When the Robert H. Gneiser family moves into the contemporary, split-level house at 8103 Lilly Stone Dr. next month, their neighbors are hoping the event will remove the specter that has haunted the Carderock Springs development in West Bethesda for the last year.

The Gneisers are buying the home that was the scene of the murders of five members of the family of William Bradford Bishop Jr. last March 1. Bishop’s mother, wife and three sons were beaten to death there, and there has been no trace of Bishop, the former State Department Foreign Service officer who is charged with the killings.

After a year of following leads from Bethesda to Botswana and hundreds of places in between, police are as baffled about Bishop’s fate as they are about a motive for the killings.

“I think he’s alive,” said Maj., Wayne Brown, director of the criminal investigation division of the Montgomery County Police Department. Brown said he is “hopeful he (Bishop) will make a mistake so we can get him back here and see what makes him tick.”

“I have a strong feeling he’s dead” said George Quinn, special agent in charge of the Baltimore field office of the Federal Bureau of Investigation. But, Quinn added, speculation is ‘a luxury we don’t indulge in. So we assume he’s alive in the absence of any other indication.”

The uncertainty of whether Bishop is dead of alive extends to the tangled legal process that occurred in the absence of heirs.

The victims were Bishop’s mother, Lobelia, 68; his wife, Annette, 37; his sons, Brad III, 14, Brent, 10, and Geoffrey, 5.

According to terms of a will Lobelia Bishop executed in 1961, her only child, William Bradford Bishop Jr., inherited all of her estate. Neither Annette Bishop nor her sons left a will.

Brad Bishop has no close surviving relatives. Robert Wels, Annette’s brother, said in a telephone interview from his home in La Habra, Calif., that an exhaustive search had discovered just three “distant” cousins, living in San Francisco, San Diego and Paris.

Annette Bishop’s estate goes to her parents, Gilbert and Eunice Wels of San Clemente, Calif., and her brother, Robert.

In the absence of relatives on Bishop’s side of the family, Robert Wels was named receiver of his brother-in-law’s property.

Acting in that capacity, Wels authorized the sale of Bishop’s motorcycle and the family’s rust-colored, 1974 Chevrolet station wagon. The latter vehicle was the object of a nationwide search before it was located last March 18 at a resort campsite deep in the Great Smoky National Park on the North Carolina Tennessee border.

To protect the Gneisers from a possible claim sometime in the future by Bishop or his heirs, the title company they employed in the purchase of the house insisted that a guardian, who has greater legal authority than a receiver, be named in Bishop’s behalf.

To carry out that formality, Bethesda attorney Charles H. Burton made application Friday for Wels to be also named the guardian. To fulfill the notification requirements, a legal advertisement will be published the next three Thursdays in the weekly Montgomery County Sentinel.

The ad, in effect, will notify Brad Bishop that if he has any objection to the sale of his half-share in the house, he better come forward immediately.

Barring that unlikely possibility, the Gneisers then will be able to complete the transaction that has been delayed by the complex legal technicalities since they signed a contract to buy the house last November.

The last confirmed contact with Bishop occurred last March 2, when he used BankAmericard, his only credit card, to purchase $15.50 worth of sporting goods in Jacksonville, N.C., about 100 miles south of Tyrrell County, N.C., where the bodies were discovered earlier that day.

A forest ranger, patrolling the swampy forest near the hamlet of Columbia, N.C., spotted the bodies, which had been set afire, about noon. But it was almost a week before the charred remains were connected to the Bishop family, whose absence from home was attributed by friends to a spring skiing trip that the close-knit, athletic family had planned.

Bishop, a highly regarded, $26,000-a-year career Foreign Service officer, had left his office at the State Department unusually early on March 1, complaining a cold.

Police later determined that Bishop drove from his Foggy Bottom office to Montgomery Mall, where he bought a five-gallon gasoline can at Sears and had it filled at the Texaco station there.

Investigators also have concluded that the first victim was his wife, Annette, who was slain in the den. They theorize that Bishop’s mother, who lived with the family, returned from walking the family dog and surprised the killer, who hurriedly placed one of Brad Bishop’s jackets over Annette’s body. After the two women were fatally bludgeoned, the three boys, who were wearing pajamas and apparently were asleep in upstairs bedrooms, were then killed by a powerful blows to their heads.

The killer then stuffed the bodies in the family’s station wagon and drove through the night to North Carolina, where the bodies were dumped into a bathtub-size grave and set afire.

The station wagon, which was found more than two weeks later, contained a blood-stained blanket, an ax and a shotgun. A massive search of the park, from the air and on foot, followed discovery of the station wagon. But except for some early false reports, there was no trace of Bishop, or the family’s missing golden retriever, Leo.

In the intervening year, police have found no rational motive for the murders: No evidence of infidelity, or financial or job problems. The Bishops, friends and associates insisted, were the archetypical All-American family, blessed with beauty brains and togetherness.

The lone imperfection investigators uncovered was that Bishop had consulted three psychiatrists in recent years, and that he had been taking the prescription drug Serax to treat symptoms of depression and insomnia. A quantity of Serax was found in the glove compartment of the station wagon.

“When he stepped out of that car,” said the FBI’s Quinn, “the trail ended.”

North Carolina Attorney general Rufus Edmisten, who directed the hunt for Bishop in that state, said last week that Bishop’s disappearance is “the most baffling mystery I’ve ever encountered.”

Edminsten, the former deputy counsel to the Watergate committee, discounted the possibility that Bishop, an experienced outdoorsman, wandered off into the park and met his death.

Jack Linahan, assistant chief ranger of the Great Smoky park, said “the number of people who utilize the park” make it unlikely that a body could go unreported “visually or by one of the other senses.”

As a State Department employee, Bishop was stationed in Ethiopia, Botswana and Italy and earlier was with Army intelligence in Italy. He speaks Italian and Serbo-Croation fluently, and in addition to his undergraduate degree from Yale, heared tow master’s degrees, in Italian from Middlebury College and African Studies from UCLA. With his education, language abilities and diplomatic credentials, investigators agree that Bishop could get along relatively well in a foreign land.

At least one of Bishop’s former neighbors said she would “like to see more investigation of Brad’s involvement in intelligence activities.”

“That’s more vital than what has happened to the neighborhood,” he woman said. Neighbors are just recovering from two violent crimes that stunned their upper-middle-class subdivision last March. Less than a month after the Bishop slayings, two county police officers were shot to death while chasing a robbery suspect.

Last August, Robert Daly Angell, 19, who lived a couple of blocks from the Bishops, was convicted of those murders.

When Carolyn Gneiser was shown the Bishops’ house last November, neither she nor her real estate agent, owned it, although the Gneisers were vaguely aware that both Bishop and Angell had lived in the area.

“I fell in love with the house,” Mrs. Gneiser recalled. Her husband, WMAL/radio anchorman Bob Gneiser, inspected it a few days later and agreed that it was just what they were seeking. It had an addition that would be perfect for Mrs. Gneiser’s mother, who was moving from Florida to become part of their extended family.

“We talked it out,” and decided to make the move, Gneiser said, “although frankly, we renegotiated (the price) a little bit” after learning from Mrs. Kate that the house had belonged to the bishops.

The Gneisers apparently got a good deal, financially. They paid $106,000, while the house next door, which is identical except that it does not have a extra suite, sold recently for $113,000.

Another broker, unaware the house was the Bishops’ until she entered with a prospect and saw that parts of the carpeting had been cut away for evidence, reportedly gasped and ran from the house.

“The new family will help a lot,” said Alvina Long, who lives down the street. Mrs. Long, who was a tennis partner of Annette Bishop, and whose husband was a classmate of Bishop at Yale, said she was anxious to see “new life in the house.”

Gneiser is as anxious as anyone for the lovely neighborhood to recapture its former anonymity, but he also understands the macabre curiosity seekers who still drive by - and, according to the new people next door, steal wood from the side of the house.

“When someone asks me about living in the Bishop house,” he jested, “I tell, them I’m selling glossy prints of it for $25” to help with the mortgage.

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