A few hours after the Presidency descended upon Harry Truman, he learned about the atom bomb project, and thereupon determined that no future Vice President should be as ill-informed and unprepared as he. After that blast-off, which is also a tip-off to Mr. Dorman's thesis, he goes back to ""The Beginnings"": the original intent that the Vice President be the second most qualified man; the Jefferson-Burr tie, prompting an amendment providing for separate ballots; Burr's erratic conduct, and the subsequent drop in the caliber of candidates, chosen primarily to balance the ticket geographically or ideologically. For more than a hundred years the office would be an annex (not ""worth a pitcher of warm spit""--John Nance Garner). In a continuous narrative that is also a side-long history of successive administrations, each of the incumbents appears briefly but vividly: a few had ability (wasted); several were nincompoops; very few got along with their chiefs for very long. In any case Coolidge was the first to sit in on cabinet meetings regularly. Wallace the first to exercise influence. Half of the book deals with personalities and especially politics since 1932; in 1944 Roosevelt's indecisiveness kept Truman (and several others) on tenterhooks up to the last minute; Eisenhower's guarded reaction to disclosure of Nixon's personal fund (and the ""cloth coat and Checkers"" speech) was even more unnerving, and Nixon was set to withdraw. Examination of the responsibilities of Barkley, Nixon, Johnson and Humphrey reveals an ascending curve--also a declining candor on the part of the author. But for the most part (and regardless of who is No. 2), this is intelligent history, viable for reference, and refreshing, often amusing to read.