centauri and all their empires to us!” He breathed deeply, preparing a new onslaught. “ Twice I’ve asked for a safe orbit, and twice ships disappear ! Finally, when the Tertullians are willing to overlook everything, the Thunderstone vanishes under the nose of the Spacecar and her load of copywriters, and every newsagency on the planet has it on every newscreen within five minutes.” He paused for breath, wilting them with his glance. Jerry smiled. “ Let them go. General.”

Frazer reddened. “ Go, with no negotiation! This will cost me my career . . .”

“ Not when you explain you have another method of reaching systems beyond Alpha Centauri — and further,” Jerry said. “ It’s all a matter of modulation — the inter-relationship of moving bodies — ” Alan saw her hand close on General Frazer’s arm. She smiled. “ Any ship can do it. General. It’s swift, neat, and makes a few light-years seem like a walk next-door.”

She was guiding him away from the landing disc. She looked back, and smiled. .
“ I shall need to see you later, Mr. Spey. A matter of the practical application of theoretical considerations.”
Alan laughed as her grip again tightened on Frazer’s arm. “ As I said, this series of moduli show space is not finite. You may remember my grandfather’s work on the modulatory fields of sub-atomic nuclei—” Her voice faded from hearing. Alan put his hands on his hips and chuckled, oblivious to the officers nearby, the control building awaiting, of the whine of a ship dropping from the stack towards the landing disc. Jerry Jakandi was trumps!

Francis G. Rayer.



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