What was the origin of the no-third-term tradition

In practical presidential politics the outstanding question of the day is whether President Coolidge will be a candidate for renomination and reelection in 1928. The President has given no indication of his own attitude, nor is it likely that any direct announcement of his intention to be or not to be a candidate will be forthcoming until shortly in advance of the Republican National Convention. A premature announcement that he was not a candidate would measurably weaken, if not destroy, the President's influence with the leaders of his party, while an announcement of his candidacy would provide definite basis for the organization, both within and without the party, of opposition to his renomination and reelection.

Nicholas Murray Butler, in an address six weeks ago in which he described himself as “a working Republican who is both a personal friend and a political supporter of President Coolidge,” said he was taking it for granted “that when he thinks the right time has come he will make public statement of his unwillingness to have his name considered in connection with the Republican presidential nomination of 1928.” The President's good common sense, Dr. Butler believed, would dictate against “inviting certain defeat through injecting the third term issue into the campaign.”

As early as July 1926, the late Senator Albert Cummins, following his defeat and the defeat of other administration senators in the senatorial primaries, had expressed the opinion in a widely published statement that the President would not be a candidate in 1928, that he would have “had enough of it by that time.” Neither the Cummins statement, nor the Butler speech seven months later both of which were interpreted as “an effort to smoke out the President” brought any announcement from the White House of the President's attitude toward his renomination.

both include an amendment process.