Patricia Edwards stood in a line 15 people deep that snaked away from the library check-out counter and around a corner pillar leading to the periodicals rack of the Potomac Branch Library in Woodbridge.

She clutched an armful of books and wore a forlorn expression. "This is less crowded than usual for a Sunday, believe it or not," she said, surveying the knots of kids sitting cross-legged on the floor and the crowd of people clustered at the information desk a week ago. "Maybe it's because the Redskins game is on television."

The scene was a familiar one in Prince William County, where the expansion of library facilities has not kept pace with one of the sharpest population booms in the country during the past 20 years. The county has grown from 50,000 in 1960 to approximately 165,000, but no library space has been added in a decade, and the number of library books per resident remains below the average for public library systems in communities with more than 100,000 people, according to a national study.

Patrons of Prince William's two public libraries are paying the price: jammed parking lots, study areas with no free seats and check-out lines where patrons often wait up to 45 minutes.

The problem is compounded by the county's dispersed population, large number of school-aged youths and a modest collection of books, according to library officials.

In March 1982 county voters rejected at referendum a bond issue that would have financed two new libraries -- one in the eastern part of Prince William, and one in the west. The $5.3 million bond issue, which came before voters at the height of the recession, was seen as unaffordable, county officials say.

"People tell me that they've been able to read a couple of chapters of their books while waiting in line here," said Cathy Chang, the co-administrator of the Potomac Branch library, where the crowds are particularly heavy and the parking lot sometimes is full before the library doors open on weekends.

"You have to want a book pretty bad to stand in line for 30 minutes," Edwards said.

A half-dozen mini-libraries -- storefront lending facilities that display paperbacks as a bookstore does -- are scheduled to open beginning in January 1985, but they are considered stopgaps. Although chief librarian Mary Jo Detweiler said she expects the mini-libraries to take some of the pressure off the Potomac Branch and add about 90,000 new books to the system's collection (currently at about 250,000 volumes), she says they will not address the shortages of research and study space.

"I don't expect the minis to be enough to forgo the construction of a full-service facility," said Detweiler. "By any standards what we have now is hopelessly inadequate."

With only two branches -- the one in Woodbridge, the other near Manassas Park -- Prince William's library system compares poorly with those of comparably sized jurisdictions. In Arlington County, which has a slightly smaller population than Prince William in less than one-tenth the area, there are seven public libraries. In HenricoCounty, which adjoins Richmond, there are six outlets and a bookmobile in an area about two-thirds the size of Prince William.

Detweiler says thickly populated eastern Prince William needs three times the library space provided by the Potomac Branch, and she has recommended that a branch be built by 1990 near the new county administration center on Davis-Ford Road at a cost of $3.5 million. The new library may be included in an omnibus bond referendum tentatively set to be placed on the ballot in 1986.

In the meantime, the complaints about crowding and noise at the Potomac Branch are growing more frequent as circulation and door counts continue to rise. Library administrators and workers are bracing themselves for the winter crunch -- the peak season for library use -- from February to April.

"A lot of people are still under the assumption that libraries should be silent places," Chang said. "But when we get enough bodies in here the noise escalates, especially with all the kids. And there's not a lot you can do about that."

The first of six planned mini-libraries was scheduled to open in Lake Ridge this month, but it has been delayed until January because of construction snags at Tackett's Mill, a Williamsburg-style development where the facility will be located.

Another mini-library is scheduled to open in March in Dumfries. Four others are scheduled for Nokesville (fall of 1985), Dale City (early 1986), Independent Hill (1987) and Haymarket-Gainesville (1987). They are likely to remain part of the county library system even after a third branch is built.

The mini-libraries will cost $150,000 apiece to stock with books and equipment, according to Detweiler, and another $100,000 each to operate each year. They will have current paperback popular books for adults as well as children's books in hard cover.

Although the worst congestion is now concentrated at the Potomac Branch, officials say they expect the problem to spread westward in the coming years to the Central Library near Manassas Park.

"In a few years we'll have kids sitting on the floor here on a Tuesday night in January," said Detweiler. "It'll be just like at Potomac, where that's routine now. The crowds will just be taken for granted."