Each Sunday afternoon, Danielle Grieshaber, a 17-year-old volunteer, drives four miles to the yellow rambling house in northeastern Montgomery County where 91-year-old Beulah Horne has been confined since she broke her hip in January.

"It's amazing how that girl has helped me," said Horne, smiling broadly and reaching eagerly for Grieshaber's hand. "She reads the Bible to me. She writes letters for me. She has been a wonderful girl."

Horne, who lives with her daughter and son-in-law, is one example of a growing number of dependent elderly people in the Washington area who need and cherish companionship. A companion can help them feel more connected to the outside world and prevent a sense of isolation, which may lead to deterioration and possible institutionalization.

Grieshaber, a Montgomery County high school senior, is among the 36 unpaid teen-age and adult volunteers recruited and trained by Hands of Shared Time (HOST), a new program sponsored by Montgomery General Hospital Inc. to bring some sunshine into the lives of the elderly and make them feel less lonely -- whether they live alone, in nursing homes or with their families.

"By averting isolation, we stand a better chance of keeping elderly people in their homes in the community longer," said HOST director Theadora N. Marcot. "If they are in institutions, we can keep them healthier if we can keep them from being isolated."

In the Washington area, volunteer visitor programs -- long provided by offices on aging, churches, synagogues and other public and private groups -- are becoming more important as the elderly population increases, specialists on aging agree.

Iona House Senior Services operates a visiting program for the elderly living in Northwest Washington west of Rock Creek Park. Fairfax County has a program called Friendship Senior, which recruits and trains volunteers and matches them with dependent elders. These and other programs serve older people of all incomes, including many of limited means.

In Montgomery, the Mental Health Association sponsors Friendly Visitors Pets on Wheels, a venture in which volunteers pack their pets and sometimes their children into the family car to visit an elderly person.

The volunteer programs are especially important for many older people living with relatives, specialists say. Such elderly persons often are confined to one room, face difficulty getting about and may be left alone while their families are at work. Visitors can be helpful and encouraging, officials say.

HOST says it puts considerable emphasis on recruiting young volunteers -- some only 15 years old -- to provide a "truly intergenerational program that benefits people of all ages."

Funded by a $1 million grant from the W.K. Kellogg Foundation of Battle Creek, Mich., HOST is one of the latest additions to the network of volunteer services for the elderly.

"The difference is that we are a storefront; we are in the community and drawing upon the community for support," said Marcot, 45, a registered nurse with a master's degree in gerontological nursing from Georgetown University.

"We not only recruit and train volunteers but we also act as an information and referral source to route the person in need to other services," said Marcot, who conceived the idea for HOST and wrote the grant proposal.

From its headquarters in an Olney shopping center, HOST and its four-person administrative staff operate an aggressive outreach program, serving a 100-square-mile area of northeastern Montgomery. The outreach work includes identifying elderly persons in the community who would benefit from volunteer services along with recruiting volunteers.

Because of work and other pressures, volunteers are not always easy to find. "The attrition rate nationally for volunteers is very high," Marcot said. "So we are trying to keep close to our workers. We had a picnic for them; we have certificates for graduates of the training program, and we have blue HOST T-shirts for them to wear."

In a 12-hour training course, volunteers are shown how to help elderly people by providing companionship, doing shopping and household chores, making reassuring telephone calls during the week and substituting for relatives who normally care for the elderly, to allow them a respite.

Marcot cited Horne and Grieshaber as illustrative of one-on-one relationships that may develop.

"Mrs. Horne is able to talk and express her life and history, and she wants somebody to listen to her," Marcot said. "That is what Danielle does. She is a very good listener. She is very patient. She is very warm, and she will accommodate Mrs. Horne. If Mrs. Horne feels sad, Danielle knows how to respond. If Mrs. Horne is happy, Danielle knows how to be happy."

The one hour that Grieshaber spends each week with Horne is a short enough time to fit into the teen-ager's active schedule and yet is long enough to provide Horne with a special experience, Marcot said.

"Mrs. Horne knows when Danielle will be there, and she knows she has one hour with her," Marcot said. "She asks for nothing more. At the same time, Danielle doesn't feel so overwhelmed with activites in her life that she can't expend the hour. One hour is not as threatening to either of them."

The importance of that one hour was especially evident one recent Sunday when Grieshaber was unable to go for the visit, Marcot said. "Even though Danielle called to say she couldn't come, Mrs. Horne sat and watched the clock, thinking Danielle might show up anyway."

Grieshaber usually drives over to Horne's home after lunch on Sunday, she said. "But I try not to go too soon after lunch," she added, "because if I get there too early and she is still eating, she will send away her tray without finishing her lunch."

Grieshaber is an energetic honors student who plans to study engineering in college. She plays clarinet in the Sherwood High School Marching Warriors band in Sandy Spring and in the Greater Olney Community Band, and she belongs to the National Honor Society and the French Honor Society.

Visiting with Horne gives her a "warm feeling," Grieshaber said. "I can't make her better. I can't change her life. But I am making her day a little brighter, and it helps knowing that."

Horne has three children, six grandchildren and two great-grandchildren. Until 1982, when she had her first stroke, she lived in her own home in Whiteville, N.C., where she was a community correspondent for the Whiteville News Reporter.

"I was a news reporter from 1910 to 1982," Horne said. She said she wrote about "people visiting each other . . . people dying in the community" and other items of local interest.

Horne also was an active volunteer in her community. "When I was about 17, my daddy bought me a gentle little pony," Horne said. "And when someone was sick, I would visit them. I would set a jar of food in the buggy and the pony would pull and I would go off to visit. If I could speak one word to brighten their day, I would do it."

Lucille Rundle, Horne's daughter, said her mother was so active in Whiteville that "we called her the 'Blue Tail Fly' because she was always on the go. Right before her stroke, she and a young man were going around to the old cemeteries in a campaign to get the stones refurbished."

Horne fought her way back from the 1982 stroke, but there have been two more since then. In recent years, she has been unable to read her Bible or to write.

Since her fall in January, Horne has been unable to walk and has lived with her daughter and son-in-law, William Rundle. "We help her get from the bed to her chair, but that is about all she can do," Lucille Rundle said.

Rundle contacted the HOST program to ask for a volunteer visitor for her mother after seeing a HOST pamphlet, she said. "No one should be left in a room all the time," she explained. "I wanted to bring in something for her. They came up with Danielle."