The N.S.A. also programmed computers to map the connections between telephone numbers in the United States and suspect numbers abroad, sometimes focussing on a geographic area, rather than on a specific person?for example, a region of Pakistan. Such calls often triggered a process, known as "chaining," in which subsequent calls to and from the American number were monitored and linked. The way it worked, one high-level Bush Administration intelligence official told me, was for the agency "to take the first number out to two, three, or more levels of separation, and see if one of them comes back"—if, say, someone down the chain was also calling the original, suspect number. As the chain grew longer, more and more Americans inevitably were drawn in.

FISA requires the government to get a warrant from a special court if it wants to eavesdrop on calls made or received by Americans. (It is generally legal for the government to wiretap a call if it is purely foreign.) The legal implications of chaining are less clear. Two people who worked on the N.S.A. call-tracking program told me they believed that, in its early stages, it did not violate the law. "We were not listening to an individual's conversation," a defense contractor said. "We were gathering data on the incidence of calls made to and from his phone by people associated with him and others." Similarly, the Administration intelligence official said that no warrant was needed, because "there's no personal identifier involved, other than the metadata from a call being placed."

But the point, obviously, was to identify terrorists. "After you hit something, you have to figure out what to do with it," the Administration intelligence official told me. The next step, theoretically, could have been to get a suspect's name and go to the FISA court for a warrant to listen in. One problem, however, was the volume and the ambiguity of the data that had already been generated. ("There's too many calls and not enough judges in the world," the former senior intelligence official said.) The agency would also have had to reveal how far it had gone, and how many Americans were involved. And there was a risk that the court could shut down the program.

Instead, the N.S.A. began, in some cases, to eavesdrop on callers (often using computers to listen for key words) or to investigate them using traditional police methods. A government consultant told me that tens of thousands of Americans had had their calls monitored in one way or the other. "In the old days, you needed probable cause to listen in," the consultant explained. "But you could not listen in to generate probable cause. What they?re doing is a violation of the spirit of the law." One C.I.A. officer told me that the Administration, by not approaching the FISA court early on, had made it much harder to go to the court later. [Emphasis mine]