ALEXANDRIA'S MAYOR Rank E. Mann has a secret plan to lower the tax rate. It would involve, he says, a tremendous reduction. Precisely what city services would he cut? Well, that's the secret. The mayor rebuffs all inquiries with irritated comment to the effect that he will specify the cuts when he gets good and ready. It appears that perhaps he won't be ready until sometime after next Tuesday's city election in Alexandria, in which Mayor Mann is being vigorously challenged by Charles E. Beatley.

While the mayor's tax plan doesn't seem to offer much comfort to the voters, it brings up the serious and delicate subject of tax rates and assessments. Several of Alexandria's neighborhoods, particularly in the older east end of the city, have had the bad luck to become fashionable. That has generated a lot of speculative buying, and real-estate assessments are soaring. The city's tax law offers special protection to the elderly, but there's nothing similar for families with children and a great many of them are being pressed severely by rising property taxes.

That's the dilemma, for severe and hasty budget cuts are apt to hit the schools hardest. When the Fairfax County Board of Supervisors cut their tax rate on Monday, the schools bore the brunt of it. That would happen in a much bigger and harsher way in Alexandria, in the improbable event that Mr. Mann's far larger tax-cut proposal ever went into effect.

No public budget is sacrosanct. But Alexandria has built a fine school system, well adapted to a city in which a geat variety of people live. Cutting the outlays on those schools requires the most careful consideration. Voters who don't like pit-in-a-poke tax schemes will have a chance to make their views felt in the election next Tuesday. The voters will also choose six city councilmen. There we make no recommendations, on grounds that both parties offer unusually strong slates.