The person having the greatest number of votes for President, shall be the President if such number be a majority of the whole number of Electors appointed; and if no person have such majority, then from the persons having the highest numbers not exceeding three on the list of those voted for as President, the House of Representatives shall choose immediately, by ballot, the President. But in choosing the President, the votes shall be taken by states, the representation from each state having one vote; a quorum for this purpose shall consist of a member or members from two-thirds of the states, and a majority of all the states shall be necessary to a choice. And if the House of Representatives shall not choose a President whenever the right of choice shall devolve upon them, before the fourth day of March next following, then the Vice-President shall act as President, as in the case of the death or other constitutional disability of the President.
This kind of question that asks for pure speculation always amuses me; I suspect you’re a teenager because no mature person would ask such a thing. If by some freak circumstances Lincoln had been elected in 1860 and then Civil War didn’t break out, but he was assassinated in 1865 anyway, a civil war probably would have broken out at that time. Vice Presidents often become leading contenders for their party’s presidential nomination. In recent years, we have found LBJ was followed by Humphry, Carter by Mondale, Reagan by Bush Sr., Clinton by Gore, and now many mention Biden as a successor to Obama. No doubt this tradition would have played an even more important role in determining who should follow a president—as Adams followed Washington. Many of our military phrases like court-martial come from French, where the adjective comes after the noun. The noun is a court, martial is an adjective describing it, so pluralize the noun.