Like the governments of other area jurisdictions, the Fairfax County Board of Supervisors has not been reluctant to swat Metro - to criticize the mounting costs of subway construction and bus operating deficits, even to question the agency's basic premises in financial planning.

But this week the supervisors, by decisive majorities, stood firmly behind Metro. In the process, they left their chairman, John F. Herrity, a persistent critic of Metro, in the embarrassing position of being on the short side of lobsided votes.

In perhaps the most important vote, the supervisors, 7-2, backed - with one stipulation - Metro's formula for dividing up the subway operating deficit among jurisdictions the system is or will be serving.

Under the Metro formula, Fairfax's share of the deficit for the fiscal year beginning July 1 would be $1,825,000. The formula is based on the number of county riders, the number of stations in Fairfax and county population.

Herrity urged the board to reject the Metro formula in favor of one that used the number of riders and stations but excluded population. Under this formula, supported by the Fairfax County Federation of Civic Associations, Fairfax's share of the fiscal 1978 Metrorail deficit woul be $1,082,000 or almost $800,000 less.

In recommending that the supervisors stay with the Metro formula, County Executive Leonard Whorton noted that if the other formula was adopted, by 1980 Northern Virginia's share of subway deficit would be $9.5 million instead of $9.3 million, even though Fairfax's share would be $1.2 million less. Arlington's share would jump 25 per cent - from $4.9 million to $6.5 million.

The implication was clear: Fairfax's gain would be at the expense of its Northern Virginia neighbors.

Herrity picked up support only from Supervisor Audrey Moore (D-Annandale). With Supervisor Joseph Alexander (D-Lee), a member of the Metro board making the motion, the supervisors adopted the recommendation of Whorton and his staff. The only stipulation is that if Fairfax's share of the defict changes by more than 10 per cent from what Metro projects, the county can damand a renegotiation of the formula.

On another vote, the supervisors refused to walk away from the county's share of liability for Metro revenue bonds, which were sold to pay the region's share of the escalating costs of subway construction. Herrity argued that because the bonds were supposed to be paid off with farebox revenues - now no longer realistic because Metro operates at a deficit - the county has no legal obligation to help pay the bonds off. But again, a majority of the board refused to listen to Herrity.

When the supervisors were considering Metro's ongoing analysis of alternatives to a 100-mile subway system, Herrity was rebuked by Alexander. The rebuke came when Herrity prefaced a criticism of Metro with his oftstated observation that. "This is the biggest public works project in history . . ." Before he could go on, Alexander said curtly: "Let's do without the speeches."