On the day Sonia Landau was elected chairman of the Corporation for Public Broadcasting, the outgoing chairman, Sharon Percy Rockefeller, cautioned the board to serve "the best interests of the American people" and protect the concept of CPB as a "heat shield" from political interference.

The short speech brought into the open some philosophical divisions that had been festering at CPB for more than a year. Rockefeller says she was simply underscoring what she saw as a trend. But Landau interpreted the remarks as a warning shot. "It said you guys better watch what you do. And quite frankly, how dare she? How dare anybody?" says Landau.

The CPB board, which meets here today, has been more in the spotlight now than since the early 1970s, when the Nixon administration charged it with "left-liberal" bias and tried to influence the public affairs broadcasts.

Since Rockefeller's speech in September 1984, the world of CPB -- from its board members to managers of television and radio stations around the country to independent producers -- has been warily watching increasingly frequent spurts of disharmony on the board -- disharmony ranging from simple philosophical disagreements to name-calling and shouting matches.

At its last meeting, in September, the board deadlocked at 5-5 and couldn't even elect a chairman. It has yet to fill the important post of general counsel and has been without a president and chief operating officer since Edward Pfister walked out last May during a board fracas over his projected trip to Moscow.

Some are questioning whether the fundamental nature and business of the nation's public broadcasting agency is being eroded by conflict. Others say reports of friction on the board have been overblown, and amount to nothing worse than bad public relations at a time when public radio and television need unified voices.

Established by Congress in 1967, CPB is a nongovernment body that distributes federal money to independent producers and to 181 public television and 288 public radio station grantees. Its board is appointed by the White House and approved by the Senate.

Most public radio and television officials who discussed the board division have adopted a wait-and-see attitude, hoping that the clashes are temporary or that the five appointments due next March from the White House will iron out the conflicts.

Landau says the splits don't affect the "business" of the board and the divisions are natural: "You have 10 people who are somewhat outspoken and have their different views. The real question is, are we really moving ahead? Are we doing our business and our work? And we are."

"It is not a pleasant situation," says Vice Chairman R. Kenneth Towery, a Texas Republican appointed by President Reagan. "It is quite obvious that the split in the board is delaying the search for a president and the general counsel. That is unfortunate but I don't find it a critical situation." Lillie Edens Herndon, a Republican appointed by President Ford, says the split "prevents new initiatives from taking place . . . It is the atmosphere in which one thinks a bold new idea would not get passed." Herndon, an educator, is the senior member of the board and a former chairman.

"It is tragic," says Jack McBride, general manager of the Nebraska Educational Telecommunications Commission. "It takes the focus off genuine problems we face in trying to provide improved services."

For all but a relative handful of public broadcasting's 109 million listeners and viewers, the board's disputes have remained decorously out of sight. "The MacNeil-Lehrer NewsHour" and "WonderWorks" still appear on time. Garrison Keillor and "All Things Considered" are still heard in the land. Just Wednesday night Senate and House conferees approved a CPB budget of $214 million for fiscal 1988, up 69 percent from $159.5 million in fiscal 1986. Yet one watchful party to the fractiousness is Congress. Rep. Timothy Wirth (D-Colo.), one of the powerful pro-public broadcasting voices, says, "It is important that CPB play a role in the long-range planning of public broadcasting, whose future is dependent on strong funding commitments that all of us have worked so hard to secure. I am hopeful that the apparent internal dissension will not thwart CPB's pursuit of this important mission."

Though the CPB has been periodically plagued by politics, its current dissension has emerged since Reagan vetoed two CPB authorizations in August and October 1984 and since Landau, a Republican appointed by Reagan in 1981 and the former chairman of Women for Reagan-Bush, became chairman. The tensions flared most dramatically last May when former president Pfister announced that he and another senior staffer were taking a trip to the Soviet Union. The uproar at the board meeting, which was held in conjunction with the annual meeting of the Public Broadcasting Service, included a heated argument between Pfister and Landau, in which he charged her with interfering with the "independence" of public broadcasting and she called him a "schnook" who didn't "give a damn about this organization."

Six Reagan appointees voted against Pfister's trip -- Landau, Towery, Republicans Richard Brookhiser, William Lee Hanley Jr. and Harry O'Connor and independent Howard Gutin. The four voting for the trip included Republican Herndon and independent Lloyd Kaiser as well as Democrats Sharon Percy Rockefeller and Howard White.

Landau says the board has always been political. "If I really sit down and look at the stuff, I don't think it is any different from before," she says. "CPB, because it is CPB, is always in a position of defending itself."

But both she and O'Connor, who runs a radio production business in California, say there has been no control from the White House. "If there is an effort by anyone in the White House to influence CPB, I didn't get a phone call. I have got to assume since I am such a strong supporter of the administration and a friend of the president, I would have been called," says O'Connor, an outspoken critic of Landau.

Rockefeller says the board has indeed been politicized. "I can't say it is a master plan. But they act in lock step. We have never had that before." She cites a discussion of "Concealed Enemies," a dramatization of the Alger Hiss-Whittaker Chambers spy case in which some members complained that Hiss was more favorably portrayed than Chambers. "There appears to be constant contact with the White House on CPB and other matters," she says.

Towery says other board members have asked him "what his agenda is," and he replies, "I don't have an agenda except to get off the board as quick as I can and to see that it works effectively while I am there. This is not a right-wing agenda."

"The board has always been viewed with distrust though some members have been viewed with trust," says Virginia Fox, president of the Southern Educational Communications Association. "When the appointments were made by a Democratic president, there was apprehension that there might be a hidden agenda. Whenever the stations see the turnover, and the potential dominance of one political party, the stations get nervous." Fox has attended every board meeting in the last 5 1/2 years. "The perception is not new. It has to do with a fear . . . that the good of public broadcasting might be submerged by this philosophical split and personality differences." She says the current rift is "a holy war and each side feels they hold the grail. I don't see either side giving in."

Besides varied philosophies, the board members say, the rift has been fueled by personality differences and power plays. Comparisons between Landau and Rockefeller have led some to see the problems solely as a feud between the two women. Both vigorously resent that view. "I think that is something that is used against women," says Landau. "If it were two guys having the same fight, I don't think it would be described the same way."

One male board member cautions that the divisions have changed substantially during the year because the personality conflicts keep changing. Rockefeller disagrees."This unfortunate turn of events results largely from different understandings of what the leadership of public broadcasting should be and what the future of public broadcasting is," she says. "It has nothing to do with personalities."

The leadership function, says Douglas Bennet, president of NPR, has been the one most severely hampered, making it hard for producers and stations "to take iniatives." White, the general counsel for ITT Communications & Information Services, disagrees. "I would think the industry would follow the needs of people and then CPB should shed some light. But that doesn't mean the light isn't out there somewhere else."

As for a falloff of CPB services to its constituency, David Ives, vice chairman of WGBH in Boston, says, "I'm not aware of any."

But one broadcaster complains that an administrative bottleneck has caused some delays in the grant process. "We are having difficulty securing payments on grants on which we have already done a great deal of work. I don't know if it is staff paralysis due to board uncertainty or whether it is a lack of sufficient staff," says O. Leonard Press, executive director of Kentucky Educational Television.

Some members have criticized Landau's management style, but Brookhiser, a senior editor with National Review, feels the board under Landau has been revitalized. "The split, of course, makes it interesting," he says.

Ron Hull, director of the $25 million programming fund, says in his three years, "there hasn't been one instance we received pressure from the board . . . They have kept their own opinions and politics out of programming." But even some board members say the staff doesn't have stability because of the board actions and the lack of a president.

The biggest guessing game is whether the appointment of new members or the reappointment of current ones will change the dynamics. The terms of Landau, Towery, O'Connor, Herndon and White expire in March 1986. Herndon and White can't serve again. There is a possibility the board could function at some point next year with just five members, because members can't continue to serve if replacements aren't named at the time their terms expire. There is a possibility that President Reagan could have shaped a completely new CPB board by 1987.

Towery is anxious to get off and is optimistic that new members will help change the divisions.

Landau isn't banking on being reappointed and is reluctant to speculate on whether the new composition will change the dynamics of the board. "Boards take on their own character when you get a body of 10 people together who will be there for three or four years."