The hallways are dim at Lincoln Junior High School, and terribly battered. Overhead, more than half the ceiling tiles have been punched out and students use the rods that support them for chin-ups. On the walls live electrical wires protrude from outlets which once held thermostats or light switches that have been ripped away.

The school at 16th and Irving Streets NW was opened in November, 1967, less than 10 years ago, but its destruction is so widespread that some members of the District School Board are talking about closing it and converting it to offices.

Where there used to be display cases, there are now massive holes, some patched by wood adorned with graffiti, others just open with pipes and wires exposed.

Almost all the lockers for students clothing and books are broken and unused. On a cold day last week, most students carried their coats from class to class, even though the school was well-heated, because there was no safe place to keep their belongings.

"When they fix things up, they're destroyed again almost right away," said teacher William Francis. "No one can keep up with it."

At Murch Elementary School, a block off upper Connecticut Avenue NW, there has been virtually no damage from vandals, but much of the building is shabby and drab.

It hasn't been painted for almost eight years, and in some rooms paint is peeling so badly that teachers brush it off chalk trays and desks almost every day to make sure children don't eat it.

Outside porch pillars and window frames are cracking, gutters are rusting, and wood trim is exposed to the weather.

Murch was built in 1929 with high ceilings, terrazo floors in the halls, and tile or wood paneling on most of the walls.

"It's much better built than many of the new buildings," said principal Miriam Kaufman. "We keep it clean, but no one is doing the major painting and maintenance."

Throughout the city, many of Washington's public schools are becoming dilapidated as repairs have been put off. Despite soaring costs and steady vandalism, the annual budget for repairs, painting, and major maintenance - now about $5.7 million - has increased only 15 per cent over the past seven years. As a result, the amount of work that can be accomplished has dwindled severely.

At the same time as much of its existing plant has become run down, the school system has carried out the largest building program in its history. In the past five years the District has spent $180 million to build 22 new schools and $80 million on addition and modernization projects, even though school enrollment has dropped by about 24,000.

"It's absurd," said one junior high principal, "to spend so much on big new schools while the ones we have are being allowed to go to seed.A lot of the old buildings were well built. They could really look nice for a modest amount of money."

The explanation for the paradox is that school construction and maintenance come from two different parts of the budget and are financed separatly. School building projects are listed in the city-wide capital improvements budget. They are financed by U.S. Treasury loans, repayable over 30 years, and debt service costs are not included as part of the school budget.

Maintenance and repairs, on the other hand, are part of each year's regular school operating budget that are paid out of current taxes. They must compete for money against other current expense items, the biggest of which are teaching positions and salaries.

School board vice president Carol Schwartz said that over the past few years the board has deliberately held back on maintenance in order to avoid firing any teachers.

One result of this policy last year was the firing of 68 workers in the department of general services, which does major maintenance work for the school system and other city agencies.

"They've saved their teachers," said Sam Starobin, director of the General Services Department, "but they cut my craftsmen, and they're letting the schools deteriorate."

Starobin added that the maintenance and repair problem has been made worse by the new construction because it has added new space to keep up while very few old, under-used schools have been closed.

"It's a question of money," Starobin said, "and everyone is dancing around it. One rather obvious solution is to close down the old schools and make better use of the new ones, but the school board hasn't faced up to that yet."

In early 1976, Starobin said he made an effort to take care of all the work orders the school system was sending him. But he ran out of money, he said, just half-way through the year. When the school board couldn't come up with any more, he laid off workmen and stopped all projects except for patching leaky roofs and taking care of dangerous emergencies, most of which are caused by vandalism, he said.

In one school, McCogney Elementary, at Wheeler Road and Mississippi Avenue SE, the painters left with only part of the building repainted. They never returned.

Starobin said the traditional six-year cycle for painting schools in Washington has been dropped completely. Some schools haven't been painted for more than 10 years.

At Murch Elementary, parents are filling some of the gap by painting chipped doors themselves.

Last fall parents at Eaton Elementary School in Cleveland Park raised about $500 to fix up their school, then, about 200 parents, children, and teachers turned out to do the work themselves on Saturday.

The chairman of the effort was Bardyl Tirana, who later served as cochairman of President Carter's inaugural committee.

"It was the sort of thing that would have taken hundreds of man-hours and thousands of dollars for the school system to do," Tirana said. "But with volunteer labor it really wasn't so hard; it was a lot of fun."

At Syphax Elementary, Half and N Streets SW, Gloria Younger, a second grade teacher, painted her own room last September.

"It was really in such terrible condition," Mrs. Younger said, "that instead of doing my planning (in the few days of preparation before classes started), I did my painting. I did the planning later at home."

In other rooms at Syphax, however, plaster is coming off walls and paint is flaking. Generally, the school looks shabby and drab despite determined efforts to clean it and relatively little vandalism.

But throughout the school system, Starobin said, vandalism is so serious that repairing it consumes about a quarter of the maintenance budget, and severely reduces the funds that should be available for routine work.

"The schools where vandalism is such that it creates safety and security hazards get first attention," Starobin said. "The ones that don't have vandalism suffer deterioration."

"We're being penalized when we keep a building up to snuff," said Betty Brooks, principal of Hyde Elementary School in Georgetown. "And I have a problem with that. To me painting a building is a pretty minimal thing to ask for."

Officials of both the school system and the General Services Department said the destruction at Lincoln Junior High is probably worse than that in any other school in the city, but they said many other junior high schools also have serious damage. The damage in elementary schools and senior highs is generally less.

Usually, the destruction is greatest in schools drawing students from rough, low-income neighborhoods, but a few such schools, for example Kelly Miller Junior High, 49th and Brooks Streets NE., have remained in good condition for years.

In other cases a change in principals has brought about a considerable improvement in a building's condition. James Adams, chief of the school system's branch of repairs and improvements, said that in recent years vandalism has dropped substantially in three junior highs that got new principals: Hart, in Anacostia; Paul, 8th and Oglethorpe Streets NW, and Deal, Fort Drive and Nebraska Avenue NW.

"Schools can turn around," Adams said, "and you can see it in the amount of money spent in repairs. What happens depends a lot on the administration."

How school buildings are designed and what materials they're made of also are important factors in how much vandalism occurs.

Edward G. Winner, the school system's deputy superintendent for management, said that many schools built before World War II can withstand rough use while those built with lower ceilings and cheaper materials in the two decades after the war are more vulnerable.

He said that Lincoln, with its eight-foot ceilings and hundreds of ground floor windows, has become "an object lesson, a very painful lesson, that has taught everyone what not to do." The new schools opening this year, he said, were deliberately designed to reduce vandalism.

For example, the new schools have almost no windows, and the ones they do have are made of unbreakable plastic. (All replacement windows now also are plastic, and last year cost about $600,000.) In most of the buildings, the ceilings are high. Pipes and heating ducts are exposed instead of being hidden by lower ceilings that students can reach and damage.

Instead of having individual classrooms with walls and hallways, all the new schools use an open-space design with large teaching areas that make it difficult for vandals to avoid being seen.

Each new school also has a secure supply room to protect expensive equipment. The rooms are built "almost like a vault," Strobin said, with heavy masonry walls, heavy steel doors, and "super-heavy locks."

In addition, the buildings have elaborate security alarm systems, heavy outside doors, and some iron security grates.

"There's so much defensive designing," said David Huie, an architect who works for the school system, "that some of the public is up in arms about it. They say the new schools look like forts, that they look like jails.

"But these people just disregard the fact that if you used different materials and designed a different way there would be serious problems. I guess there is no happy medium."