The Alexandria City Council and the Alexandria School Board, which have spent much of the year throwing spitballs at each other and then trying to patch things up, closed their last major meetings of the summer in another scuffle.

This time, the two boards took a few swings at each other with a nicely seasoned baseball bat. Within an hour and one mile of each other, but light years away in terms of cooperation, each of the two bodies announced that it, and it alone, controlled the minor league baseaball field next to Cora Kelly Elementary School. If that weren't enough to leave city observers shaking their heads in amazement, the next two decisions may have left baseball fans and the Alexandria Dukes ready to hang up their spikes.

The City Council voted to give the Dukes continued use of the field, just after the School Board voted to throw the team off the diamond.

"I thought to myself, now Alison, the school system needs parents, and these parents have voiced their opposition to the team using the field," said outgoing school board President Alison M. May, in recalling why she cast the tie-breaking vote to close the field to the Dukes.

"I'm amazed by the vote taken by the school board," said City Council member Donald C. Casey (D) less than an hour after the board decision. "I talked to Alison May three times and three times she said she would vote" to let the team use the field. (May later denied having made commitment.)

Casey proposed the successful motion in which the council informed the Dukes that the team could use the Cora Kelly field for the next year, with the possibility of a two-year renewal after that. no one suggested the two bodies might sue each other, although some observers said it would be a delicious, if far-fetched possibility.

The City Council appoints the school board, which historically acts independently of the council, despite receiving nearly all of its $41 million budget from the council.

The inherent antagonism created by this system was nicely summed up last week when outgoing school board member Michael Mulroney advised two new members that their allegiance "is to the state of Virginia, and not to the City Council."

Which brings us to the Alexandria Dukes, currently in second place in the Virginia division of the Class A Carolina League, but first in the hearts of several hundred loyal fans.

The team started using the Cora Kelly fields in Del Ray when the school was closed two years ago. Last year, the school board decided to reopen the school this fall and said that a minor league baseball team using the field would be inappropriate. Neighborhood residents had complained to the school board and the City Council that fans leaving the field in the evening were loud, noisy, messy and disruptive.

Team owners, in an effort to find a solution before the school reopens this falls, asked the city for funds to build a stadium in the Cameron Valley area of the city, or at least give it permission to float a refundable bond issue. The council said no to both requests, since the facilities at Cora Kelly had been built by the city specifically for the team and the city owned the land.

Apparently the city's understanding of who owned the land did not filter to the school board since the board began telling the team several months ago to find another base to call home.

The owners, desperate to find a place to plant their spikes next year, found themselves caught between the rock and hard place of city politics.

City Attorney Cyril D. Calley hit the high hard one and announced that the city owned the land, by gum. But the school board shot back that its lawyers said the school board owned, or at least controlled the land.

The issue festered until the school board's last major meeting before the summer break. The board heard from neighborhood and PTA members who complained they didn't want the team around fearing a detrimental impact on their neighborhood and the community. Finally, the board, which already had banned the Dukes from Cora Kelly locker rooms, decided on a 5-to-4 vote to ban the team from the field.

The split vote eventually turned on neighborhood concerns. Tagging the team out was May, Vice Chairman Shirley Tyler and members John O. Peterson, William D. Euille and Shirley Waller. Going in with their spikes up, but losing, were Mulroney, Harvey Harrison, Judy Feaver and Lou Cook.

"After nine years on the board I didn't want to go out dropping education for baseball," said May, who always votes last.

Moments later, the City Council was informed of the vote, and council members clenched their teeth and tightened their fists. All were holding back their urge to push this dispute into an all-out brawl. After all, it was early summer, and the council hoped the appointment of Connecticut educator Robert W. Peebles as the new Alexandria superintendent would usher in an era of good feelings.

Council members began falling over each other trying not to say the wrong thing. Council member Casey, who throws a pen or pipecleaner whenever he gets mad, twisted in his swivel chair, but said nothing. Other council members reluctantly followed suit. Carlyle C. Ring Jr. (R), a former school board president, noted that the vote might change in favor of the team once the new school board was sworn in.

Council member James P. Moran Jr., (D) tried to show that the issue was Bigger than Baseball by exclaiming, "We're getting involved in the issue of our relations with the school board."

Casey then proposed that the council simply tell the school board the city owned the land and that the school board could not evict people from land it didn't own. City Manager Douglas Harman worked out the proposal to inform the clut it could use the field, and the council voted to meet with Peebles to explain the situation to him.

The vote was five in favor of letting the Dukes use the field, with Nelson E. Greene Sr. voting no because he wanted to be on record backing the residents and Ring abstaining because he said he wanted more information.

So the Dukes can use the field, at least for the next three years. Which should be enough time for Peebles to decide if he wants to give up his lifelong allegiance to the Boston Red Sox -- who despite their less than glorious finishes over the past few years, at least can count on the undivided support of their own hometown.