They have worked for 4 1/2 months, operating out of a Holiday Inn in Manassas, piecing together the life of Virginia State Trooper Johnny Rush Bowman in minute and intensely personal detail.

The investigators can speak in depth about the unassuming, 31-year-old law officer, his personality and upbringing. They know about his work habits, his telephone calls, his daily routine.

They know intimate facts about his wife, about hundreds of his neighbors, his friends, his wife's friends, his relatives and his acquaintances.

"I feel like I know just about as much about him as maybe anybody else does -- maybe even his wife," says Darrel E. Stilwell, one of the investigators.

There is little Stilwell and the other 17 state investigators assigned to the case do not know about Bowman -- except who killed him before dawn on Aug. 19, and why.

More than four months after Bowman was attacked and stabbed 42 times on the threshold of his Manassas town house, there has been no arrest, and police investigators -- even those who hold passionately to one theory or another in the case -- acknowledge that the motive for the killing remains a mystery.

Investigators say the case will not be closed until it is solved, but they concede they are baffled by key elements of the crime.

And they say the likelihood of an arrest dwindles with time.

"You cannot go home and leave this case," said Robert C. Martin, the 28-year veteran of the Virginia force who is heading the investigation. "I think about it constantly. I even dream about it -- about various people who we're working on."

The slaying of the trooper has touched off one of the most extensive and costly murder investigations in the history of the Virginia State Police, which has never let the killing of one of its troopers go unsolved.

Eighteen hand-picked special agents from the force -- nearly 20 percent of all the agency's nonnarcotics investigators -- remain assigned to the Bowman case full-time, working 12-hour shifts daily. Until a few days before Christmas, the state police investigators working on the Bowman case had their own headquarters, manned 24 hours a day, in four adjacent rooms of the Manassas Holiday Inn. The weekly motel bill: $1,092.

The reward for information leading to the arrest of a suspect in the Bowman case is more than $26,000 -- one of the largest incentives the investigators can remember in a recent murder in the state.

More than 3,000 people in 41 states have been interviewed by police, some of them repeatedly. More than 1,600 leads have been checked. Thousands of pages of documents and notes have been collected, analyzed and computerized, and police have developed an elaborate cataloging system, practically a small library, to keep track of the sheer mass of information.

"If you just take the time to look at the pictures of the mutilated body of Johnny Bowman," said special agent Ralph Marshall, reaching into a file for photos of the victim at the morgue, "that alone will give you the drive and the determination to say to yourself, 'Well, this person who did this should be taken out of society for quite a while, for the protection of all men.' "

Bowman received stab wounds all over his upper body. Police say the first blow to Bowman's chest punctured the pulmonary artery. But the wounds were also in the neck, the face, the stomach, a shoulder. A large number of the wounds were bunched together on one side of his back, where, police say, the killer, in a frenzy, stabbed Bowman repeatedly after he had fallen to the ground in a fetal position.

"I'd never seen anything like that," said Martin. "I don't know that any of us have."

The police account of Bowman's murder, much of it based on interviews with the trooper's wife, Terri Lee, has not changed significantly since the crime.

About 4:15 a.m. on a Sunday, Bowman was awakened by the doorbell ringing repeatedly at his town house at 8988 Patterson Place in the Bristoe Station subdivision of Manassas. Parked directly in front of the town house front door was Bowman's state police car: There was no mistaking who lived at that address. Bowman came downstairs wearing Adidas athletic shorts, a T-shirt and sneakers.

As Bowman unlocked the door, the killer used an obscenity and said, "I'm from the power company." He then began a three-minute attack, stabbing Bowman with what police think is a folding knife with a four-inch blade. The knife has not been found.

"You want to know what it was like?" said W.T. Poindexter, an investigator who photographed the scene. "If you can imagine being able to take pure, unadulterated rage out of a paper bag and throw it into a four- or five-foot-square area and locking the door for five minutes -- that's what the scene was like. That's what stays with me to this day."

During the attack, Terri Bowman came within several feet of her husband on her way to the telephone, from which she twice called the 911 emergency number, telling Manassas police that her husband was being assaulted. She said later it was too dark to see the killer.

Bowman's brother, Bobby, who with his wife was staying for the weekend at the town house, told police he came to the head of the stairs, saw the killer leaving the house and chased him. He told police they grappled briefly and that the killer was a large black man. Police later said that other evidence suggests the killer was a white man.

The killer appears to have fled on foot; police found large-sized bloody shoeprints leading across the parking lot in front of the town house and veering left onto the sidewalk across the street.

The key items of evidence found at the scene are a plastic construction hard hat, a cheap brown curly wig and a pair of nonprescription, tinted sunglasses -- all believed to have been worn as a disguise by the killer. Although hairs were recovered from the wig and police have traced the hard hat to a Army-Navy surplus store in Baltimore, the three items have not yielded major breaks in the case, police say.

The crime was extraordinary in a number of ways, according to investigators, and aspects of it have generated a number of theories about the case.

The fury of the killing is frequently a characteristic of a homosexual killing or a dispute touched off by a sudden rage, the investigators say. They add, however, there is no evidence to support either scenario in the case.

Police have also theorized that the extreme violence of the killing may have been induced by drugs, possibly PCP, or that the crime may have been committed by a mentally deranged person, perhaps a schizophrenic, who may not have realized what he had done.

Some investigators also theorize that the killer may have feared that Bowman knew some bit of information about him that could prove harmful.

Most investigators, citing the disguise worn by the killer and the hour of the attack, say they believe the crime was planned carefully. And while some say it is likely the killer knew Bowman, all agree it is possible that the murder was random.

The variety of theories and the absence of a known motive have led to an investigation that some officers say is unnecessarily broad.

Police are questioning every person who received a summons from Bowman -- even those who received speeding tickets -- in the last 20 months of his life. Because Bowman was assigned to highway duty and worked mostly on interstates 95 and 66, that means the motorists he stopped live all over the country.

The Virginia State Police have interviewed people in 13 states. In another 28 states, local police agencies are tracking down men and women who were stopped by Bowman.

There are other, more promising leads, most of which police will not discuss. Martin says there are a number of people -- he declines to call them "suspects" -- who "we are looking at closely." Several people have been interviewed repeatedly; hair samples and fingerprints have been taken and analyzed by the FBI; polygraph tests have been administered. Bowman's wife, the only witness to the fatal stabbing, has been interviewed scores of times.

Police have reconstructed Bowman's hour-to-hour activities during his last two weeks, plotting each day on a separate sheet along with a map depicting his movements. The schedule was drawn up to determine if Bowman had some peculiar routine, but police concluded that he did not.

In fact, one of the things that has plagued investigators is what they describe as Bowman's ordinariness. They say he was a polite, well-liked homebody with few friends outside the state police, where he had worked since 1979.

He was born and raised in southwest Virginia's rural Pulaski County and entered the Marine Corps for five years after graduating from Dublin High School in 1971 and briefly attending a community college.

"At this point, I can say that from all outward appearances, from all that we've learned, there's just no reason for Johnny Bowman to have been killed," investigation leader Martin said. "He was a good trooper and a good husband and a good father. He wasn't a ball of fire, but he was a steady worker. . . . There was no one who said he was rude or abrasive or arrogant. That may seem kind of incongruous considering what happened to him."

The pace and character of the investigation have changed substantially since August, when 26 special agents were assigned full-time to the case, in addition to a dozen officers from the Manassas city police force.

The number of telephone calls to police -- prompted by a reward "most people would turn their mother in for," according to one investigator -- has slowed to a trickle. Although a number of the tips were less than credible -- one caller said Bowman had been murdered because he probably murdered someone in a previous life -- nearly all were pursued, police said.

The product of 4 1/2 months' work is more than 30 thick volumes of typed notes from the interviews police have conducted, several computer floppy disks full of data, more than 10,000 pages of documents -- and a team of frustrated detectives.

"There is not a thing that we have not looked at," said Marshall, the number two man in the investigation. "And we have tried to look at it from every conceivable angle. And we will continue to do that. We don't give up on a case like this."

Top officials of the Virginia State Police in Richmond echo Marshall's statement, stressing that the case will be open until solved. The cost, estimated at well over $100,000, is irrelevant, they say. They point to the threat posed to society by a man who kills a state trooper, a man of the law. They say he must be caught, that he may kill again.

William Hamblen, a Prince William County prosecutor, expresses reservations. "I think that you could do all that's humanly possible and not solve this case," he said. "That's the kind of case it is."