The amendment also outlined what to do if the president was “unable to discharge the powers and duties of his office.” After suffering a severe stroke, President Woodrow Wilson was virtually incapacitated late in his tenure, and President Dwight D. Eisenhower suffered a heart attack and two other major illnesses. The nightmare situation was a president who was in a coma but could not be removed because there was no provision for it. In the nuclear age, when a commander in chief might have to make world-altering decisions in minutes, that was no longer considered tolerable.

The amendment has since been invoked to temporarily transfer power to the vice president during short periods of medical procedures, as when President George W. Bush twice underwent colonoscopies. But only once before has a White House staff been known to seriously contemplate invoking the amendment to permanently replace the president.

When President Ronald Reagan appointed former Senator Howard H. Baker Jr. as chief of staff after the Iran-contra scandal broke, the new team arriving in the West Wing heard that the aging president was increasingly “inattentive and inept,” as a report prepared by a Baker aide put it. White House officials signed Mr. Reagan’s initials to documents for him.

But after Mr. Baker ordered aides to observe the president closely to see if it might be necessary to invoke the 25th Amendment, he came to the conclusion that Mr. Reagan, while older, was still fit. “Within a couple days of when we got there, we had this lunch and Senator Baker says, ‘You know, boys, I have no doubt this president’s fully capable of performing the job of president of the United States,’” recalled Tom Griscom, one of Mr. Baker’s aides.

As a practical matter, the notion that Mr. Trump would be removed through the 25th Amendment is more opposition fantasy than plausible outcome, absent a significant change in circumstances. The amendment does not define “unable to discharge” and was devised mainly for a situation when a president had a serious health problem, not for a president whose behavior seems erratic and would fight removal.

The amendment can be put to use only if the vice president agrees, and few can imagine Mr. Pence, who has made public loyalty to Mr. Trump his calling card, going along without a more extreme situation. The amendment then requires the support of a majority of the cabinet or some other body designated by Congress. Congress has never designated such a body, leaving the matter to the cabinet.

Even if the vice president and a majority of the cabinet were to decide to invoke the amendment, there is an appeals process. The deposed president could inform Congress that he is, in fact, capable of carrying out the duties, and it would require a two-thirds vote of both the House and the Senate to reject that determination and remove him — a burden even higher than impeachment, which requires only a majority in the House as well as a two-thirds vote of the Senate for conviction and removal.