Some presidents appear more genuine in their religious adherence than perhaps we are accustomed to thinking. Nixon used religious rhetoric for electoral advantage—no one would dispute that—but also used such rhetoric, Mr. Smith concludes, “to express the better side of his nature, convey how he generally perceived himself, and highlight the character and spiritual qualities he valued for himself and other Americans.” Mr. Clinton, too, appears more genuine in Mr. Smith’s treatment than his reputation would suggest; he used biblical language in public addresses more than almost any other president, and in a few of his remarks you can hear a man struggling with his own impulses, as when he told reporters in 1992 that “the biggest moral challenge is trying to live by what you believe in every day.”

Mr. Smith is only partly successful, however, in finding the ways in which faith directed or informed policy. Earlier presidencies yield more insights than recent ones.

James Madison was reticent about his faith—he seems to have written and said almost nothing about his religious views after he left Princeton. In his early years Madison felt strongly that established religion was both unwise and wrong; he was appalled to learn of the Anglican Church’s persecution of Presbyterians and Baptists in prerevolutionary Virginia, and his Princeton teacher John Witherspoon impressed the future president with his emphasis on freedom of conscience. As president, accordingly, Madison criticized Congress’s practice of paying chaplains, and he fiercely opposed the granting of charters to local churches. Although he frequently issued religious pronouncements—during the War of 1812 he issued four national days of “public humiliation and prayer”—he deliberately used generic language. One critic complained that nothing in one of Madison’s proclamations would offend “a pagan, an infidel, [or] a deist.”