Spring showers came early yesterday at Woodbridge High School.

Students and faculty members wondering about the weather didn't need to leave the building; they could glance toward the ceiling for convincing evidence of a warming trend.

A 40-gallon trash can collected water from the leaking roof by the library checkout counter. Elsewhere, water dripped into hallways, classrooms, the auditorium, even onto students in the cafeteria lunch line.

Woodbridge's leaking roof was among the school facilities that would have been renovated under an $8.4 million initiative that was thwarted Tuesday by the Prince William Board of County Supervisors.

The supervisors -- citing the need for more control over a spending process that they said has been governed too often by whimsy rather than careful planning -- rejected the county School Board's request to seek bonds from the Virginia Public School Authority to pay for roof repairs at Woodbridge and air conditioning at several other schools.

Melted snow in the hallways of Woodbridge is only the latest and most vivid example of the needs in a county where the ability to pay for them is sharply constrained, according to county officials.

Prince William's 39,100-student school system, the county parks authority, and the other agencies funded through the county government have "capital improvement" programs -- long-range estimates of the new facilities they will need -- that total more than $600 million, according to county budget officials. But the county's financial experts say the county prudently can absorb only about $150 million in bond debt to pay for the projects.

That disparity portends that conflicts of the sort at Tuesday's supervisor meeting may become common in Prince William, some county officials predicted yesterday.

After the county board rebuffed the school system's request Tuesday, board Chairman Kathleen K. Seefeldt (D-Occoquan) and other members of that board said they weren't opposed to the requests, but the board could no longer tolerate the idea of funding them outside the county's planning process conducted annually in February. Seefeldt said spending decisions in Prince William often have been made in a haphazard fashion, whenever new needs arose. But, she said, those methods are no longer acceptable.

"We've been trying for years" to conduct more careful fiscal planning, Seefeldt said.

Because the supervisors rejected the improvements on Tuesday, they will miss a Jan. 19 deadline to finance the renovations through state bonds this year. Nonetheless, Prince William officials said the most urgent items in the $8.4 million spending proposal will likely be funded through the county operating budget to be passed this spring.

"I feel we must take some emergency action on the roof," Supervisor Hilda Barg (D-Woodbridge) said as she toured the high school yesterday. "What I don't understand is why it got into this condition."

Edwin C. King, a Dumfries Democrat and the only supervisor who supported the school system's request, said he was suspicious of the reasoning offered by his colleagues. The supervisors themselves have been "perfectly willing" to spend money outside the capital improvements progam when it fit their purposes, he said, most recently when they approved $3.4 million in new county debt to pay for expansion of Prince William's sanitary landfill.

"It seems to me that consistency is in order," King said, noting that the School Board's proposals for spending "seem to be much more popular with voters than" the board of supervisors'. "Maybe we ought to learn something from them."