Extreme weather means expensive headaches for Prince William County school officials. When it rains, it pours through Woodbridge High School's leaky roof. When it swelters, students in western county schools complain about the lack of air conditioning.

The schools estimate it would cost $6.52 million to solve the two problems. That, combined with the nearly $2 million more needed for maintenance, will be the focus of discussion Tuesday when School Board members and county supervisors meet to review the schools' request for $8.4 million in Virginia Public School Authority bonds.

Early reaction by members of the new Board of County Supervisors has been generally positive but cautious. New members said they weren't yet familiar enough with details of the needs to comment. Incumbents said they needed more information.

"I haven't discussed this with anyone on the new board," said Edwin C. King (D-Dumfries). "My initial concern is that we have some kind of phased program."

"We're looking at rather massive maintenance problems," said Kathleen K. Seefeldt (D-Occoquan). "Philosophically, I don't have any problems with the request."

Seefeldt said she would reserve judgment until the county finance office provides a full staff report on the costs of paying off the bonds. Although school authority bonds are sold by the state, each locality must pay its own debts.

If approved by the supervisors, more than half of the school authority bond request -- $5.02 million -- would go toward air-conditioning schools in the western part of the county: Coles, Nokesville, Sinclair, Tyler and Yorkshire elementary schools, Brentsville High School and Woodbine special education facility.

Air conditioning was installed in most of the county's eastern schools a decade ago when crowding forced year-round schooling on the county. Since then, air-conditioning the western schools has been discussed but little has been done to accomplish it.

West county parents who worked for last fall's $44.89 million bond referendums, which will build schools in the eastern portion of the county, say that fairness necessitates air-conditioning the schools serving their end of the county.

The other big item on the school authority bond list is $1.2 million to repair the roof at Woodbridge High School. The roof, which has been a problem since last spring, has so many leaks that on rainy days the auditorium is unusable, according to principal Tom Gaul. He said that there also are major leaks in the cafeteria, the library, classrooms and hallways.

"I think we have a critical situation over there," School Board member Ilona Salmon told her colleagues at a December board meeting. "That building is used a great deal by the community. It's really an embarrassment. One parent suggested that we raise money by selling umbrellas."

Other items on the school authority bond list are: renovation of the Dumfries elementary school heating system and removal of asbestos, $511,000; repairs to roofs at Tyler and Nokesville elementary schools and Brentsville High School, $300,000; a new heating and air-conditioning system in Woodbridge Middle School, $900,000, and expansion of classroom space at Potomac View, Vaughan, Loch Lomond and Featherstone elementary schools, $317,000.

School Board Chairman Gerard Cleary said he hopes that next week's meeting will be useful to both boards. "I'd like to get away from the same old song and dance we've been doing for years," he said.

Cleary said he also wants the two boards to discuss the six-year plan for improving instruction in county schools presented last month by Superintendent Edward L. Kelly as well as a long-range capital improvements plan for fiscal 1989-94.

"We need to lay our cards on the table. Say these are our needs, what can we expect from you . . . . They need to know the impact all of this will have on the tax rate," said Cleary.

Debt service on the $8.4 million school authority bonds would translate to 1.25 cents added to the property tax rate in the next fiscal year, according to Tucker.

Deadline for county approval of the school authority bonds and paper work is Jan. 19.