For four years, Eunice Graham has risen at 5:30 every Wednesday morning and spent a couple of hours at the D.C. Jail before going to her job as a secretary in a prestigious downtown law firm.

Seated in a glass booth on the third floor of the jail, she faces a stream of sleepy-eyed inmates arrested over the previous 24 hours, who ask her to fulfill obligations left dangling by their incarceration.

Graham is one of 100 volunteers who assist a District agency, the Visitors' Services Center, which helps the newly jailed, usually by telephoning relatives, girlfriends or employers to inform them of the men's whereabouts. Occasionally, odd requests to locate false teeth, feed dogs and make funeral arrangements are handled by paid VSC staff members.

VSC was created in the late 1960s by several chaplains at the old D.C. Jail who were swamped with small but urgent requests from inmates. The jail staff was too busy to respond to those needs, so the chaplains sought volunteers. Today, the volunteers answer more than 12,000 inmate requests annually.

The volunteers include clergymen, attorneys, housewives, teachers and students from colleges nationwide that offer academic credit for work with VSC. They include people with a variety of views on imprisonment and capital punishment.

"One reason I think we've been so successful in recruiting volunteers, as well as getting support from the prison administration, is because we aren't an advocacy program," VSC director Ann Cunningham said. "We offer simple social services."

"I don't have a terribly sympathetic view of prisoners," said Graham, who joined VSC six years ago. "But there is something helpless about them."

VSC has two components: intake and casework. Graham works with intake, which is operated Tuesday through Friday, from 7:30 a.m. until each new inmate who has a request is seen and the volunteer has made the requested telephone calls, and Saturday from 10 a.m. to 1 p.m.

Casework volunteers, at the jail from 4 to 7:30 p.m. Monday through Saturday, allow inmates to make calls up to five minutes long while they monitor the conversations.

On a recent Wednesday, Graham sat on one side of a table, dressed in a gray wool suit with a paisley scarf at her neck, while one inmate after another in wrinkled blue jumpsuits sat down opposite her to ask for help.

"This is a pretty shabby list," she said, commenting on the small, petty charges of the men, detailed on a paper given to her by correction officers. "Tampering with an automobile . . . second-degree burglary . . . failure to pay child support."

Her requests this day, include calling a Baltimore man's wife to notify her that he is in jail, calling a girlfriend to tell her to visit her boyfriend who escaped from work release, and informing one young man's parents that he has run away from his halfway house and is in jail.

The latter kind of call is the most difficult for the volunteers to make, said Dwight Datcher, a paid VSC staff member, a former assistant basketball coach at Georgetown University who directs the intake program.

"Sometimes you get a parent who doesn't know that the son is in jail," Datcher said. "You might get one crying and asking you for all kinds of information."

A VSC volunteer for six years, Graham has done casework follow-ups, helped raise money and even written articles about the program. Now she is filling out tax forms for the inmates, too.

The program's student intern, Betty Gatewood, 22, a senior social work major at Longwood College in Farmville, Va., does casework, writing letters for inmates, picking up property and taking a telephone into the jail afternoons so inmates can make calls.

"I thought I was going to be nervous and upset when I visited jail for the first time," said Gatewood. "Instead, I was real comfortable. . . . Sometimes, though, I would hear stories that were unbelievably tragic. I would take everybody's problems home with me. I'm getting better at that now."

At the VSC office, a weathered row house at 1422 Massachusetts Ave. SE, Billy Chandler, who has been with the organization since its early days 14 years ago, checks over a stack of recent inmate requests.

"You name it, I've done it," said Chandler, 44, a native Washingtonian with thinning hair and a calm demeanor. "Now I open savings accounts for prisoners and I pick up personal property they leave at the precinct."

"One of my first cases was to go and fetch a guy's false teeth," Chandler recalled. "He had left them at the precinct. In another case a man left his dog in the house. The man was sentenced to 30 days, so we kept the dog here in the basement until he got out.

"We've arranged funerals for guys who have had their last relative die while they're incarcerated. The guy is inside and doesn't know how to handle it. We arranged for one guy to visit his wife and newborn baby in the hospital. Residents look at us as their only hope."

"Visitor's Services Center is the most outstanding volunteer organization in town," D.C. Jail Superintendent George E. Holland said without hesitation. "They do a tremendous job for us. They really serve almost as a staff support unit. . . . The work they do lifts a tremendous burden off my staff."