The hopes of thousands of private high school athletes in Virginia eager to compete against their public schools counterparts in football and other major sports were dashed yesterday by a federal appeals court in Richmond that upheld the Virginia High School League's policy banning private schools from membership.

By a 2 to 1 vote, the 4th U.S. Circuit Court of Appeals found that the league's policy of excluding private schools in order to enforce its transfer rule is a "legitimate state objective" and does not violate the constitutional rights of the state's private schools.

The decision overturns an order to the league from a federal district court judge in Alexandria in October that it accept the Bishop Denis J. O'Connell High School in Arlington and that students from the school be allowed to compete in league games and tournaments.

William G. McMurtie, attorney for O'Connell,said he will appeal to the U.S. Supreme Coutr. McMurtie said the league's transfer rule applies both to private and public schools and that 46 states permit league sports competition between Private and public schools.

In the court case, the league argued that allowing private schools to become members would make it difficult to enforce the transfer rule because private schools do not have specifically defined geographic areas from which to draw students.

Thus, the league argued, a good athelete at a private school with a mediocre team could transfer to a public school with a better team and receive more media exposure and college scholarship opportunities but not be required to wait one semester before he could again participate in interscholastic sports.

"If you start changing schools for purposed of athletics then you put athletics above everything else, and it shouldn't be," said John Dezio, attorney for the league. Dezio added that the NCAA operates under a similar transfer rule.

But McMurtie classified the transfer rule a "redherring" and said that it did not apply to private school students anymore than it does to those who attend public schools. McMurtie added that like public schools, private institutions also draw students from defined geographic areas, an argument specifically rejected by the Appeals Court.

". . . Even assuming that there are some Virginia private schools which do draw from strictly defined areas, these schools, unlike their public counterparts, are not so limited by state law and could therefore at any time decide to modify or abolish their self-imposed drawing restrictions and recruit students from anywhere," the court decision said.

The league is an unincorporated association of 284 public high schools in Virginia supported by public funds from a variety of sources, including the University of Virginia and local schoolboards, as well as from the gate receipts from sports events.

Founded in 1913, the league included private and public secondary schools, but in 1925 private schools were excluded from tournaments involving major sports football, baseball and basketball. Private schools still participate as a distinct class in statewide tournaments including tennis, debating and speaking.

Besides the private school athletes, perhaps the man most disppointed by the Appeals Court decision was Alward V. Burch, pricipal of the 1,600-student O'Connell High School.

"The schedules that we have now work a hardship on our students," he said yesterday. "They take us to West Virginia and all over Virginia and we can't even play our next-door neighbors.