One of Washington's oldest musical traditions is about to end -- those long lines of stalwart music lovers that form on downtown sidewalks Monday mornings to pay 25 cents for the week's Library of Congress concerts. The lines have been forming for 60 years.

Starting in September, the library announced yesterday, tickets will be reserved only by phone (287-5502), thus sparing listeners the experience of standing out in sometimes wintry blasts to be able to hear, for instance, the Budapest String Quartet, or its successor as the library's resident ensemble, the Juilliard String Quartet.

And the events, which are among the most prestigious chamber concerts in the world, will become an even bigger bargain. They will be free.

For years the distribution point was the box office of the Campbell Music Co. -- succeeded by Jordan-Kitt's. For most of those years, the ticket service was run as a public service by impresario Patrick Hayes, now the director emeritus of the Washington Performing Arts Society. (There's not much money to be made selling 25-cent tickets to the 500-seat Coolidge Auditorium.)

In a 1982 article for The Quarterly Journal of the Library of Congress, Hayes described the ticket ritual: "No line is so unusual and consistent . . . It forms over 30 times a year. . . . One morning last spring the first man in the line arrived at 6:15 a.m. for the 8:30 start of the sale. He knew what he wanted -- a particular seat for a Juilliard String Quartet concert. He got it."

Hayes wrote that "both method and price were established when the concerts began in 1925, which makes the 25-cent charge a classic case of price control and inflation restraint. For the patrons it is a trade of their time and patience for the luxury of attending a fine chamber music concert for a quarter."

There has been no more loyal musical audience here over the years than the library crowd.

Hayes tells the story of Mr. and Mrs. George Papas, who met in the line. "They asked for tickets together, and for over 20 years have sat in seats D-107 and D-108, dead center fourth row. After the first several Mondays of their acquaintance, Mr. Papas gallantly spared his companion the chore and he got their two tickets."

In recent years the library has accepted some phone reservations, but being in the line was still the surest way of getting the right seat.

The decision to go entirely to phone reservations "has been under consideration for some time," Nancy Bush, the head of the library's information office, said yesterday.

"It will be more of a convenience to concert-goers."

Under the new system, reservations for most concerts can be made by calling on the previous Saturday, between 11 a.m. and 1 p.m. Exceptions will be made for individual concerts (Juilliard Quartet concerts are repeated, on Thursdays and Fridays) and for the Saturday series. In those cases reservations will be made on the preceding Monday, starting at 9:30 a.m.

There will be a limit of two tickets per call, and they can be picked up at the door of the Coolidge Auditorium, one hour before concert time.