THE TRIBULATIONS OF Yale University have become extremely public in the course of its embarrassing attempts to recruit a new president. The university's corporation encountered great difficulty finding a candidate brave enough even to consider the job. The man who finally agreed to take it, A. Bartlett Giamatti, professor of English and chairman of humanities at Yale, is not the first person to whom it was offered. But the friends and admirers of the university will not necessarily be sorry to see that the corporation was finally driven, in desperation, to turn to a scholar and teacher from its own faculty. Yale's troubles deserves attention precisely because thay are shared in one degree or another by all of the country's first-rate universities.

Taken together, the universities are now probably the strongest of all institutional influences on the American future. But the process works both ways: As the country changes, the results often become apparent first on the campuses. Anyone who thinks that academia offers the quiet life has not visited there recently.

The last time that the country put new demands on the universities, two decades ago, they responded with enormous enthusiasm. They are being pushed, after all, in the direction in which they wanted to go. The cry then was for enormous expansion of the graduate schools and the research institutes. The country wanted scientists and scholar to establish American technology as the world's leader and to staff the vast expansion of colleges that, as the birth rates showed, lay ahead. The federal government poured in money at an accelerating rate, not only in the scientific subjects but also in foreign languages and international studies to prepare students for wider national responsibilities.

Then, in time, the country changed itsmind. Federal aid, for example, has shifted its purposes sharply since the late 1960s. Federal support for graduate study has been cut the sciences. At the same time student assistance has greatly increased, most of it going to students from families of limited income.The empnasis is off technology and competition with the Russians; it is on equality of opportunity. That change means a much smaller share of federal aid for the universities with the outstanding graduate school, explicitly training an elite. It means more for the public colleges that teach youngsters who, a few years ago, would not have gone to college at all and are now trying to make up for past deprivation.

The number of babies born in this country last year was 25 per cent lower than in 1959, when most of this year's college freshmen were born. The effect on the graduate schools is already dire. Because the number of college teachings jobs is evidently going to contract between now and the end of the century, job prospect for young scholars are exceedingly bleak. Even at the most heavily endowed of unversities, the undergraduates are suddenly more important. The dean of Harvard College took himself out of consideration for the presidency of Yale with explanation that he is deeply involved in a campaign to improve undergraduate education at Harvard.

The conventional prescription for the troubles of the universities is simply more money. But no very dramatic increase in funds seems likely. The stock market's fainting spells have severely curtailed private philanthropy, and it's hard to think that public aid will increase greatly in a time of declining enrollments.

The great euphoric expansion is long over, but it engendered habits of mind that live on. Changing them means shifting the balance between research and teaching. It means dropping some courses and programs to protect the quality of others. It means struggling, on a limited budget, to reconcile the standards of the intellectual aristocracy with the social ideals of democracy. At Yale, Prof. Giamatti is entitled to more than the usual congratulations as he steps into his new office. He isn't likely to get much sleep, but on the other hand, he won't find it dull.