then, and there was probably little or no leapfrogging. Whereas millions of worlds were settled, perhaps chaotically, during the second expansion, only fifty were settled, probably in an orderly manner, in the first. Whereas the millions of worlds of the second expansion were settled over a period of twenty thousand years; the fifty of the first expansion were settled over a period of a few centuries-almost instantaneously, in comparison. Those fifty, taken together, should exist in roughly spherical symmetry about the world of origin.
"We have the co-ordinates of the fifty worlds. You photographed them, remember, from the statue. Whatever or whoever it is that is destroying information that concerns Earth, either overlooked those co-ordinates, or didn't stop to think that they would give us the information we need. All you have to do, Golan, is to adjust the co-ordinates to allow for the last twenty thousand years of stellar motions, then find the center of the sphere. You'll end up fairly close to Earth's sun, or at least to where it was twenty thousand years ago."
Trevize's mouth had fallen slightly open during the recital and it took a few moments for him to close it after Pelorat was done. He said, "Now why didn't I think of that?"
"I tried to tell you while we were still on Melpomenia."
"I'm sure you did. I apologize, Janov, for refusing to listen. The fact is it didn't occur to me that-" He paused in embarrassment.
Pelorat chuckled quietly, "That I could have anything of importance to say. I suppose that ordinarily I wouldn't, but this was something in my own field, you see. I am sure that, as a general rule, you'd be perfectly justified in not listening to me."
"Never," said Trevize. "That's not so, Janov. I feel like a fool, and I well deserve the feeling. My apologies again-and I must now get to the computer."
He and Pelorat walked into the pilot-room, and Pelorat, as always, watched with a combination of marveling and incredulity as Trevize's hands settled down upon the desk, and he became what was almost a single man computer organism.
"I'll have to make certain assumptions, Janov," said Trevize, rather blankfaced from computer-absorption. "I have to assume that the first number is a distance in parsecs, and that the other two numbers are angles in radians, the first being up and down, so to speak, and the other, right and left. I have to assume that the use of plus and minus in the case of the angles is Galactic Standard and that the zero-zero-zero mark is Melpomenia's sun."
"That sounds fair enough," said Pelorat.
"Does it? There are six possible ways of arranging the numbers, four possible ways of arranging the signs, distances may be in light-years rather than parsecs, the angles in degrees, rather than radians. That's ninety-six diferent variations right there. Add to that, the point that if the distances are light-years**, I'm uncertain as to the length of the year used. Add also the fact that I don't know the actual conventions used to measure the angles-from the Melpomenian equator in one case, I suppose, but what's their prime merid-"
Pelorat frowned. "Now you make it sound hopeless."
"Not hopeless. Aurora and Solaria are included in the list, and I know where they are in space. I'll use the co-ordinates, and see if I can locate them. If I end up in the wrong place, I will adjust the co-ordinates until they give me the right place, and that will tell me what mistaken assumptions I am making as far as the standards governing the co-ordinates are concerned. Once my assumptions are corrected, I can look for the center of the sphere."
"With all the possibilities for change, won't it make it difficult to decide what to do?"
"What?" said Trevize. He was increasingly absorbed. Then, when Pelorat repeated the question, he said, "Oh well, chances are that the co-ordinates follow the Galactic Standard and adjusting for an unknown prime meridian isn't difficult. These systems for locating points in space were worked out long ago, and most astronomers are pretty confident they even antedate interstellar travel. Human beings are very conservative in some ways and virtually never change numerical conventions once they grow used to them. They even come to mistake them for laws of nature, I think. Which is just as well, for if every world had its own conventions of measurement that changed every century, I honestly think scientific endeavor would stall and come to a permanent stop."
He was obviously working while