The Barry administration has taken another swing at the D.C. school system with its budget-cutting tax, formally notifying the schools that they will have $6 million less to spend in fiscal 1982 than in 1981.

Because of inflation, the loss in buying power to the school system would be much greater than that, and school officials say that as many as 260 more staff positions may have to be eliminated.

Budget director Gladys Mack, in a letter to school board president R. Calvin Lockridge, said the schools will be allocated $238.2 million in operating funds for the 1982 fiscal year, which begins Oct. 1, 1981, down from the $244.5 million budget for fiscal 1981.

The proposed cut for 1982 would give the schools $42 million less than they would need to keep programs and staffs at the level they were last September, before the city's financial plight was uncovered and cuts ordered.

Those have included eliminating 1,038 staff positions, including 714 teaching jobs, and scrapping programs deemed less important, such as driver's education.

The school system's original request for 1981 was for $252 million, a figure that Barry sent to Congress but that went by the boards months ago as the city's fiscal plight became known. It would have been nearly $280 million for 1982 to keep all programs and staffs at their levels of last September -- $42 million more than now proposed.

In her letter, Mack said that "the mayor has always demonstrated his unyielding commitment to public education," which is why he put the schools in the "first priority" group of agencies to receive 1982 funds. Despite the smaller budget, she said, "the declining school population provides an opportunity to minimize" the impact. Mack said she thinks that the proposed 1982 budget will enable the schools to "maintain the current pupil-teacher ratio, meet special education needs and make necessary purchases of supplies, books and equipment."

The allocation was based on the assumption that enrollments will decline by 6,600 pupils in the 1981-82 school year, to about 92,000, and that "a number of school buildings" will be closed.

Ransellear Shorter Jr., associate superintendent of schools for management services, said yesterday that despite the projected drop in enrollment, the cutbacks "will make major inroads in some of our programs." He said that uncontrollable costs, such as those for energy and food, are going up faster than expenses can be trimmed without hurting classroom programs.

As Mack prepares the city's proposed 1982 budget, which Barry must submit to the City Council next month, she is assigning to each department a "mark," or maximum amount it can expect to receive out of the city's total $1.52 billion budget.

If services were maintained at their current levels, she said, expenditures for 1982 would exceed those revenues by about 10 percent, which the mayor will not permit.

"The mayor directed my office to bring in a balanced budget," she said. "He directed that the projected gap of nearly 10 percent between revenues and expenditures be closed without a tax increase."

Of the $1.52 billion expected to be available, she said, nearly 40 percent is obligated to fixed costs, such as Metro subsidies, pensions, debt service and welfare payments, and cannot be trimmed. That leaves $927 million to pay for everything else, she said, and "first priority" has been assigned to education, health and public safety.