Metro is now spending $5 million a year just to find out how much each of its eight Washington area juridictions will have to kick in to keep the transit system running.

That $5 million cleans no buses, pays no train operators, fixes no Farecard machines. It goes for accountants, computer time, consultants and survey cards. It is a $5 million cost of doing business that is forced on the Washington Metropolitan Area Transit Authority by a peculiar tangle of political and financial alliances that only Washington could produce.

The process is known as the "subsidy allocation formula." Metro actually has two formulas, one for buses and one for subways. Both are incredibly complex; both are under continual review and occasional renegotiation. The formulas include credits and debits for such items as the residence of Metro's passengers (that's really what those annual surveys are all about), how many miles of bus routes are run in each jurisdiction, the cost of diesel fuel, where the subway stations are located and how many subway riders climb on or off east of the Anacostia River and are therefore eligible for the District of Columbia's special 10-cent discount.

The formulas take a long time and a lot of people to administer. Because they are complex, they produce answers long after the questions are asked. Because people are involved, they sometimes make mistakes.

All of that is one way of saying that Arlington County is angry about its projected Metro subsidy payment for the next fiscal year -- not just because the payment is so large ($10.8 million), but because it is $1.8 million larger than it was projected to be last December, when Metro's budget was under review.

What makes it even more galling for Arlington is that its financial people said loudly, several times, that they thought Metro's staff had made a mistake and had underestimated Arlington's costs. Turns out they were right.

Furthermore, the beneficiary of the mistake is Fairfax County, which is wealthier and larger and devotes a much smaller percentage of its annual operating budget to Metro than Arlington does (11.1 percent in 1980 compared with 5.3 percent).

Does it make any difference to the size of the total Metro budget that Arlington is expected to pay $1.8 million more and Fairfax County $1.8 million less?

In a better world -- Atlanta, Denver and Pittsburgh leap to mind -- transit authority budget officers sit down and work with three figures:

The cost of operating the transit system.

The revenue that will be collected from fares, charter fees and advertising.

The difference, otherwise known as the subsidy, because public transit does not make money anywhere and some government has to make up the difference.

In Atlanta, Denver and Pittsburgh, the subsidy is paid from taxes that are given directly to the transit authority. Thus, once those three figures are worked out, the budget process is essentially complete.

At Metro, once the system's costs, revenues and subsidies are determined, the process has just begun. The subsidy must then be allocated among the eight local governments, because Metro isn't a system, it is eight systems with eight different philosophies on the value of public transit and how much should be provided.

This organizational gargoyle has created a fare structure that is almost beyond comprehension -- buses that are "owned" by Montgomery County and thus refuse to pick up passengers in the District; high density bus service along Shirley Highway in Virginia, but almost nothing along Indian Head Highway in Prince George's County.

A certain amount of information about costs and revenues is essential and prudent for Metro to collect, but $5 million worth seems a little high, General Manager Richard S. Page has been saying for some weeks now.

Metro is not blameless. Partly because of inaction by its political board, partly because of administrative ignorance and partly because of inertia, Metro still does not know which of its thousands of bus trips every day are profitable and which are losers. It knows what they cost; it doesn't know what they make.

The "stable and reliable source of revenue" that Virginia and Maryland Metro partners are seeking from their legislatures would simplify this costly problem, but only if the two Maryland counties and Virginia's five jurisdictions could agree to share costs and revenues without continually arguing about how to divide them. That may be asking too much of a group of individual governments that are jealous of their own prerogatives and quick to see ulterior motives in the actions of their neighbors.

Five million dollars is just a drop in the bucket out of Metro's projected $276 million operating budget. However, $5 million is three-fourths of the revenue Metro expects to collect from the fare increase its board proposed last week.