“To be what?” I asked him. He explained that tapped meant being invited to join the fraternity. “But what’s secret about this society, and what’s all wrong about it?” I asked him.

“I can’t tell you—it’s a secret,” Zimmer said. Zim was obdurately honest—the worst person to be burdened with keeping secrets. By telling me he was a Bonesman—this was in 1965—had Zim violated one of the rules of membership? He would say no more about “belonging to Bones,” as he’d ominously put it, but his being a Bonesman clearly weighed on his conscience.

Mr. Barlow, who had a Harvard prejudice against Yale, was sympathetic to Zim’s having a stricken conscience over his membership in this particular society. “Being a member of Bones is a big deal for Yalies,” Elliot told me. “It’s convenient that everything about the society is a secret, because the rest of us can’t evaluate if the club is an empty vessel—a virtual crock of shit—or if it really is a big deal.”

Skull and Bones was an honors society; students from distinguished and successful families seemed to be singled out for membership, but the students themselves must have demonstrated their own capabilities for success. “Zim was always an excellent student, and I don’t doubt that the Zimmermanns are an illustrious family,” the snowshoer said. Both Zim’s father and his grandfather had gone to Yale, Zimmer had told me, but Mr. Barlow knew that Zim’s father and grandfather had been big deals in the military, too. “The grandfather was an army general in World War One,” Elliot informed me. “I think Zim’s dad was an army colonel in World War Two.”

It still troubles me that I never learned what bothered Zim about his “belonging to Bones.” Were his fellow Bonesmen anti-Semites? What made them feel so entitled to their secrets? What made Matthew Zimmermann feel so burdened by the secrets he couldn’t share?

“I trust that boy’s moral barometer,” the snowshoer always said about Zim. In reference to the Skull and Bones clubhouse, called the “tomb,” the little English teacher said: “These tomb societies don’t usually bring out the best in young men.”

When Zimmer and I were at Exeter, the Republican senator from Connecticut was Prescott Bush—he’d been a Bonesman at Yale, where he was also a cheerleader, played varsity golf and baseball, and was president of the Yale Glee Club. In Skull and Bones lore, Prescott Bush and a few of his fellow Bonesmen dug up and removed the skull of Geronimo from the grave of the Native American warrior at Fort Sill, Oklahoma, in 1918.