A veneer of civility at Metro board meetings usually conceals tensions between the city and its suburbs, but the veneer was stripped away this week when District representatives in effect accused the suburbs of trying to cheat on the cost of operating the bus system.

The debate placed on view a fact about Metro that is rarely discussed in public: There is a fragile balance between the suburbs and the city that is complicated by social philosophy and race. It has long been the contention of black District residents that they receive second-class service in comparison with their white suburban neighbors but bear more than their share of the cost. w

Many suburban residents believe the city creates problems for Metro and that suburbanities, who generally pay much higher fares, are carrying the city on their backs.

It was in that context that the Rev. Jerry A. Moore Jr., D.C. City Council and Metro board member, turned to his suburban colleagues near the end of a Metro committee meeting and said, "If I were somewhere else and somebody else were paying my share of the costs, I would like it to continue too. . . . At this point, the District feels unfairly treated."

Moore reminded everyone that he has fought alongside the suburbs in battling for federal approval of suburban subway lines; that the District has contributed to Metro subway construction more than $2 billion in highway funds that could have been spent on bridges and potholes in the city. Many of those subway miles are in the suburbs.

Moore's speech was a not-so-subtle reminder that the district needs to feel it is being fairly treated. His comments came during debate on whether Metro should study how to divide among eight local governments the cost of such things as the time drivers spend on lunch breaks and layovers. Those items are not included in the complicated cost-sharing formula now in use.

If they were, according to early estimates, the financially strapped District would save about $500,000 in subsidy.

Metro General Manager Richard S. Page recommended the study be deferred indefinitely because it would cost about $250,000, would divert staff from more important projects, and would affect only about 2 percent of the $101 million Metrobus subsidy.

"With the many millions of dollars the District of Columbia puts into buses, we don't sneeze at 2 percent," said Gladys Mack, District budget director and Metro board member. The estimated District subsidy for buses this year is $52 million.

Fairfax County supervisors Marie Travesky and Joseph Alexander, both Metro board members, couldn't move fast enough to say what a wonderful idea Page had. (If the preliminary numbers are right, Fairfax County would have to pay about $400,000 of the subsidy the District pays.)

"I think there are a lot of other ways we can achieve equity," Travesky said. "Cost reduction is one of them."

Lunch breaks and layover times for drivers probably do cost more on suburban routes than on city routes. But there are undivided cost items on city routes that are higher than those on suburban routes. For example, security problems are greater in some parts of the city than in the suburbs and more accidents (and legal claims) occur on the District streets than in the suburbs.

If the suburbs are forced to approve a lunch break study, Page said, they will insist on expanding the study to analyze how "to allocate the costs of providing security for the buses and the cost of accidents."

The list of things one jurisdiction could blame on the others is potentially endless. The existing formula is so complicated, Page has estimated, that it costs about $5 million annually to administer and does nothing to make the buses run better.

Subsidy allocation, Page said, is "a live animal on the loose. It gets bigger every year. I want to shoot that animal and start with a blank piece of paper that includes only three or four factors that really affect costs, and go with that."

Board members realized after the meeting that the discussion had extended beyond the normal boundaries. "This study may not be the only solution," Mack said.

Cleatus Barnett, chairman of the full Metro board and the representative from Montgomery County, said, "Clearly there is a conflict between D.C. and some of the outer suburbs. The general manager and I will be looking for solutions during the next week that will be satisfactory to all parties."

Both Barnett and Moore said they did not think the incident eroded the board's confidence in Page. "No indeed," Moore said. "He's a good general manager."

Page did not lobby for his recommendation before the meeting, he said, because "I didn't realize the District feels that strongly about the study." The committee technically approved Page's recommendation to defer the study, but committees at Metro are informal bodies and the full board must take all binding actions. Under board rules, the District alone can block the deferral, and it doubtless will.

This is just another example of Metro's Achilles heel -- its lack of taxing power and concurrent dependence on the eight local governments. Each government has a different proposal for how costs should be divided among them. Each proposal, as former Metro General Manager Theodore C. Lutz noted, "just happens to work out to the advantage of the government that proposes it."