LAWRENCEVILLE, N.J. — Lawrenceville School students trickled out of the brick buildings of the campus on a recent afternoon to begin their activities of dance, soccer and community service.

But no one suited up for a revered Lawrenceville tradition that dates back more than a century: intramural tackle football.

The school recently replaced its intramural tackle football program with flag football, a concession to growing concerns about the dangers of head injuries and an acknowledgment that many Lawrenceville students were not interested in the full-contact sport....

Randy Roberts, a history professor at Purdue who has studied the history of football, said the sport had long held a singular place in American society. He traced modern American football’s roots to Ivy League universities in the late 19th century.

“Football was the testing ground for the next generation of leaders,” Roberts said. “It was played by the Roosevelts and the elite. It was consciously aimed at that.”

But now, Lawrenceville students and teachers say football plays a markedly different role on campus....