And then, Tessa, just before 5 p.m., ship-time, on the second day after the transition that had curved instead of being straight, burst into the room. Her eyes were wild and she was breathing hard. Her dark hair, which, in the last year had become liberally salted with gray, was mussed.

Fisher rose in consternation. ‘Bad?’

‘No, good!’ she said, throwing herself into a chair rather than sitting down.

Fisher wasn't sure he had heard correctly, wasn't sure that perhaps she might only have been speaking ironically. He stared at her and watched her as she visibly gathered herself together.

‘Good,’ she repeated. ‘Very good! Extraordinary! Crile, you're looking at an idiot. I don't suppose I'll ever recover from this.’

‘Well, what happened?’

‘Chao-Li Wu had the answer. He had it all along. He told me. I remember him telling me. Months ago. Maybe a year ago. I dismissed it. I didn't even listen, really.’ She paused to catch her breath. Her excitement had completely disoriented the natural rhythm of her speech.

She said, ‘The trouble was that I thought of myself as the world authority on superluminal flight, and was convinced that no-one could possibly tell me anything I didn't know or hadn't thought of. And if someone did suggest something that seemed strange to me, the idea was simply wrong, and, presumably, idiotic. Do you know what I mean?’

Fisher said grimly, ‘I've met people like that.’

‘Everyone's like that, now and then,’ said Wendel, ‘given certain conditions. I suppose aging scientists are particularly like that. That's why the daring young revolutionaries of science become old fossils after a few decades. Their imaginations harden with encrusted self-love and that's their end. It is now my end… But enough of that. It took us over a day to really work it out, to adjust the equations, to program the computer and set up the necessary simulations, to go down blind alleys and catch ourselves. It should have taken a week, but we were all driving each other like maniacs.’

Wendel paused here, as if to catch her breath. Fisher waited for her to continue, nodding encouragement as he reached out to grasp her hand.

‘This is complex,’ she continued. ‘Let me try to explain. Look- We go from one point in space through hyperspace to another point in space in zero time. But there's a path we take to do that, and it's a different path each time, depending on the starting and ending points. We don't observe the path, we don't experience it, we don't actually follow it in space-time fashion. It exists in a rather incomprehensible way. It's what we call a “virtual path”. I worked out that concept myself.’

‘If you don't observe it, and don't experience it, how do you know it's there?’

‘Because it can be calculated by the equations we use to describe the motion through hyperspace. The equations give us the path.’

‘How can you possibly know that the equations are describing anything that has actual reality? It could be just - mathematics.’

‘It could be. I thought it was. I ignored it. It was Wu who suggested it might have significance - maybe a year ago - and like a full-grown idiot, I dismissed it. A virtual path, I said, had merely virtual existence. If it couldn't be measured, it was outside the realm of science. I was so shortsighted. I can't endure myself when I think of it.’

‘All right. Suppose the virtual path has some sort of existence. What then?’

‘In that case, if the virtual path is drawn near a sizable body, the ship experiences gravitational effects. That was the first breathtakingly true and useful new concept - that gravitation can make itself felt along the virtual path.’ Wendel shook her fist angrily. ‘I saw that myself, in a way, but I reasoned that since a ship would be moving at many times the speed of light, gravitation would have insufficient time to make itself felt to any measurable extent. Travel would therefore be, by my assumption, in a Euclidean straight line.’

‘But it wasn't.’

‘Obviously not. And Wu explained it. Imagine that the speed of light is a zero point. All speeds less than that of light would have negative magnitude, and all speeds gre.ater than that of light would have positive magnitude. In the ordinary Universe we live in, therefore, all speeds would be negative, by that mathematical convention, and, in fact, must be negative.

‘Now, the Universe is built on principles of symmetry. If something as fundamental as speed of movement is always negative, then something else, just as fundamental, ought to be always positive, and Wu suggested that that something else was gravitation. In the ordinary Universe, it is always an attraction. Every object with mass attracts every other object with mass.

‘However, if something goes at a superluminal speed - that is, faster than light - then its speed is positive and the other something that was positive has to become negative. At superluminal speed, in other words, gravitation is a repulsive force. Every object with mass repels every other object with mass. Wu suggested that to me a long time ago and I wouldn't listen. His words just bounced off my eardrums.’

Crile said, ‘But what's the difference, Tessa? When we're going at enormous superluminal speeds, and gravitational attraction doesn't have time to affect our motion, neither would gravitational repulsion.’

‘Ah, that's not so, Crile. That's the beauty of it. That reverses, too. In the ordinary Universe of negative speeds, the faster the speed relative to an attractive body, the less gravitational attraction affects the direction of movement. In the Universe of positive speeds, hyper-space, the faster we go relative to a repulsive body, the more gravitational repulsion affects the direction of movement. That makes no sense to us, since we're used to the situation as it exists in the ordinary Universe, but once you are forced to change signs from plus to minus and vice versa, you find these things falling into place.’

‘Mathematically. But how much can you trust the equations?’

‘You match your calculations against the facts. Gravitational attraction is the weakest of all the forces and so is the gravitational repulsion along the virtual paths. Within the ship and within us, every particle repels all other particles while we are in hyperspace, but that repulsion can do nothing against the other forces that hold it together and have not changed signs. However, our virtual path from Station Four to here carried us close to Jupiter. Its repulsion along the virtual hyperspatial path was just as intense as its attraction would have been along a nonvirtual spatial path.

‘We calculated how Jupiter's gravitational repulsion would affect our path through hyperspace, and that path curved exactly as it had been observed to do. In other words, Wu's modification of my equations not only simplifies them, but it makes them work .’

Fisher said, ‘And did you break Wu's neck, Tessa, as you promised you would?’

Wendel laughed, remembering her threat. ‘No, I didn't. Actually, I kissed him.’

‘I don't blame you.’

‘Of course, it's more important now than ever that we get back safely, Crile. This advance in superluminal flight must be reported, and Wu must be properly honored. He built on my work, I admit, but he went on to do what I might never have thought to do. I mean, consider the consequences.’

‘I can see them,’ said Fisher.

‘No, you can't,’ said Wendel sharply. ‘Now, listen to me. Rotor had no problems with gravitation because they merely skimmed the speed of light - a little below it at some times, a little above it at others - so that gravitational effects, whether positive or negative, attractive or repulsive, had immeasurably small effects on them. It was our own true superluminal flights at many times the speed of light that makes it imperative to take gravitational repulsion into account. My own equations are useless. They will get ships through hyperspace, but not in the right direction. And that's not all.

‘I have always thought that there was a certain unavoidable danger in emerging from hyperspace - the second half of the transition. What if you merge into an already existing object? There would be a fantastic explosion that would destroy the ship and everything in it in a trillionth of a trillionth of a second.

‘Naturally, we're not going to end up inside a star because we know where the stars are located and can avoid them. In time, we might even know where a star's planets are and avoid them, too. But there are asteroids by the tens of thousands and comets by the tens of billions in the neighborhood of every star. If we end up overlapping one of those, that would still be deadly.

‘The only thing that would save us, in the situation as I had thought it to be before today, is the laws of chance. Space is so huge that the chance of striking any object larger than an atom or, at most, a grain of dust is extraordinarily small. Still, given enough trips through hyperspace, the overlapping of matter is a catastrophe just waiting to happen.

‘But under conditions as we now know them to be, the chances are zero. Our ship and any sizable object would repel each other and tend to move apart. We are not likely to run afoul of anything deadly. They would all automatically move out of our path.’

Fisher scratched at his forehead. ‘Wouldn't we move out of our path, too? Won't that upset our course unexpectedly?’

‘Yes, but the small objects we are likely to encounter will alter our path in very limited fashion and we could easily make it up - a small price to pay for safety.’

Wendel took a deep breath and stretched luxuriantly. ‘I feel great. What a sensation all this will make when we get back to Earth.’

Fisher chuckled. ‘You know, Tessa, before you came in, I was building a morbid picture in my head of our being irretrievably lost; of our ship wandering for ever, with five dead bodies aboard; of its being found someday by intelligent beings who would mourn the obvious space tragedy-’

‘Well, it won't happen, you can count on that, my dear,’ said Wendel, smiling, and they embraced.