"Yes，" said two voices at once. Deniador， who was the owner of one of the voices， said to Pelorat， "Are you thinking of Yariff"s project？"
"I am，" said Pelorat.
"Then would you explain it to the Councilman？ I think he would more readily believe you than me."
Pelorat said， "You see， Golan， in the last days of the Empire， there was a time when the Search for Origins， as they called it， was a popular pastime， perhaps to get away from the unpleasantness of the surrounding reality. The Empire was in a process of disintegration at that time，you know.
"It occurred to a Livian historian， Humbal Yariff， that whatever the planet of origin， it would have settled worlds near itself sooner than it would settle planets farther away. In general， the farther a world from the point of origin the later it would have been settled.
"Suppose， then， one recorded the date of settlement of all habitable planets in the Galaxy， and made networks of all that were a given number of millennia old. There could be a network drawn through all planets ten thousand years old； another through those twelve thousand years old， still another through those fifteen thousand years old. Each network would， in theory， be roughly spherical and they should be roughly concentric. The older networks would form spheres smaller in radius than the younger ones， and if one worked out all the centers they should fall within a comparatively small volume of space that would include the planet of origin Earth."
Pelorat"s face was very earnest as he kept drawing spherical surfaces with his cupped hands. "Do you see my point， Golan？"
Trevize nodded. "Yes. But I take it that it didn"t work."
"Theoretically， it should have， old fellow. One trouble was that times of origin were totally inaccurate. Every world exaggerated its own age to one degree or another and there was no easy way of determining age independently of legend."
Bliss said， "Carbon-14 decay in ancient timber."
"Certainly， dear，" said Pelorat， "but you would have had to get co-operation from the worlds in question， and that was never given. No world wanted its own exaggerated claim of age to be destroyed and the Empire was then in no position to override local objections in a matter so unimportant. It had other things on its mind.
"All that Yariff could do was to make use of worlds that were only two thousand years old at most， and whose founding had been meticulously recorded under reliable circumstances. There were few of those， and while they were distributed in roughly spherical symmetry， the center was relatively close to Trantor， the Imperial capital， because that was where the colonizing expeditions had originated for those relatively few worlds.
"That， of course， was another problem. Earth was not the only point of origin of settlement for other worlds. As time went on， the older worlds sent out settlement expeditions of their own， and at the time of the height of Empire， Trantor was a rather copious source of those. Yariff was， rather unfairly， laughed at and ridiculed and his professional reputation was destroyed."
Trevize said， "I get the story， Janov. Dr. Deniador， is there then nothing at all you could give me that represents the faintest possibility of hope？