Private schools, for which the bell was tolling in the early 1970s, are enjoying an enrollment boom that reflects growing dissatisfaction with public education.

The dissatisfaction extends beyond the urban areas from which many people fled in the 1950s and 1960s seeking better schools than the ones they found.

"More and more applications we get are from families that have no tradition of private school experience," said the headmaster of one New England boarding school.Another said that in the last two years his relatively small school has begun receiving applications from some of the Northeast's most affluent suburbs which have high schools boasting excellent reputations.

Private day schools also are flourishing and large numbers of new ones have been started in large cities.

George Gallup said in summing up 10 years of annual polls on public education for Phi Delta Kappa that "educators should no longer assume that citizens feel deeply committed to support public school education." Cost of public education have almost doubled last 10 years, and the high failure rate of school bond issues across the country indicates that public confidence has been eroded, Gallup said.

Although laments about public education have been heard for years, it has been only in the last few years that more Americans have indicated they are willing to cut their standard of living to take their children out of public school systems. Tuitions at secular day schools run up to $4,000, and up to $6,500 at boarding schools.

School enrollment - both public and private - is declining about 2 percent a year because of the "baby bust" that followed the post-World War II "baby boom." Despite this trend, enrollment in the 825 private secular schools that belong to the National Association of Independent Schools has been growing by 1 to 1.5 percent annually for the last five years, Thomas Wilcox, a spokeman for the organization, said.

Between 1965 and 1975 more than 20 of the association's schools failed and the predictions in the early 1970s were for more failures to come as the school-age population declined. "If the schools that went under had been able to borrow money they probably could have survived," Wilcox said. Most secular private schools are now turning away applicants.

Catholic schools - which still have 70 percent of the nation's private school students - went through an even steeper decline in the late 1960s and early 1970s, Catholic enrollment was 87 percent of the nation's private school population.

Although the decline continues, Catholic schools are now losing students only at the same 2 percent rate of decline for the nation's school-age population.

Other church-related schools, like the secular schools, have been increasing enrollments in recent years. All private schools have about 5 million students - about 10 percent of the nation's school population.

Dissatisfaction with public schools is based more on perception than fact, said James Keefe, director of research for the National Association of Secondary School Principals. "It's opinion creating opinion," he said.

Keefe and representatives of private schools agree that current public attitudes toward education are changing as a result of the consumer movement that has raised people's awareness of what services they are getting for their tax dollars.

Parents who were enamored of a new public school 10 years ago because it had extraodinary athletic facilities, language laboratories and other special facilities are now pushing for a return to education in basic subjects - and a stronger school discipline.

In each of the 10 years of Gallup's polls, discipline has been named the most serious school problem by increasing numbers of people.

Private schools have the advantage of being free to discipline students to their own standards. In a public school, one member of a New England school board said "If you discipline a kid, before you know it, it's a court case."

He added, "The society has become so litigious that it's axiomatic that every major decision we make ends up in litigation."

For private schools, their recent good fortune has not been all serendipitous. At the beginning of the decade, smaller boarding schools might have had a part-time admissions officer. Now the same schools are likely to have two full-time admissions officers visiting public schools around the country recruiting as colleges do.

If the interest in private schools reflects unhappiness with public education, a more striking - and much smaller - example is the newly revived interest in educating children at home.

John Holt, a Boston-based apostle of teaching children at home, is a former teacher who describes his evolution of thought this way: "I used to say reform the schools. Then I said start your own school. Now I say take the children out altogether."

Holt predicts that private school enrollment will continue to grow and that home education will grow along with it as more and more people give up on the public system.