D.C. Board of Education President David H. Eaton said last night that the board would take only two ballots tonight when it attempts to appoint a successor to the seat vacated by Frank Smith's electioon to the City Council.

The Ward 1 school board post has been vacant since Dec. 31, and 11 applicants are vying for it. The board is scheduled by a majority vote to appoint a successor to fill out Smith's term, which ends in December.

However, several factors, including the apparent fact that none of the applicants has won the support of more than a few board members, are likely to hamper the selection process. The winning applicant must get at least six votes from the 10 sitting members of the board.

"I don't see that any of them has six votes," board member R. David Hall (Ward 2) said yesterday. "We have looked to the people of Ward 1 to clearly state who they want and that hasn't happened."

Board member Wanda Washburn (Ward 3) added that the selection process has also been hampered because the board is locked in a budget battle with city officials and has not devoted as much time to the matter of the Ward 1 seat as it normally would.

"It's a tiresome thing to come up right now," Washburn said.

After an informal gathering of several board members last night, Eaton said the board would try two ballots today and that if none of the applicants received six votes, the board would recess and meet to determine what to do next, rather than sit through several ballots.

"Previously there never have been more than three candidates for a board vacancy," said Eaton, adding that the decision about the two-ballot limitation had been reached because of the number of candidates and the lack of a clear choice among them.

It has been reported that the board's leadership, concerned about the possible appointment of a member who would not be sympathetic to their concerns, would favor a deadlock in which no applicant received six votes, allowing the board leadership to maintain its balance of power.

Eaton denied this report last night, saying the "seat may be left open but it won't be because I fear someone's selection; it is because there are four good candidates and I think all four are very good. I have no need to control anything."