This microwave oven is a truly remarkable feat of engineering. The rapid heating that makes microwaves popular is made possible by power provided from this vacuum tube. Now, if you picture a vacuum tube at all, it's likely in a radio like this.  Microchips can't easily replace tubes for producing power, for example, in heating food. Now, a microwave contains three main components. A vacuum tube called a magnetron. It generates the energy that heats food. A wave guide hidden in the wall to direct that energy to the food. And a chamber to hold the food and safely contain the microwave radiation. In principle, a microwave oven heats no differently than any other type of heat transfer. At a molecular level, heat is a transfer of energy that results in increased motion of the molecules in a substance. Since we aren't quantum-sized, we observe this increase in motion as a rise in temperature. In a traditional oven or stove, we heat food by placing a pan on a burner, or in the oven where the walls radiate heat, which cooks the outside of the food. The insides cook when heat transfers from the surface of the food to its interior. In contrast, energy from the magnetron penetrates into the food, which means the whole mass of the food can be cooked simultaneously. How does it do this? Well, our food is filled with water, which is positively charged at one end and negative at the other. To give these molecules more energy, we expose it to electromagnetic waves that emanate from the tube. By definition, the waves have the electrical and magnetic fields that change direction rapidly. For this oven, the direction of the fields change 2.45 billion times per second. Water will try to align with the radiation's electric field. The changing field rocks the water molecules back and forth rapidly, and molecular friction from this creates heat as the motion disrupts the hydrogen bonds between neighboring water molecules. Now, you can get an idea of the wavelength of the energy emitted from the magnetron using cheese. Now, you can see on here sections where the cheese is completely melted and other sections where it's completely unheated. The oven's metal walls only reflect waves of a length that fits inside the oven. This standing wave causes hot and cold spots inside the oven. The three-dimensional pattern of waves is difficult to predict, but the principle can be seen by looking at the waves in a single dimension. The peaks and valleys in the wave represent the greatest energy of the wave. Well, the nodes here correspond to the cold spots inside the chamber. If I measure the distance between melted cheese spots, I find about 2.5 inches. That would be half the wavelength the distance between nodes and is pretty close to the actual wavelength of microwave radiation used. Using that wavelength, I can estimate the microwave radiation's frequency. The frequency is related to the wavelength by the speed of light. I get an answer that only has a 4 or 5% error, not bad for this primitive measurement. Now, the real engineering in the microwave oven lies in creating the magnetron that generates high-powered radio waves. It's truly an amazing and revolutionary device. The vacuum tube is inside here. These are cooling fins, thin pieces of metal that dissipate the heat as the magnetron operates. The key parts are these two magnets and the vacuum tube. Now, I have another one so you can see the inside. You apply a large voltage across both the inner filament and the circular copper outside. This voltage boils electrons off the center filament and they fly toward the circular copper section. The filament is made from tungsten and thorium. Tungsten because it can withstand high temperatures and thorium because it's a good source of electrons. The magnets bend these electrons if they swing back toward the center filament. We adjust the magnetic strength so that the now orbiting electrons just brush past the opening of these cavities. Like blowing over a half-filled pop bottle to make it whistle, this creates an oscillating wave, the microwave radiation that heats food. It's simply astonishing that these cavities can be made with high precision, low cost, and incredibly high reliability. I'm Bill Hammack, the Engineer Guy. This video is based on a chapter in the book Eight Amazing Engineering Stories. The chapter features more information about this subject. Learn more about the book at the address below.


14 Hawks took over, explaining the proposition to a now very much-awake Allen. There's going to be a currency transfer at the World Reserve Bank downtown next Friday. At least ten million credits are going to be picked up by an armored truck and taken to branch banks for distribution. Hollis here happens to have found out the wave pattern of the robo-guards who will be protecting the currency shipment, and Allen Webber has some equipment that can paralyze robo-guards if we know their operational wavelength. So it's a simple matter to leave the car unprotected. We wait till it's loaded, then blank out the robots, seize the human guards, and drive away with the truck. Allen frowned thoughtfully. Why am I so indispensable to this business? He had no desire to rob banks or anything else. Because you're the only one of us who isn't registered on the Central Directory. You don't have any televector number. You can't be traced. Suddenly Allen understood. So that's why you didn't let me register? You've been grooming me for this all along? Hawks nodded. As far as earth is concerned, you don't exist. If any of us drove off with that truck, all they need to do is plot the truck's coordinates and follow the televector patterns of the man who's driving it. Capture is inevitable that way. But if you're aboard the truck, there's no possible way of tracing your route. Get it? I get it, Allen said slowly, but I don't like it, he added silently. I want to think about the deal a little longer, though. Let me sleep on it. I'll tell you tomorrow whether I'll go through with it. Puzzled expressions appeared on the faces of Hawks' eight guests, and Weber started to say something, but Hawks cut him hastily off. That boy's a little sleepy, that's all. He needs time to get used to the idea of being a millionaire. I'll call each of you in the morning, OK? The eight were shepherded out of the apartment rapidly, and when they were gone Hawks turned to face Allen. Allen now was the bland friendliness, gone the warm-hearted brotherliness of the older man. His lean face was cold in business like now, and his voice was harsh as he said, what's this talk of thinking it over, who said you had any choice about this thing? Don't I have any say in my own life, Allen said hotly? Suppose I don't want to be a bank robber, you didn't tell me. I didn't need to. Listen, boy, I didn't bring you in here for my health. I brought you in because I saw you had the potential for this job. I've coddled you along for more than three months now, given you a valuable education in how to get along on this planet. Now I'm asking you to pay me back, a little. Bing told the truth, you're indispensable to this project. Your personal feelings are irrelevant just now. Who says? I do. Allen stared coldly at Hawks' transformed face. Max, I didn't bargain for a share in your bank robbing syndicate. I don't want any part of it. Let's call it quits right now. I've turned over quite a few thousand credits of my winnings to you. Give me five hundred and keep the rest. It's your pay for my room and board and the instruction the last three months.  Hawks laughed sharply. Just as simple as that. I pocket your winnings and you walk out of here.  You know the names of the syndicate, you know the plans, you know everything. A lot of people would pay big money for an advance tip on this bit, he shook his head. I'll go my way and you'll go it to Allen or else. You know what that or else means? Angrily Allen said, you'd kill me too if I back down now. Friendship doesn't mean a thing to you. Help us rob this bank or else. Hawks' expression changed again. He smiled warmly and when he spoke his voice was almost weadling. Listen, Allen, you've been planning this thing for months. I put down seven thousand to clear your brother just so I'd be sure of getting your cooperation. I tell you there's no danger. I didn't mean to threaten you but try to see my side of it. You have to help out. Allen looked at him curiously.  You earn a fortune every night. You don't need a million more credits. No, I don't. But some of them do. Johnny Bing does and Kovac too. He owes Bryson thirty thousand. But I organized the scheme. Hawks was pleading now. Allen, I'm bored. Deadly bored. Gambling isn't gambling for me. I'm too good. I never lose except when I want to. So I need to get my kicks someplace else. This is it. But it won't come off without you. They were silent for a moment. Allen realized that Hawks and his group were desperate men. They would never let him live if he refused to cooperate. He had no choice at all. It was disillusioning to discover that Hawks had taken him in mostly because he would be useful in a robbery. He tried to tell himself that this world was a jungle where morality didn't matter and that the million credits he'd gain would help finance hyperdrive research. But those were thin arguments that held no conviction. There was no justification for what he was going to do, none whatsoever. But Hawks held him in a cleft stick. There was no way out. He had fallen among thieves and willy-nilly he would be forced to become one of them. All right, he said bitterly. I'll drive the getaway truck for you. But after it's over I'll take my share and get out. I won't want to see you again. Hawks seemed to look hurt, but he masked the emotion quickly enough. That's up to you, Allen, but I'm glad you gave in. It would have been rough on both of us otherwise. Suppose we get some sleep. Allen slept poorly during what was left of the night. He kept mulling the same thoughts round and round endlessly in his head until he wished he could unhinge the front of his skull and let the thoughts escape somehow. It irritated him to know that Hawks had taken him in primarily because he fit the qualifications for a plan concocted long before and not for his own sake. All the intensive training the gambler had given him had been directed not merely toward toughening Allen, but toward preparing him for the role he would play in the projected robbery. He felt unhappy about the robbery, too. The fact that he was being coerced into taking part made him no less a criminal, and that went against all his long ingrained codes of ethics. He would be just as guilty as Hawks or Weber and there was no way out. There was no sense brooding over it, he decided, finally. When it was all over he would have enough money to begin aiming for his real goal, development of a workable hyperspace drive. He would break completely with Hawks, move to some other city, perhaps. If his quest were successful it would in some measure be an atonement for the crime he was going to commit, only in some measure, though. The week passed slowly and Allen did poorly at his nightly work. His mind was anywhere but on the flashing games board and the permutations and combinations eluded him. He lost, though not heavily. Each night the ten members of the syndicate met at Hawks' apartment and planned each step of the crime in great detail, drilling and redrilling until it was second nature for each man to recite his particular part in the robbery. Allen's was at once the simplest and most difficult. He would have nothing to do until the others had finished their parts, but then he would have to board the armored car and outrace any pursuers. He was to drive the car outside the city limits where he would be met and relieved of the cash by Bing and Hollis, then he was to lose the truck somewhere and return to the city by public transport. The day of the robbery dawned cold and clear, and autumn chill was in the air. Allen felt some anticipatory nervousness, but he was calmer than he expected to be, almost fatalistically calm. By nightfall he would be a wanted criminal. He wondered whether it would be worth it, even for the million credits. Perhaps it would be best to defy Hawks and make some sort of escape try. But Hawks as always a shrewd judge of human character seemed obviously aware that Allen was wavering. He kept a close watch over him, never allowing him to stray. Hawks was taking no chances. He was compelling Allen to take part in the robbery. The currency transfer was scheduled to take place at twelve forty, according to the inside information that Hollis had somehow obtained. Shortly after noon Hawks and Allen left the apartment and boarded the undertube, their destination the downtown section of York City where the World Reserve Bank was located. They reached the bank about twelve thirty. The armored truck was parked outside looking sleek and impregnable, and four massive robo-guards stood watch, one at each wheel. There were three human policemen, too, but they were strictly for effect. In case of any trouble the robo-guards were expected to handle the rough work. The bank was a mighty edifice indeed, over a hundred stories high, rising and sweeping setbacks to a point where its tapering top was lost in the shimmering noonday sky. It was, Allen knew, the center of global commerce. Armed guards were bringing packages of currency from within the bank and were placing them on the truck. Allen's heart raced. The streets were crowded with office workers out for lunch. Could he get away with it? It was all precisely synchronized. As Hawks and Allen strolled toward the bank, Allen caught sight of Kovac lounging across the street, reading a telephax sheet. None of the others were visible. Weber, Allen knew, was at this moment sitting in an office overlooking the bank entrance, staring out the window at the scene below. At precisely twelve forty Weber was to throw the switch on the wave damper that would paralyze the four robo-guards. The instant the robo-guards froze, the other conspirators would go into action. Jensen, McGuire, Freeman and Smith, donning masks, would leap for the three human guards of the truck and pin them to the ground. Bing and Hawks, who would enter the bank a moment before, would stage an impromptu fist-fight with each other just inside the main entrance, thereby creating confusion and making it difficult for reinforcement guards to get past them and into the street. Just outside the door, Hollis and Kovac would lurk. As the quartet pounced on the truck's guards, they would sprint across and yank the driver out of the cab. Then Allen would enter quickly from the other side and drive off while the remaining nine would vanish into the crowd as many different directions as possible. Bing and Hollis, if they got away, would head for the rendezvous to meet Allen and take the cash from him. If it went off properly, the whole thing should take less than fifteen seconds from the time Weber threw the switch to the time Allen drove away with the truck. If it went off properly, the seconds crawled by, the time was twelve-thirty-five now. At twelve-thirty-seven, Hawks and Bing sauntered into the bank from opposite directions, three minutes to go. Allen's false calm deserted him. He pictured all sorts of possible calamities. Twelve-thirty-eight, everyone's watch was synchronized to the second. Twelve-thirty-nine, twelve-thirty-nine-thirty, thirty seconds to go. Allen took his position in a crowd of bystanders as prearranged. Fifteen seconds to go. Ten. Five. Twelve-forty. The ropoguards were in the act of redirecting the locking of the truck. The loading had been carried out precisely on schedule. The truck was sealed. The ropoguards froze. Weber had been right on time. Allen tensed, caught up in the excitement of the moment and thinking now only of the part he was to play. The three policemen glanced at each other in some confusion. Jensen and McGuire came leaping out at them. The ropoguards returned to life. The sound of blaster shots was heard within the bank. Allen whirled, startled. Four guards came racing out of the building, blasters drawn. What had happened to Hawks and Bing? Why weren't they obstructing the entrance as it had been arranged? The street was a scene of wild confusion now. People milled everywhere. Allen saw Jensen writhing in the steel grip of a ropoguard. Had Weber's device failed? Evidently so. Allen was unable to move. He saw Freeman and McGuire streaking wildly down the street with policing keen pursuit. Hollis stood staring dumbly inside the bank door. Allen saw Kovac come running toward him. Everything's gone wrong, Kovac whispered harshly. The cops were waiting for us. Bing and Hawks are dead.  CHAPTER XV Allen sat very quietly in the empty apartment that had once belonged to Hawks, and he stared at nothing in particular. It was five hours since the abortive robbery. He was alone. The news had been blared out over every form of communication there was. He knew the story by heart. A daring robbery had been attempted, but police detection methods had yield advanced warning, and the robbers had been frustrated. The ropoguards had been specially equipped ones which could shift to an alternate wavelength in case of emergency. They had blanked out only momentarily. And special guards had been posted within the bank, ready to charge out. Bing and Hawks had tried to block the doorway and they had been shot down. Hawks was killed instantly. Bing died an hour later in the hospital. At least two other members of the gang had been apprehended. Jensen and Smith, both trapped by the ropoguards. It was known that at least two other men and possibly more had participated in the attempt, and these were being traced now. Allen was not worried. He had not been within a hundred feet of the crime, and it had been easy for him to slip away unnoticed. The others had had little difficulty either. Weber, Hollis, Kovac, McGuire and Freeman. There was a chance that Hollis or Kovac had been recognized. In that case they could be tracked down by Televector. But Allen was not registered on the Televector screens, and there was no other way of linking him with the crime. He glanced around the apartment at Hawks' bar and his audio system and all the dead man's other things. Yesterday, Allen thought, Hawks had been here, alive, eyes sparkling as he outlined the plans for his robbery a final time. Now he was dead. It was hard to believe that such a many-sided person could have been snuffed out so soon, so quickly. A thought occurred. The police would be investigating the disposition of Hawks' property. They would want to know the relationship between Hawks and Allen, and perhaps there would be questions asked about the robbery. Allen decided to forestall that. He reached for the phone. He would call security, tell them he had been living with Hawks and that he had heard of the gambler's sudden violent death, and in all innocence asked for details. He would, the door announcer chimed. Allen whirled and put down the receiver. Reaching out, he flicked down the door screen and was shown a view of a distinguished-looking middle-aged man in the silver-gray uniform of the police. So soon, Allen thought, I didn't even get a chance to call. Who is it, he asked, in a surprisingly even voice. Inspector Gaynor of Global Security. Allen opened the door. Inspector Gaynor smiled warmly, walked in, took the seat that Allen offered him. Allen felt tense and jumpy and hoped not too much of it showed. The security man said, your name is Allen Donald, isn't it?  That's right, sir. Gaynor checked a notation on a pad he carried. I suppose you've heard that the man who lived here, Max Hawks, was killed in an attempted robbery this morning? Yes, sir. I heard it a little while ago on the newscasts.  Would you care for a drink, Inspector? Not on duty. Thanks, Gaynor said cheerfully. Tell me, Allen, how long did you know Max Hawks? Since last May, I'm an ex-star man. I jumped ship. Max found me wandering around the city and took me in. But I never knew anything about any robberies, Inspector. Max kept his mouth pretty well sealed most of the time. When he left here this morning, he said he was going to the bank to make a deposit. I never thought— He stopped, wondering whether he sounded convincing. At the moment a long jail sentence or worse seemed inevitable. And the worst part of it was that he had not wanted to take place in the robbery. Indeed, he had not taken part, but in the eyes of the law he was undoubtedly as guilty as any of the others. Gaynor raised one hand. Don't misunderstand, son. I'm not here as a criminal investigator. We don't suspect you had any part in the attempt. Then why? He drew an envelope from his breast pocket and unfolded the papers it contained. I knew Max pretty well, he said. About a week ago he came to see me and gave me a sealed envelope, which was to be opened only in the event of his death, on this particular day, and to be destroyed unopened otherwise. I opened it a few hours ago. I think you ought to read it. With trembling fingers Allen took the sheaf of papers and scanned them. They were neatly typed. Allen recognized the blocky purple characters of the voice-write Hawks kept in his room. He started to read. The document explained that Hawks was planning a bank robbery to take place on Friday October 3, 3876. He named none of his accomplices. He went on to state that one Allen Donnell, an unregistered ex-star man, was living with him and that this Allen Donnell had no knowledge whatsoever of the intended bank robbery. Furthermore, Hawks added, in the event of my death in the intended robbery, Allen Donnell is to be sole heir and a sign of my worldly goods. This supersedes and replaces any and all wills and testaments I may have made at any past time. Appended was a schedule of the properties Hawks was leaving behind. Accounts in various savings banks totaled some three-quarters of a million credits. Besides that there were scattered investments, real estate holdings, bonds. The total estate, Hawks estimated, was worth slightly over one million credits. When Allen finished he looked up startled and white-faced at the older man. All of this mine? You're a pretty rich young man, Gainer agreed. Of course there are formalities the will has to be probated and contested and you can expect it to be contested by somebody. If you still have the full estate when the courts get through with you, you'll be all right. Allen shook his head uncomprehendingly. The way he wrote this, it's as if he knew. Hawks always knew, Gainer said gently. He was the best hunchman I've ever seen. It was almost as if he could see a couple of days into the future all the time. Sure, he knew. And he always knew it was safe to leave this document with me, that he could trust me not to open it. Imagine announcing a week ahead of time that you're going to rob a bank and then turning the announcement oversealed to a police officer. Allen started. The police officer had known about the robbery in advance. That was how Max and the dream duster Bing had been killed. Had Gainer been the one who had betrayed them? Had he opened the sealed envelope ahead of time and sent Max to his death? No, it was inconceivable that this soft-spoken man would have done such a thing. Allen banished the thought. Max knew he was going to be killed, he said, and yet he went ahead with it. Why? Maybe he wanted to die, Gainer suggested. Maybe he was bored with life, bored with always winning, bored with things as they were. The man was never born who could figure out Max Hawks anyway. You must have found that out yourself. Gainer rose. I'll have to be moving along now, but let me give you some suggestions first. Sir? Go downtown and register yourself in free status. Have them give you a televector number. You are going to be an important person when you get all this money. And be very careful about who your friends are. Max could take care of himself. You may not be so lucky, son. Is there going to be an investigation of the robbery, Allen asked? It's underway already. You may be called down for some questioning, but don't let it worry you. I turned a copy of Max's will over to them today, and that exonerates you completely. It was strangely empty in the apartment that night. Allen wished Gainer had stayed longer. He walked through the dark rooms, half expecting Max to come home. But Max wasn't coming home. Allen realized he had been tremendously fond of Hawks. He had never really shown it. He had never demonstrated much warmth toward the gambler, especially in the final days when they both lived under the pressure of the planned robbery. But Allen knew he owed much to Hawks, rogue and rascal though he was. Hawks had been basically a good man, gifted. Too gifted, perhaps, whose drives and passions led him beyond the boundaries of society. And at thirty-five he was dead, having known in advance that his day was at hand. The next few days were busy ones. Allen was called to security headquarters for questioning, but he insisted he knew nothing about the robbery or Hawks' friends, and the document Hawks had left seemed to bear him out. He was cleared of all complicity in the robbery. Next he went to Central Directory Matrix and registered in free status. He was given a televector transmitter. It was surgically embedded in the fleshy part of his thigh. And he accepted to drink from fat old Heinz Macintosh in remembrance of Hawks. He spoke briefly with Macintosh about the process of collecting on Hawks' estate, and learned it was a complex process, but nothing to be afraid of. The will was being sent through channels now. He met Hollis in the street several days later. The bloated Lonesman looked pale and haired, and his skin hung flabbily over his bones now. Little as Allen liked the Lonesman, he insisted on taking him to a local restaurant for lunch.  Allen asked. I thought the heat was on for any of Mac's old buddies. It is,' Hollis said, wiping sweat from his white shiny forehead. But so far I'm in the clear. There won't be much of an investigation. They killed two and caught two, and that'll make them happy. After all, the robbery was a failure. Any notion why it failed?' Hollis nodded. "'Sure, I have a notion.  Mike? But he looked OK to me. And to everybody, but he owed Bryson a lot, and Bryson was anxious to dispose of Mac's. So Kovac turned the plans of the robbery over to Bryson's boys, in exchange for a quit claim on the money he owed, and Bryson just forwarded it all on to the police. They were waiting for us when we showed up. That cleared Gainer, Allen thought in some relief. How did you find this all out?' Bryson himself told me. "'What?' I guess he didn't know exactly who besides Mac's was in on the deal. Anyway, he certainly didn't know I was part of the group,' Hollis said. "'Old man Bryson was laying off some bets with me, and he let something slip about how he tipped the police to Mac's. Then he told me the whole thing.' "'And Kovac?' "'Dead,' Hollis said bluntly. Bryson must have figured that if he'd sell Mac's out he'd sell anybody out, so Kovac got taken care of. He was found yesterday. Heart failure, the report said. Bryson has some good drugs. Say, kid, any word yet on what's going to happen to all Mac's's dough?' Allen thought a moment before replying. I haven't heard a thing. I guess the government inherits it.' "'That would be too bad,' Hollis said speculatively. Mac's was well loaded. I'd like to get my hands on some of that dough myself. So would Bryson and his bunch, I'd bet.' Allen said nothing. When he was through eating he paid the check and left.  In three days Hawks Will would go through the courts. Allen wondered if Bryson, who seemed to be York City's major criminal syndicate man, would try to angle some share of Mac's's money. A Bryson man did show up at the hearing, a slick-looking operator named Berwyn. His claim was that Hawks had been affiliated with Bryson for a number of years, and that Hawks money should revert to Bryson for virtue of an obscure law of the last century involving the estates of professional gamblers killed in criminal actions. The Robocomputer, who was in charge of the hearing, pondered the request a few moments. Then relays clicked, and the left-hand panel on the computer face lit up with a bright-red, application-denied signal. Berwyn spoke for three minutes, ending up with a request that the Robocomputer disqualify itself from the hearing, and allow itself to be replaced by a human judge. The computer's decision was even quicker this time. Application-denied. Berwyn tossed Allen's side of the courtroom a black look and yielded ground. Allen had engaged a lawyer recommended once by Hawks, a man named Jespersson. Briefly and concisely Jespersson cited Allen's claim to the money, read the terms of the will, and stepped back. The computer considered Jespersson's plea for a few moments, reviewing the brief which the lawyer had taped and fed into the computer earlier. Time passed. Then the green panel lit, and the words, Application, granted. Allen smiled. Bryson had been defeated. Alex's money was his. Money that could be turned toward intensified research on the hyperdrive. Well, son, Jespersson asked. How does it feel, to be a millionaire? CHAPTER XVI. At the time he had been much too excited and flustered to answer anything. But, as the next twelve months went by, he learned that being a millionaire was quite pleasant indeed. There were headaches, of course. There was the initial headache of signing his name several hundred times in the course of the transfer of Hawks' wealth to him. There were also the frequent visits from the tax collectors and the payments to them of a sum that staggered Allen to think about, in the name of rotation tax. But, even after taxes, legal fees, and other expenses, Allen found he owned better than nine hundred thousand credits, and the estate grew by investment every day. The court appointed a legal guardian for him, the lawyer Jespersson, who was to administer Allen's money until Allen reached the biological age of twenty-one. The decision was an involved one, since Allen had unteniably been born three hundred years earlier, in thirty-five seventy-six. But, the Robo-judge that had presided over that particular hearing, cited a precedent seven hundred years old, which stated that for legal purposes a star man's biological and not his chronological age was to be accepted. The guardianship posed no problems for Allen, though. When he met with Jespersson to discuss future plans, the lawyer told him, you can handle yourself, Allen.  That sounded fair enough. Allen had reason to trust the lawyer. Hadn't Hawks recommended him? I agreed to that, said Allen. Suppose we start right now. I'd like to take a year and travel around the world. As my legal guardian you'll be stuck with the job of managing my estate and handling my investments for me. Jespersson chuckled. You'll be twice as wealthy when you get back. Nothing makes money so fast as money. Allen left the first week in December, having spent three weeks doing virtually nothing but sketching out his itinerary. There were plenty of places he intended to visit. There was London where James Hudson Cavor had lived and where his hyperdrive research had been carried out. There was the Lexman Institute of Space Travel in Zurich, where an extensive library of space literature had been accumulated. It was possible that hidden away in their files was some stray notebook of Cavor's, some clue that would give Allen a lead. He wanted to visit the area in Siberia that Cavor had used as his testing ground, and from which the last bulletin had come from the scientist before his unexplained disappearance. But it was not only a business trip. Allen had lived nearly half a year in the squalor of Hasbrook, and because of his free status he would never be able to move into a better district despite his wealth. But he wanted to see the rest of Earth. He wanted to travel just for the sake of travel. Before he left he visited Rare Book Dealer in York City, and for an exorbitant fifty credits purchased a fifth edition copy of An Investigation Into the Possibility of Faster Than Light Space Travel by James H. Cavor. He had left his copy of the work aboard the Vahala along with the few personal possessions he had managed to accumulate during his life as a star man. The book dealer had frowned when Allen asked for the volume under the title he knew, the Cavor Theory. I don't think ah, wait, he vanished for perhaps five minutes and returned with an old, fragile, almost impossibly delicate looking book. Allen took it and scanned the opening page. There were the words he had read so many times. The present system of interstellar travel is so grossly inefficient as to be virtually inoperable on an absolute level. Yes, that's the book. I'll take it. His first stop on his round the globe jaunt was London, where Cavor had been born and educated more than thirteen centuries before. The straddle liner made the trip across the Atlantic in little less than three hours. It took a half hour more by overshoot from the airport to the heart of London. Somehow, from Cavor's few autobiographical notes, Allen had pictured London as a musty town, picturesque, reeking of medieval history. He couldn't have been more wrong. Sleek towers of plastic and concrete greeted him. Overshoots roared by at the tops of the buildings. A busy network of bridges connected them. He went in search of Cavor's old home in Bayswater with the nebulous idea of finding some important document wedged in the woodwork. But the local security officer shook his head as Allen asked for directions. Sorry, lad, I've never heard of that street. Why don't you try the information robots up there? The information robot was a blocky, green-skinned synthetic planted in a kiosk in the middle of a broad, well-paid street. Allen approached and gave the robot Cavor's thirteen-century old address. There is no record of any such address in the current files, the steely voice informed him. No, it's an old address. It dates back to at least twenty-five seventy. A man named Cavor lived there. The robot digested the new data, relays hum softly within it as it scanned its memory banks. Finally it grunted, data on the address you seek has been reached. Fine, where's the house? The entire district was demolished during the general rebuilding of London in twenty-nine eighty-two to twenty-nine ninety-seven. Nothing remains. Oh! said Allen. The London trail trickled out right then and there. He pursued it a little further, managing to find Cavor's name inscribed on an honor roll of the impressive London Technological Institute for the year twenty-five twenty-nine, and discovered a copy of Cavor's book in the Institute Library. There was nothing else to be found. After a month in London Allen moved on eastward across Europe. Most of it was little like the descriptions he had read in the Vahala's Library. The trouble was that the starships, visits, to earth were always at least a decade behind, usually more. Most of the library books had come aboard when the ship had first been commissioned, far back in the year twenty-seven thirty-one. The face of Europe had almost totally altered since then. Now shiny new buildings replaced the ancient houses which had endured for as much as a thousand years. A gleaming bridge linked over and Calais, elsewhere the rivers of Europe were bridged frequently, providing easy access between the many states of the Federation of Europe. Here, there, monuments of the past remained, the Eiffel Tower, absurdly dwarfed by the vast buildings around it, still reared its spidery self in Paris, and Notre Dame still remained as well. But the rest of Paris the ancient city Allen had read so much of, that had long since been swept under by the advancing centuries. Buildings did not endure forever. In Zurich he visited Lexman Institute for Space Travel, a magnificent group of buildings erected on the royalties from the Lexman Space Drive. A radiant statue sixty feet high was the monument to Alexander Lexman, who in twenty-three thirty-seven had first put the stars within the reach of man. Allen succeeded in getting an interview with the current head of the Institute, but it was anything but a satisfactory meeting. It was held in an office ringed with mementos of the epoch-making flight of twenty-three thirty-eight. I'm interested in the work of James H. Cavor, Allen said almost immediately, and from the bleak expression that appeared on the scientist's face he knew he had made a grave mistake. Cavor is as far from Lexman as possible, my friend. Cavor was a dreamer. Lexman, a doer. Lexman succeeded, but how do you know Cavor didn't succeed as well? Because my young friend, faster than light travel is flatly impossible. A dream. A delusion. You mean that there's no faster than light research being carried on here? The terms of our charter set down by Alexander Lexman himself specify that we are to work toward improvements in the technique of space travel. It is nothing about fantasies and daydreams. No hyperdrive research is taking place at this institute, and none will take place so long as we remain true to the spirit of Alexander Lexman. Allen felt like crying out that Lexman was a bold and daring pioneer never afraid to take a chance, never worried about expense or public reaction. It was obvious, though, that the people of the institute had long since fossilized in their patterns. It was a waste of breath to argue with them. Discouraged he moved on, pausing in Vienna to hear the opera. Max had always intended to spend a vacation with him in Vienna, listening to Mozart, and Allen felt he owed it to Hawks to pay his respects. The operas he saw were ancient, medieval in fact, better than two thousand years old. He enjoyed the tinkly melodies but found some of the plots hard to understand. He saw a circus in Ankara, a football game in Budapest, a Nalgrav wrestling match in Moscow. He journeyed to the far reaches of Siberia where Kavor had spent his final years and found that what had been a bleak wasteland suitable for spaceship experiments in twenty-five seventy was now a thriving modern city of five million people. The site of Kavor's camp had long since been swallowed up. Allen's faith in the enduring nature of human endeavor was restored somewhat by his visit to Egypt, for there he saw the pyramids nearly seven thousand years old. They looked as permanent as the stars. The first anniversary of his leaving the Vahala found him in South Africa. From there he traveled eastward through China and Japan, across the highly industrialized islands of the far Pacific, and from the Philippines he returned to the American mainland by jet express. He spent the next four months traveling widely through the United States, gaping at the Grand Canyon and the other scenic preserves of the West. East of the Mississippi life was different. There was barely a stretch of open territory between York City and Chicago. It was late in November when he returned to York City. Jesperson greeted him at the airfield and they rode home together. Allen had been gone a year. He was past eighteen now, a little heavier, a little stronger. Very little of the wide-eyed boy who had stepped off the Vahala the year before remained intact. He had changed inwardly. But one part of him had not changed, except in the direction of greater determination. That was the part that hoped to unlock the secret of faster than light travel. He was discouraged. His journey had revealed the harsh fact that nowhere on earth was research into hyperdrive travel being carried on. Either they had tried and abandoned it as hopeless, or, like the Zurich people, they had condemned the concept from the start. Did you find what you were looking for? Jesperson asked.  Not a hint, and I really covered ground. He stared at the lawyer a moment. How much am I worth now? Well, offhand, Jesperson thought for a moment. Say, a million three hundred. I've made some good investments this past year. Allen nodded. Good, keep the money piling up. I may decide to open a research lab of my own, and we'll need every credit we've got. But the next day an item arrived in the morning mail, which very much altered the character of Allen's plans for the future. It was a small, but thick package, neatly wrapped, which bore as return address the name Dwight Bentley, with a London number. Allen frowned for a moment trying to place the name. Then it came back to him. Bentley was the vice-provost of the London Institute of Technology, Kavor's old school. Allen had had a long talk with Bentley one afternoon in January about Kavor, about space travel, and about Allen's hopes for developing a hyperspace drive. The parcel was the right size and thickness to contain a book. Allen slipped the fastenings and folded back the outer wrapper. A note from Bentley lay on top. London, 3 November, 3877. My dear Mr. Donald, perhaps you may remember the very enjoyable chat you and I had one day at this institute last winter, on the occasion of your visit to London. You were, I recall, deeply interested in the life and work of James H. Kavor, and anxious to carry on the developments he had achieved in the field of space travel. Several days ago, in the course of an extensive resurveying of the institute's archives, the enclosed volume was discovered very thoroughly hidden in the dusty recesses of our library. Evidently Mr. Kavor had forwarded the book to us from his laboratory in Asia, and it had somehow become mis-filed. I am taking great liberty of forwarding the book on to you, in the hopes that it will aid you in your work and perhaps ultimately bring you success. Would you be kind enough to return the book to me, care of this institute, when you are finished with it? Cordially, Dwight Bentley. Allen let the note slip to the floor as he reached for the enclosed book. It was leather-bound and even more fragile than the copy of the cavor theory he had purchased. It looked ready to crumble at a hostile breath. With mounting excitement he lifted the ancient cover and turned it over. The first page was blank. So were the second and third. On the fourth page Allen saw a few lines of writing in an austere, rigid hand. He peered close and with awe and astonishment read the words written there. The Journal of James Hudson Kavor, Volume 16, January 8 to October 11, 2570. CHAPTER 17 The Old Man's Diary was a curious and fascinating document. Allen never tired of pouring over it, trying to conjure up a mental image of the queer, plucky fanatic who had labored so desperately to bring the stars close to earth. Like many embittered recluses, Kavor had been an enthusiastic diarist.  His digestion, the weather, any stray thoughts that came to him, tart observations on humanity in general. But Allen was chiefly interested in the notations that dealt with his researches on the problem of a faster than the speed of light space drive. Kavor had worked for years in London, harried by the reporters and mocked by scientists. But late in 2569 he had sensed he was on the threshold of success. In his diary for January 8, 2570, he wrote, The Siberian site is almost perfect. It has cost me nearly what remains of my savings to build it, but out here I will have the solitude I need so much. I estimate six months more will see completion of my pilot model. It is a source of deep bitterness in me that I am forced to work on my ship, like a common laborer, when my part should have ceased three years ago with the development of my theory and the designing of my ship. But this is the way the world wants it, and so shall it be. On May 8 of that year, today there was a visitor, a journalist no doubt. I drove him away before he could disturb me, but I fear he and others will be back. Even in the bleak Siberian steps I shall have no privacy. Work is moving along smoothly, though somewhat behind schedule. I will be lucky to complete my ship before the end of the year. On August 17 planes continue to circle my laboratory here. I suspect I am being spied on. The ship is nearing completion. It will be ready for standard Lexman drive flights any day now, but the installation of my space-warp generator will take several months more. On September 20. Interference has become intolerable. For the fifth day an American journalist has attempted to interview me. My secret Siberian laboratory has apparently become a world tourist attraction. The final circuitry on the space-warp generator is giving me extreme difficulties. There are so many things to perfect. I cannot work under these circumstances. I have virtually ceased all machine work this week. And on October 11, 2570. There is only one recourse for me. I will have to leave earth to complete the installation of my generator. The prying fools and mockers will not leave me alone, and nowhere on earth can I have the needed solitude. I shall go to Venus. Uninhabited, uninhabitable. Perhaps they will leave me alone for the month or two I need to make my vessel suitable for interstellar drive. Then I can return to earth, show them what I have done, offer to make the demonstration flight to Rigel and back in days. Perhaps. Why is it that earth so tortures its few of original mind? Why has my life been one unending persecution ever since I declared there was a way to shortcut through space? There are no answers. The answers lie deep within the dark recesses of the human collective soul, and no man may understand what takes place there. I am content to know that I shall have succeeded despite it all. Someday a future age may remember me, like Copernicus, like Galileo, as one who fought upstream successfully. The diary ended there, but in the final few pages were computations, a trial orbit to Venus, several columns of blast-off figures, statistics on the geographical distribution of the Venusian land masses. Kevor had certainly been a peculiar bird, Alan thought. Probably half the persecutions he complained of had existed solely inside his own fevered brain. But that hardly mattered. He had gone to Venus. The diary that had found its way back to the London Institute of Technology testified to that. And there was only one logical next step for Alan. Go to Venus. Follow the orbit Kevor had scribbled at the back of his diary. Perhaps he might find the Kevor ship itself. Perhaps the site of his laboratory, some notes, anything at all. He could not allow the trail to trickle out here. He told Jesperson, I want to buy a small spaceship. I'm going to Venus. He looked at the lawyer expectantly and got ready to put up a stiff argument when Jesperson started to raise objections. But the big man only smiled. Okay, he said, when are you leaving? You aren't going to complain. The kind of ship I have in mind costs at least two hundred thousand credits. I know that. But I've had a look at Kevor's diary too. It was only a matter of time for you to decide to follow the old duck to Venus. And I'm too smart to think that there's any point of putting up a battle. Let me know when you've got your ship picked out and I'll sit down and write the check. But it was not as simple as all that. Alan shopped for a ship. He wanted a new one, as long as he could afford it. And after several months of comparative shopping and getting advice from the spaceport men, he picked the one he wanted. It was a sleek, glossy, eighty foot job, a Spacemaster 3878 model, equipped with Lexman converters and conventional ion jets for atmosphere flying. Smooth, streamlined. It was a lovely sight as it stood at the space field in the shadow of the great starships. Alan looked at it with pride, a slender, dark green needle yearning to pierce the void. He wandered around the spaceport and heard the fuelers and the oilers discussing it in reverent tones. That's a mighty fine piece of ship, that green one out there. Some lucky fellas got it. Alan wanted to go over to them and tell them, that's my ship. Me, Alan Donald. But he knew they would only laugh. Tall boys, not quite nineteen, did not own late model starmasters with price tags of two hundred and twenty-five thousand credits. He itched to get off-planet with it, but there were more delays. He needed a flight ticket first. And even though he had had the necessary grounding in astrogation technique and space piloting as an automatic part of his education aboard the Valhalla, he was rusty, and he needed a refresher course that took six weary months. After that came the physical exams and the mental check-ups and everything else. Alan fumed at the delay, but he knew it was necessary. A spaceship, even a small private one, was a dangerous weapon in unskilled hands. An out-of-control spaceship that came crashing to Earth at high velocity could kill millions. The shockwave might flatten fifty square miles. So no one was allowed up in a spaceship of any kind without a flight ticket, and you had to work to win your ticket. It came through finally, in June of thirty-eight seventy-nine, a month after Alan's twentieth birthday. By that time he had computed and re-computed his orbit to Venus a hundred different times. Three years had gone by since he had last been aboard a spaceship, and that had been the Valhalla. His childhood and adolescence now seemed like a hazy dream to him, far in the back of his mind. The Valhalla, with his father and Steve and all the friends of his youth aboard, was three years out from Earth, with seven years yet to go before it reached Presayan, its destination. Of course the crew had experienced only about four weeks, thanks to the Fitzgerald contraction. To the Valhalla people only a month had passed since Alan had left them, while he had gone through three years. He had grown up in those three years. He knew where he was heading now, and nothing frightened him. He understood people. And he had one great goal which was coming closer and closer with each passing month. Blastoff Day was the fifth of September, 3879. The orbit Alan finally settled on was a six-day trip, at low acceleration, across the forty million odd miles that separated Earth from Venus. At the spaceport he handed in his flight ticket for approval, placed a copy of his intended orbit on file with Central Routing Registration, and got his field clearance. The ground crew had already been notified that Alan's ship was blasting off that day, and they were busy now putting her in final departure condition. There were some expressions of shock as Alan displayed his credentials to the ground chief, and climbed upward into the control chamber of the ship he had named the James Hudson Cavor, but no one dared question him. His eyes caressed the gleaming furnishings of the control panel. He checked with the central tower, and was told how long till his blastoff clearance, and rapidly surveyed the fuel meters, the steering jet response valves, the automatic pilot. He worked out a tape with his orbit on it. Now he inserted it into the receiving tray of the autopilot and tripped a lever. The tape slid into the computer clicking softly and emitting a pleasant hum. Eight minutes to blast off came the warning. Never had eight minutes passed so slowly. Alan snapped on his view screen and looked down at the field. The ground crewmen were busily clearing an area as blastoff time approached. One minute to blast off pilot Donald, then the countdown began, second by second. At the ten seconds to go announcement, Alan activated the autopilot and nudged the button that transformed his seat into a protective acceleration cradle. His seat dropped down and Alan found himself stretched out, swinging gently back and forth in the protective hammock. The voice from the control tower droned out the remaining seconds. Tensely, Alan waited for the sharp blow of acceleration. Then the roaring came and the ship jolted from side to side, struggling with gravity for a moment and then sprang up free from the earth. Sometime later came the sudden thunderous silence as the jets cut out. There was the dizzying moment of freefall, followed by the sound of the lateral jets imparting longitudinal spin to the small ship. Artificial gravity took over. It had been a perfect take-off. Now there was nothing to do but wait for Venus to draw near. The days trickled past. Alan experienced alternating moods of gloom and exultation.  But in the moments of joy he pictured the finding of Kavor's ship, the building of a fleet of hypodrive vessels, the distant stars within an almost instantaneous reach. He would tour the galaxies as he had two years ago, toured earth. Canopus and Deneb, Rigel and Prezyon, he would visit them all, from star to bright star from one end of the universe to the other. The shining oval of Venus grew brighter and brighter, the crowd-layer that enveloped earth's sister planet swirled and twisted. Venus was virtually an unknown world. Earth colonies had been established on Mars and on Pluto, but Venus with her harsh formaldehyde atmosphere had been ignored. Uninhabited, uninhabitable, the planet was unsuitable for colonization. The ship swung down into the cloud-layer, floating wisps of gray vapor streamed past the orbiting Kavor. Finally Alan broke through, navigating now on manual, following as best he could Kavor's old computations. He guided the craft into a wide-ranging spiral orbit, three thousand feet above the surface of Venus, and adjusted his viewscreens for fine pickup. He was orbiting over a vast, dust-blown plane. The sky was a fantastic color, modelled blues and greens in an all-pervading pink, and the air was a dull gray. No sun at all penetrated the heavy shroud of vapor that hung around the planet. For five hours he scouted the plane, hoping to find some sign of Kavor's habitation. It was hopeless, he told himself. In thirteen hundred years the bitter winds of Venus would have destroyed any hint of Kavor's sight, assuming the old man had reached Venus successfully. But grimly Alan continued to circle the area. Maybe Kavor had been forced to land elsewhere, he thought. Maybe he never got here. There were a million maybes. He computed his orbit and locked the ship in. Eyes pressed to the view screen he peered downward, hoping against hope. This trip to Venus had been a wild gamble from the start. He wondered if Max Hawks would have covered a bet on the success of his trip. Max had been infallible when it came to hunches. Well, Alan thought, now I've got a hunch. Help me one more time, Max, wherever you are. Lend me some of your luck. I need it, Max. He circled once more. The Venusian day would last for three weeks more, and there was no fear of darkness. But would he find anything? What's that? He leaped to the controls, switching off the autopilot, and broke out of orbit, going back for a return look. Had there been just the faintest metallic glint below as of a spaceship jutting up from the sand? Yes, there was a ship down there, and a cave of some sort. Alan felt strangely calm. With confident fingers he punched out a landing orbit and brought his ship down in the middle of the barren Venusian desert. Alan brought the cavor down less than a mile away from the scene of the wreckage. It was the best he could do, computing the landing by guesswork, and climbed into his spacesuit. He passed through the airlock and out into the windswept desert. He felt just a little lightheaded. The gravity was only 0.8 of earth norm, and besides that the air in his spacesuit, being perpetually renewed by the Brennerman rebreathing generator strapped to his back, was just a shade too rich in oxygen. In the back of his mind he realized he ought to adjust the oxygen flow, but before he brought himself to make the adjustment the surplus took its effect. He began to hum, then to dance awkwardly over the sand. A moment later he was singing a wild space ballad that he thought he had forgotten years before. After ten feet he tripped and went sprawling into the sand. He lay there, trickling the violet sands through the gloves of his spacesuit, feeling very lightheaded and very foolish at the same time. But he was still sober enough to realize that he was in danger. It was an effort to reach over his shoulder and move the oxygen gauge back a notch. After a moment the flow leveled out, and he felt his head beginning to clear. He was marching through a fantastic Baroque desert. Venus was a riot of colors all in a minor key, muted greens and reds and overbearing gray, a strange ghostly blue. The sky, or rather the cloud layer, dominated the atmosphere with its weird pinkness. It was a silent world, a dead world. In the distance he saw the wreckage of the ship. Beyond it the land began to rise, sloping imperceptibly up into a gentle hill with bizarre sculptured rock outcroppings here and there. He walked quickly. Fifteen minutes later he reached the ship. It stood upright, or rather its skeleton did. The ship had not crashed. It had simply rotted away the metal of its hide eaten by the sand-laden winds over the course of centuries. Nothing remained but a bare framework. He circled the ship, then entered the cave a hundred feet away. He snapped on his light beam. In the darkness he saw a huddled skeleton far to the rear of the cave, a pile of corroded equipment, atmosphere generators, other tools now shapeless. War had reached Venus safely, but he had never departed. To his astonishment Allen found a sturdy volume lying under the pile of bones, a book, wrapped in metal plates. Somehow it had withstood the passage of centuries here in this quiet cave. Gently he unwrapped the book. The cover dropped off at his touch. He turned back the first three pages which were blank. On the fourth, written in the now familiar crabbed hand, were the words, The Journal of James Hudson-Cavor, Vol. 17, October 20, 2570. He had plenty of time during the six-day return journey to read and reread Cavor's final words, and to make photographic copies of the withered pages. The trip to Venus had been easy for old Cavor. He had landed precisely on schedule and established housekeeping for himself in the cave. But as his diary detailed it, he felt strength ebbing away with each passing day. He was past eighty, no age for a man to come alone to a strange planet. There remained just minor finishing to be done on his pioneering ship, but he did not have the strength to do the work. Climbing the catwalk of the ship, soldering, testing now, with his opportunity before him, he could not attain his goal. He made several feeble attempts to finish the job, and on the last of them fell from his crude rigging and fractured his hip. He had managed to crawl back inside the cave, but, alone, with no one to tend him, he knew he had nothing to hope for. It was impossible for him to complete his ship. All his dreams were ended. His equations and his blueprints would die with him. In his last day he came to a new realization. Nowhere had he left a complete record of the mechanics of his space warp generator. The key mechanism without which hyperspace drive was unattainable. So, racing against encroaching death, James Hudson-Cavor turned to a new page in his diary, headed it in firm, forceful letters, for those who follow after, and inked in a clear and concise explanation of his work. It was all there, Alan thought exultantly. The diagrams, the specifications, the equations. It would be possible to build the ship from Cavor's notes. The final page of his diary had evidently been Cavor's dying thoughts. In a handwriting increasingly ragged and untidy, Cavor had indicted a paragraph forgiving the world for its scorn, hoping that some day mankind would indeed have easy access to the stars. The paragraph ended in mid-sentence. It was, thought Alan, a moving testament from a great human being. The days went by and the green disk of earth appeared in the view-screen. Late on the sixth day the cavor sliced into earth's atmosphere, and Alan threw it into the landing orbit he had computed that afternoon. The spaceship swung in great spirals round earth, drawing ever closer, and finally began to home in on the spaceport. Alan busied himself over the radio transmitter, getting landing clearance. He brought the ship down easily, checked out and hurried to the nearest phone. He dialed Jesperson's number. The lawyer answered, When did you get back? Just now, Alan said, just this minute. Well, did you? Yes, I found it. I found it! Oddly enough he was in no hurry to leave earth now. He was in possession of cavor's notes, but he wanted to do a perfect job of reproducing them, of converting the scribbled notations into a ship. To his great despair he discovered, when he first examined the cavor notebook in detail, that much of the math was beyond his depth. That was only a temporary obstacle, though. He hired mathematicians. He hired physicists. He hired engineers. After it all he remained calm, impatient perhaps, but not overly so. The time had not yet come for him to leave earth. All his striving would be dashed if he left too soon. The proud building rose a hundred miles from York City, the Hawks' Memorial Laboratory. There the team of scientists Alan had gathered, worked long and painstakingly, trying to reconstruct what old cavor had written, experimenting, testing. Early in 3881 the first experimental cavor generator was completed in the lab. Alan had been vacationing in Africa, but he was called back hurriedly by his lab director to supervise the testing. The generator was housed in a sturdy, windowless building far from the main labs. The forces being channeled were potent ones, and no chances were being taken. Alan himself threw the switch that first turned the space-warp generator on, and the entire research team gathered by the closed circuit video pickup to watch. The generator seemed to blur, to waver, to lose substance, and become unreal. It vanished. It remained gone fifteen seconds, while a hundred researchers held their breaths. Then it returned. It shorted half the power lines in the county. But Alan was grinning as the auxiliary feeders turned the lights in the lab on again. OK, he yelled. It's a start, isn't it? We got the generator to vanish and that's the toughest part of the battle. Let's get going on model number two. By the end of the year, model number two was complete, and the tests this time were held under more carefully controlled circumstances. Again success was only partial, but again Alan was not disappointed. He had worked out his timetable well. Premature success might only make matters more difficult for him. Thirty-eight eighty-two went by, and thirty-eight eighty-three. He was in his early twenties now, a tall, powerful figure, widely known all over earth. With Jesperson's shrewd aid, he had pyramided Mac's original million credits into an imposing fortune, and much of it was being diverted to the hyperspace research. But Alan Donnell was not the figure of scorn James Hudson Kavor had been. No one laughed at him when he said that by thirty-eight eighty-five hyperspace travel would be a reality. Thirty-eight eighty-four slipped by. Now the time was drawing near. Alan spent virtually all his hours at the research center, aiding the successive tests. On March eleventh, thirty-eight eighty-five, the final test was accomplished satisfactorily. Alan's ship the cavor had been completely remodeled to accommodate the new drive. Every test but one had been completed. The final test was that of actual performance. And here, despite the advice of his friends, Alan insisted that he would have to be the man who took the cavor on her first journey to the stars. Nine years had passed almost to the week since a brash youngster named Alan Donnell had crossed the bridge from the spacers enclave and hesitantly entered the bewildering complexity of York City. Nine years. He was twenty-six now, no boy any more. He was the same age as Steve had been when he had been dragged unconscious to the Vahala and taken aboard. And the Vahala was still bound on its long journey to Prision. Nine years had passed, but yet another remained before the giant starship would touch down on the planet of Prision. But the Fitzgerald contraction had telescoped those nine years into just a few months for the people of the Vahala. Steve Donnell was still twenty-six, and now Alan had caught him. The contraction had evened out. They were twins again. And the cavor was ready to make its leap into hyperspace. CHAPTER XIX It was not difficult for Alan to get the route of the Vahala, which had been recorded at Central Routing Registration. Every starship was required by law to register a detailed route chart before leaving, and these charts were filed at the Central Bureau. The reason was simple. A starship with a crippled drive was a deadly object. In case a starship's drive conked out, it would keep drifting along towards its destination utterly helpless to turn, maneuver, or control its motion. And if any planets or suns happen to lie in its direct path, the only way a ship could alter its trajectory was to cut speed completely, and with the drive dead there would be no way of picking it up again. The ship would continue to drift slowly out to the stars while its crew died of old age. So the routes were registered, and in the event of drive trouble it was thus possible for a rescue ship to locate the imperiled starship. Space is immense, and only with a carefully registered route could a ship be found. Starship routes were restricted information, but Allen had influence. He was easily able to persuade the routing registration people that his intentions were honorable, that he planned to overtake the Vahala if they would only let him have the coordinates. A bit of minor legal jugglery was all that was needed to give him access to the data. It seemed there was an ancient regulation that said any member of a starship's crew was entitled by law to examine his ship's registered route if he wanted to. The rule was intended to apply to starmen who distrusted their captains and were fearful of being shipped off to some impossibly distant point. It said nothing at all about starmen who had been left behind and were planning to overtake their ships. But nothing prohibited Allen from getting the coordinates, so they gave them to him. The cavor was ready for departure. Allen elbowed his way through the crowd of curious onlookers and clamored into the redesigned control chamber. He paused a moment, running his fingers over the shiny instrument panel with its new dials, strange levers, unfamiliar equipment. Overdrive compensator, fuel transmuter, distortion guide, bender index, strange new names. But Allen realized they would be part of the vocabulary of all future spacemen. He began to work with the new controls, plotting his coordinates with extreme care, and checking them through six or seven times. At last he was satisfied he had computed a hyperdrive course that would loop him through space and bring him out in only a few days time in the general vicinity of the Vahala which was buzzing serenely along at near the speed of light. That was practically a snail's pace compared with hyperdrive. The time for the test had come. He spoke briefly with his friends and assistants in the control tower. Then he checked his figures through one last time and requested blast-off clearance. A moment later the countdown began and he began setting up for departure. A tremor of anticipation shot through him as he prepared to blast off on the first hyperdrive voyage ever made. He was stepping out into the unknown, making the first use ever of a strange, perhaps dangerous means of travel. The drive would loop him out of the spacetime continuum into where and back again, he hoped. He punched down the keys and sat back to wait for the automatic pilot to carry him out from earth. Somewhere past the orbit of the moon a gong told him that the caviar drive was about to come into play. He held his breath. He felt a twisting sensation. He stared at the view screen. The stars had vanished. Earth, with all its memories of the last nine years, was gone, taking with it Hawks, Jesperson, York City, the enclaves, everything. He floated in a featureless, dull, gray void without stars, without worlds. So this is hyperspace, he thought. He felt tired and he felt tense. He had reached hyperspace. That was half the struggle. It remained to see whether he would come out where he expected to come out, or whether he would come out at all. Four days of boredom, four days of wishing that the time would come to leave hyperspace. And then the automatic pilot came to life. The caviar generator thrummed and signaled that it had done its work and was shutting down. Alan held his breath. He felt the twisting sensation. The caviar was leaving hyperdrive. Stars burst suddenly against the blackness of space, the view screen brightened. Alan shut his eyes a moment as he readjusted from the sight of the gray void to that of the starry reaches of normal space. He had returned. And below him, making its leisurely journey to Presion, was the great golden hulled bulk of the vahala gleaming faintly in the black night of space. He reached for the controls of his ship radio. Minutes later he heard a familiar voice that of Chip Collier, the vahala's chief signal officer. Starship vahala picking up. We read you. Who was calling please? Alan smiled. This is Alan Donald ship. How goes everything? For a moment nothing came through the phones but astonished sputtering. Finally Collier said thickly, Alan, what sort of gag is this? Where are you? Believe it or not, I'm hovering right above you in a small ship. Suppose you get my father on the wire and we can discuss how I'll go about boarding you. 15 minutes later the caviar was grappled securely to the skin of the vahala, like a flea riding an elephant. And Alan was climbing in through the main airlock. It felt good to be aboard the big ship once again after all these years. He shucked his spacesuit and stepped into the corridor. His father was standing there waiting for him. Hello, dad. Captain Donald shook his head uncomprehendingly. Alan, how did you, I mean? And you're so much older, too. I, the caviar drive, dad. I've had plenty of time to develop it. Nine good long years back on earth. And for you it's only a couple of months since you blasted off. Another figure appeared in the corridor, Steve. He looked good. The last few months aboard the vahala had done their work. The unhealthy fat he had been carrying was gone. His eyes were bright and clear, his shoulders square. It was like looking into a mirror to see him, Alan thought. It hadn't been this way for a long time. Alan, how did you? Quickly, Alan explained. So I couldn't reverse time, he finished. I couldn't make you as young as I was, so I took the opposite tack and made myself as old as you were. He looked at his father. The universe is going to change now. Earth won't be so overcrowded. And it means the end of the enclave system and the Fitzgerald contraction. We'll have to convert the vahala to the new drive, Captain Donald said. He looked still stunned by Alan's sudden appearance. Otherwise we'll never be able to meet the competition of the new ships. There will be new ships, won't there? As soon as I return to earth and tell them I've been successful, my men are ready to go into immediate production of hyperspace vessels. The universe is going to be full of them even before your ship reaches Prussian. He sensed now the full importance of what he had done. Now that there's practical transportation between stars, the galaxy will grow closer together, as close as the solar system now. Captain Donald nodded. And what are you planning to do now that you've dug up the cavore drive? Me? Alan took a deep breath. I've got my own ship, Dad. And out there are Rigel and Deneb and from all hot and a lot of other places I want to see. He was speaking quietly, calmly, but with an undercurrent of inner excitement. He had dreamed of this day for nine years. I'm going to take a grand tour of the universe, Dad, everywhere. The hyperdrive can take me. But there's just one thing. What's that? Steve and the captain said virtually in the same moment. I've been practically alone for the last nine years. I don't want to make this trip by myself. I'm looking for a companion, a fellow explorer. He stared squarely at Steve. A slow grin spread over his brother's face. You devil, Steve said. You planned this too well. How could I possibly turn you down? Do you want to? Alan asked. Steve chuckled. Do you think I do? Alan felt something twitching at his cuff. He looked down and saw a bluish-purple ball of fur sitting next to his shoe, studying him with a rye expression. Rat! Of course, is there room for a third passenger on this jaunt of yours? Application accepted, Alan said, warmth spreading over him. The long quest was over. He was back among the people he loved, and the galaxy was opening wide before him. A sky full of bright stars growing brighter and closer by the moment was beckoning to him. He saw the crewmen coming from their posts now. The rumor had flitted rapidly around the ship, it seemed. They were all there, Art Candon and Dan Kelleher, and a gaping Judy Collier, and Roger Bond, and all the rest of them. You won't be leaving right away, will you? The captain asked. You can stay with us a while, just to see if you remember the place. Of course I will, Dad. There's no hurry now, but I'll have to go back to Earth first and let them know I've succeeded so they can start production. And then, Deneb first, Steve said, from there out to Spica and Altair. Grinning, Alan said, more worlds are waiting than we can see in ten lifetimes, Steve. But we'll give it a good try. We'll get out there. A multitude of stars thronged in the sky. He, Steve, and Rat, together at last, plunging from star to star, going everywhere, seeing everything. The little craft grappled to the vahala would be the magic wand that put the universe in their hands. In this moment of happiness he frowned an instant, thinking of a lean, pleasantly ugly man who had befriended him and who had died nine years ago. This had been Max Hawke's ambition to see the stars. But Max had never had the chance. We'll do it for you, Max, Steve and I. He looked at Steve. He and his brother had so much to talk about, they would have to get to know each other all over again after the years that had gone by. You know, Steve said, when I woke up aboard the vahala and found out that you'd shanghide me, I was madder than a hornet. I wanted to break you apart. But you were too far away. You've got your chance now, Alan said. Yeah, but now I don't want to. Steve laughed. Alan punched him good-naturedly. He felt good about life. He had found Steve again and he had given the universe the faster than light drive. It didn't take much more than that to make a man happy. And now a new and longer quest was beginning for Alan and his brother. A quest that could have no end. A quest that would send them searching from world to world out among the bright infinity of suns that lay waiting for them. End of chapter nineteen. End of Starman's quest. Written by Robert Silverberg. Read for you by Don Larson in Minnesota.


me kal bhi kye. isto pasado me palmi tohan gravity me kye cerne and this is very correct and it should not this guy who can get away お bread is taken in place only and prasko delivered with makeup me samida yarn, ka aa aa palmi sambai di a lif bheise saaj couldn't put him in person te basnder ko ehal dhe khasm dehan j Kabay


Suppose you have two sets A and B. To find the number of elements in A union B, we can add the number of elements in each set. But because there might be elements included in both sets, we need to subtract the number of elements that are in both. This is an example of what's known as the inclusion-exclusion principle. For example, suppose 25 people like chocolate chip cookies, 38 like kale, and 7 like both. How many like chocolate chip cookies or kale? So let's consider our two sets. We'll let C be the set of people who like chocolate chip cookies, and K be our set of people who like kale. Then the number of people who like either chocolate chip cookies or kale will be the number who like chocolate chip cookies, plus the number who like kale. But since this counts to people in the intersection twice, we'll need to subtract out the intersection. So filling our numbers we get. What if we have three sets? It's easiest to see how this will work using a Venn diagram for three sets. So if we draw a generic Venn diagram, we see that the number of elements in all three sets will be the number in the three sets individually. But note that this will count some elements multiple times. So anything that's in the pairwise intersection of sets will be counted twice, and so we'll need to subtract those pairwise intersections. But now consider something that's in the intersection of all three sets. Anything in this intersection would have been counted three times initially, but then we would have subtracted three for each of the intersections, so we need to add it back in to get the correct count. For example, consider a three-digit number. How many include one as the first digit, two as the second digit, or three as the third digit? So we can start off with the numbers that begin with one, and these are the numbers. To count these, we can index them. And since our last digits are changing, we'll go ahead and use the last digit as the index. So 100 last digit zero, well, that's i equals zero. 101 last digit one, that'll be i equals one, and so on. Since i equals zero is our first number, the term number is one more than the index. So our last term i equals 99 will be the one plus 99 100th number. So there are 100 numbers that begin with a one. And as a reminder of a useful principle in math and in life, if it's not written down, it didn't happen. So let's make a record of this. There are 100 numbers of the form one x, y, where x and y are the two remaining digits. The numbers that have two as a second digit are and likewise in every hundred from 100 to 900. And again, to count these, we'll index them. So to count the number in any hundred, we'll index them on that last digit again. So 120, that's our i equals zero. 121, that's our i equals one, and so on. And since i equals zero is our first number, then i equals nine will be the 10th number. And so there are 10 in every hundred. And so there are 10 times 90 numbers with nine as the second digit. The numbers whose third digit is three are and, and again, it follows that there are 10 in every hundred from 100 to 900. So there are 90 numbers with three as a third digit. Now these will count some numbers more than once. So note that some numbers with one as a first digit will have two as a second digit. And these numbers are, and there are 10 such numbers. There are also 10 numbers that have one as a first digit and three as a third digit. And 10 numbers that have two as a second digit and three as a third digit, or are there? So in combinatorial problems, it's useful to list at least three. And again, to count index. And here we can index on our first digit, so our numbers. And since i equals one is our first number, the index is the same as the term number, so i equals nine will be the ninth number. And so there are only nine numbers that have a two as a second digit and a three as a third digit. And finally, there's only one number of the form one as the first, two as the second, and three as the third. So applying the inclusion-exclusion principle, we add the singles, we subtract the doubles, we add the triples, and we get 252 numbers that have a one as their first digit, two as their second, or three as their third.


Hello friends, I am Sanjay Gupta. In this video, I am going to demonstrate you how you can implement Unary Operator Overloading in C++. Before starting, you can note my information. You can connect with me by following these details. You can download my app Techimus that is available on Google Play. You can search my channel on YouTube by typing my name in YouTube search bar. My channel will be available there. You can open it. If you want to follow my videos, you can subscribe my channel. Here, various program related videos and playlists are available. Now, coming on to the topic, I am going to demonstrate you the use of Unary Operator Overloading and how it can be implemented in C++. First, I have included a header file iostream. Then, I have used a namespace that is std, then name of classes number. Here, an integer variable as attribute is declared. Then, in public section, first read function is implemented. It will display enter the number message on console and the number will be stored inside n variable. Then, print function. It will display value on console that is available inside n variable. Then, third increment function is defined, which is increasing value of n by 1. After that, main function is implemented. Here, object n1 is created. It is calling read function. Then, it is calling print function. So, the value which is entered by the user through read function will be displayed on console using print. Then, increment function will increase the value of attribute and then print function will again display that value on console. So, right now, I have not implemented Unary Operator Overloading. It is, this program is implemented without using Unary Operator Overloading. So, first, I am executing this code. Then, I will be converting it with the help of Unary Operator Overloading. So, I am entering 5. You can see the output. Value equals to 5 and value equals to 6. 5 is before increment and 6 is after increment. Now, I am converting this function into overloaded operator function. So, this is overloaded operator function. And this is for Unary Operator. And here, I have to use this plus plus n1. So, you can see I have removed function name and I have placed an operator symbol in place of function name with the help of operator keyword. And same at calling time, I have used plus plus operator in place of function name. So, whenever you want to apply an operator on object of the class, then you have to overload that operator and you have to define a definition for that operator. This concept is known as operator overloading. Now, I am again executing this code. I am entering 5. You can see the output. It is printing same result. So, friends, if you want to apply operators on objects of the class, then you have to overload that operator and that overloaded operator becomes, sorry, that overloaded operator have to define a function definition. And that operator symbol is treated as a function name. And you have to use a keyword that is operator at the time of function definition. So, if Unary Operator Overloading is implemented, then these parenthesis will be blank. If binary operator overloading is implemented, then you have to pass an argument here because binary operators applied on two arguments and Unary operators are applied on one argument. So, this is all about Unary Operator Overloading. I hope you have understood this concept how you can convert a normal function into overloaded operator function. If you want to watch more programming related videos, you can visit my YouTube channel. Thank you for watching this video.