On Oct. 6, Mr. Bush pointed with pride to his record at a conference sponsored by the Cincinnati chapter of the Federalist Society, the elite network for the conservative legal movement. He noted that he had appointed more than a third of the federal judiciary expected to be serving when he leaves office, a lifetime-tenured force that will influence society for decades and that represents one of his most enduring accomplishments. While a two-term president typically leaves his stamp on the appeals courts — Bill Clinton appointed 65 judges, Mr. Bush 61 — Mr. Bush’s judges were among the youngest ever nominated and are poised to have an unusually strong impact.

They have arrived at a time when the appeals courts, which decide tens of thousands of cases a year, are increasingly getting the last word. While the Supreme Court gets far more attention, in recent terms it has reviewed only about 75 cases a year — half what it considered a generation ago. And Mr. Bush’s appointees have found allies in like-minded judges named by Mr. Bush’s father and Reagan.

Republican-appointed judges, most of them conservatives, are projected to make up about 62 percent of the bench next Inauguration Day, up from 50 percent when Mr. Bush took office. They control 10 of the 13 circuits, while judges appointed by Democrats have a dwindling majority on just one circuit.

David M. McIntosh, a co-founder and vice-chairman of the Federalist Society, said the nation’s appeals courts were now more in line with a conservative judicial ideology than at any other time in memory.

“The level of thoughtfulness among sitting judges on constitutional theory and the role of judges is higher than certainly any other time in my life,” said Mr. McIntosh, a former Reagan legal team member and Indiana congressman. “For somebody who has spent a lot of my life promoting those ideas, it’s very encouraging to see.”