WHISTLE STOPS; Adventures in Public Life. By Wilson W. Wyatt Sr. University Press of Kentucky. 235 pp. $24.

OH, SO FAR AWAY, so long ago. Why, oh why, do participants in great events, especially those who played peripheral roles, wait until history grows cold before telling their tales?

There is no need to challenge Wilson W. Wyatt on the grounds that his "adventures in public life" were unimportant; on the contrary, he is one of that fascinating and numerous breed of Americans, large numbers of whom, like Wyatt, are lawyers, who now and then take time out from earning a living to give a hand to city, state and/or nation -- a fifth of his career, in this case.

But it is too bad that Wyatt, now 80, waited, for example, until the history of the post- war era of the Democratic Party up to and including Adlai E. Stevenson's two failed attempts to defeat Dwight D. Eisenhower for the presidency is all but set in verbal concrete. Twenty years ago, say, he might have added something to those histories; now this is just another addendum to the literature.

Reading this small volume one gets the feeling that Wyatt simply didn't want to hurt anybody's feelings, so much does he pussyfoot around contentious matters of which he has knowledge. He won't even identify "one leading figure" at the 1968 Democratic convention who begged off speaking for the majority plank on the Vietnam war because he was up for reelection.

Although the most fascinating part of this book is Wyatt's description of the Stevenson campaigns and of the candidate himself -- Wyatt managed the '52 run and helped in '56 -- the more poignant parts concern the might-have-beens in Wyatt's own life.

In 1948, when President Truman's election chances looked hopeless, Wyatt, who had gone to the Democratic convention to boost Senator Alben Barkley for vice president, found himself a possibility for number two on the ticket. But Barkley's rousing convention speech swept him into that spot. Wyatt had been elected mayor of his home town, Louisville, at 35 and he had served as the first chairman of Americans for Democratic Action, the liberal spur to the party, and he had been Truman's housing administrator. But after the GOP congressional landslide in 1946 he had left Washington although he was offered the solicitor general's post.

In 1958, Wyatt announced for governor of Kentucky but he ended up running, successfully, for lieutenant governor. That was the campaign in which Happy Chandler, who headed the rival Democratic faction, lambasted Wyatt as a city dude who wore "ankle blankets" -- spats.

Wyatt never bothers to tell us if, in fact, he did wear spats. In fact, much of the writing is dull as a lawyer's brief. And the book is full of factual errors that any good editor should have caught: David Lawrence was mayor of Pittsburgh, not Philadelphia; Evalyn Walsh McLean, the Washington hostess, is confused with Eleanor Patterson, the Washington publisher; British Prime Minister Harold Macmillan's name is misspelled as is Walter Lippmann's; Earl Warren was not chief justice of the Supreme Court but of the United States, and so on.

THE ONE PORTRAIT that does come through is Stevenson's. Wyatt's best line: "What earned him admiration often did not gather him support." Wyatt describes Stevenson's "compulsion" to "tell the whole truth" rather than to shade it, or duck it, in the usual political campaign fashion. He offended Catholics by stating flatly that he would discontinue the Roosevelt-Truman policy of having a personal representative at the Vatican just as he offended coastal state Democrats by opposing their grab for tidelands oil revenue.

When someone, unidentified, remonstrated on the latter decision: "But Governor Stevenson, if you insist on doing that, you can't win," Adlai responded: "I don't have to win."

Wyatt says it was he and George Ball who recommended that Stevenson make public his income tax returns, then a breathtaking idea but now standard practice. However, the recommendation was the result of Republican counterfire against Stevenson when, in the midst of the massive uproar over vice presidential candidate Richard Nixon's secret fund and the resulting "Checkers speech," it turned out that Stevenson, then governor of Illinois, had a fund of his own, albeit there were major distinctions. Wyatt says the recommendation they made was "to eliminate this issue from the campaign."

Wyatt gives us no reflective view on whether he now thinks Stevenson would have been a first-rate president or whether what Wyatt concedes was the "inordinate amount of time" his candidate spent "writing, rewriting reworking, and even fiddling with his speeches" was a tipoff to an indecisiveness that would have hampered him in the White House. Wyatt is a believer in Stevenson as the "conscience of American politics," so much so, in fact, that his account of the abortive 1960 effort to win him a third nomination comes through as truly a sad story.

In 1962 Wyatt lost a close Senate race to Thruston Morton. The next year President Kennedy used Wyatt as a presidential emissary to Indonesia's mercurial President Sukarno to keep him from nationalizing the American oil firms operating in his country. Wyatt's detailed account is text book stuff for schools of diplomacy, especially in showing the uses of flattery and of a promise of a presidential visit.

Wyatt has been a useful doer of public good and it is evident from his account that he has truly enjoyed it all. Not every autobiographer can say that.