In April, 1965, the leaders of India and Pakistan, nations then on the brink of war, cancelled meetings with President Lyndon Johnson, and L.B.J. thought he knew why. While flying to Texas aboard Air Force One, he huddled with his speechwriter, Dick Goodwin. “Do you know there are some disloyal Kennedy people over at the State Department who are trying to get me; that’s why they stirred things up?” Johnson asked. “I didn’t know that,” Goodwin replied. “Well, there are,” Johnson said, “They didn’t get me this time, but they’ll keep trying.” Johnson’s obsession with his political rival, Robert Kennedy, had, by that time, become so overpowering—and his insistence on “all-out loyalty” so pronounced—that it was bogging down the Presidential-appointments process and driving good men out of government. “We cannot afford to lose them,” Harry McPherson, the White House counsel, warned Johnson in a bravely blunt memo. “Neither, in my opinion, can we afford to give them a polygraph-loyalty test. . . . If the word gets around that one has to put on horse-blinders to work for you, you will probably come out with a bunch of clipped yes-men who are afraid of their own shadows and terrified of yours.”

That advice would apply in today’s White House, too, though it’s unlikely that President Trump would welcome it any more than L.B.J. did. (He nearly fired McPherson.) Trump’s chief complaint about his own yes-men seems to be that they don’t say yes energetically enough. The people who serve at the pleasure of the current President are, according to numerous sources, causing him displeasure. Trump, in fact, is said to be enraged by the lot of them—even his adviser-in-law, Jared Kushner—for their “incompetence,” and for “tooting their own horns.” Reports say that Trump is considering a big shakeup. He has already, of course, shaken up the F.B.I., firing its director, James Comey, last Tuesday, for a multitude of asserted sins—disloyalty not least among them. A detailed account in the Times described a one-on-one dinner at the White House in January, shortly after the Inauguration, in which Trump, three times, asked Comey to pledge his loyalty to him. Comey, according to the Times, dodged, and offered the President his honesty instead. (In light of the F.B.I.’s investigation of possible collusion between the Trump campaign and the Russian government, honesty must be what Trump didn’t want from Comey.) In recent days, Trump and his staff have been insisting that if the subject of loyalty came up at that dinner—and, mind you, they’re not saying it did—it would only have concerned Comey’s loyalty to the U.S.A. “I think loyalty to the country, loyalty to the United States, is important,” Trump said on Saturday, in an interview with Fox News. “You know, I mean, it depends on how you define loyalty.”

Putting aside (if one can) Trump and his purposes, every President needs his staff, his Cabinet, and—to a reasonable extent—his party to stand by and stick with him, for an obvious reason: without loyalty to the President and his agenda, an Administration lacks a center of gravity. But loyalty, as Trump suggests, means many things. How a President defines loyalty says a good deal about how he leads and who he is.

John F. Kennedy, for example, selected his unquestionably loyal brother, Robert, as Attorney General and installed members of the so-called Irish Mafia across the government. But as he filled out the rest of his Administration he showed little interest in whether someone had voted for him. He wanted to build, he said, “a ministry of talent”; also, given the narrowness of his victory over Richard Nixon, in 1960, he wanted a few Republicans on his team. This caused Bobby Kennedy some distress, especially when J.F.K. looked to appoint Douglas Dillon—who had served in the Eisenhower Administration—as his Secretary of the Treasury. As Arthur Schlesinger, Jr., recalled in “A Thousand Days,” his account of those times, R.F.K. “kept asking what would happen if Dillon resigned in a few months with a blast against the administration’s financial policies. He warned his brother that they were putting themselves in the hands of a Republican who had no reason for loyalty to them and might well betray them.” The President-elect shrugged. “Oh, I don’t care about those things,” he said. “All I want to know is: is he able? and will he go along with the program?” In the end, he allowed Bobby to extract from Dillon a pledge (unnecessary, it turned out) that if Dillon ever felt compelled to resign, he would go quietly. But J.F.K.’s nonchalance was not a pose. He expected (and for the most part received) the devotion of his Cabinet and staff. But he knew that he needed, above all, their candor; he needed them to tell him the truth, to give dispassionate and sometimes divergent advice, and then, of course, to back his decisions. Honest debate, in Kennedy’s view, was an act of loyalty; mindless affirmation was not. ...