What stands out in piercing poignance is the innocent way in which they were going about their daily routines when suddenly, without warning or provocation, they were murdered.

The assistant engineer in a Buffalo plant was grabbing lunch at a Burger King when a man walked up to him and shot him in the head. The two teen-aged boys in Cincinnati were heading to a store to buy sodas when they were gunned down. The two black youths in Salt Lake City were jogging with two white girls through Liberty Park when the boys were slain in a sniper's ambush.

They were among 24 black Americans and two white women who were with black men at the time who have been slain in a string of murders in seven cities across the nation over the last 15 months.

Federal and local law enforcement authorities have been bewildered by the apparent random choice of victims. They have met twice in the last month to swap leads and trade information, but FBI Director William H. Webster said investigators have no substantial evidence linkng the murders.

A bureau spokesman said, nonetheless, that there are common threads: the tendency for black males to be the victims, the use of high-powered rifles in several of the shootings and the viciousness with which the crimes were carried out.

"This is the first time that we have had this type of thing on this level," said the spokesman, agent Otis Cox. "We're looking for either one person or a group of persons with the same types of things in mind."

Thomas Atkins, general counsel of the NAACP, said his organization wants to know "whether or not there is some secret and organized effort being made to foment racial strife."

Webster told reporters in Atlanta late last week that he understood that many blacks believe a nationwide conspiracy is at work. "I think it's a natural temptation born of legitimate fright that a national conspiracy is under way," he said. But, he said, the evidence does not support such a theory.

Authorities in Buffalo and Atlanta say they believe the waves of killings in their cities are unique.

The 10 victims in Atlanta were all children, nine boys and one girl, ages 8 to 15, from poor families living in rundown neighborhoods or government housing projects. Four other children -- a girl and three boys -- are missing.

The children have been disappearing at almost 3 1/2-week intervals over the last 15 months, their bodies found later with marks indicating they were strangled, stabbed or shot. Atlanta authorities say they have no solid evidence on the race or identity of the murderer or murderers.

In Buffalo, the same semi-automatic .22 cal. weapon was used in a bloody 36-hour period to kill a black teen-aged boy and three black men. On successive days, two weeks later, the battered bodies of two other victims, both black and both cab drivers, were found on remote roads in the Buffalo suburbs. Their chests had been crudely opened and their hearts cut out.

The next day a black Attica inmate -- in a Buffalo hospital after taking an overdose of barbituates -- got a look at a white man who leaned over his bed, said, "I hate niggers," then tried to choke him with a cord. A nurse walked into the room unexpectly, and the man rushed past her and disappeared. Her description of the attempted assailant was similar to one given by a withness to one of the .22 cal. shootings, authorities said.

In the five other cities -- Cincinnati, Indianapolis, Oklahoma City, Johnstown, Pa., and Salt Lake City, where still unsolved ambush-style shootings of blacks have occurred in the last year, authorities are seeking a 30-year-old native of Mobile, Ala., for questioning.

Smooth-faced and six feet tall, the man speaks with a pronounced Southern accent, and wears eyeglasses as thick as the bottom of bottles, with a nearly blind left eye. Authorities have picked up the trail of his travels across the country in fast Camaros and Novas under 20 or more aliases.

He was born James Clayton Vaughn Jr., but had his name legally changed to Joseph Paul Franklin, and that is the way he is carried in police files. He was arrested in the small industrial town of Florence, Ky., across from Cincinnati, and held for a few hours there late last month before managing an easy escape through a narrow crank-out window as officers conferred in the hallway.

A warrant has been issued for Franklin's arrest in connection with the two slayings in Salt Lake City.

The rash of murders has fallen like hot embers on a patchwork of school racial battles, cross-burnings on lawns and other strife in cities from Boston to the suburbs of Portland, Ore., and from Miami of Richmond, Calif.

Civil rights groups and government field officers privately talk of the seven straight years of racial strife over school busing in Boston as being in a special, distressed category. But files kept at the U.S. Civil Rights Commission bulge with clippings from newspapers across the country reporting isolated racial battles. Aides say they believe the numbers of incidents are growing, but have not done any studies to find out.

Minorities have filed 186 complaints with the Justice Department's Civil Rights Division since the start of the year alleging that criminal acts were used to block their access to housing. There is the sense in the division that the numbers are higher than in other years, but Justice is changing over to a new computer record-keeping process, and says there are no figures with which to compare this year.

Police authorities in the West and Midwest have tracked fugitive Franklin in a meandering course that put him, among other places, in Indianapolis in early April, Cincinnati in early June, in Salt Lake City in August and in Florence, Ky., in late September. There have been apparently racially motivated murders in all these cities and in Oklahoma City and Johnstown, Pa.

A saleswoman in Johnstown has told police that a man resembling Franklin made purchases from her in August and September. In several instances, however, the murders have taken place at times other than when the fugitive is now believed to have been in the various cities.

The FBI also wants to question Franklin in connection with the shooting of National Urban League President Vernon Jordan on May 29 in Fort Wayne, Ind. Jordan was shot in the back with a .30-06 rifle in a motel parking lot as he stepped out of the car of a white woman member of the local Urban League board. Jordan survived the attack, and recently made a public appearance at a fashion show in New York City.

Women who encountered Franklin in Salt Lake City have described to local police a man obsessive in his hatred and scorn for blacks. A desk clerk at one motel said Franklin had checked out, complaining that he had found hairs of blacks in the bed. Later, he bragged to a woman he picked up and took to another motel that he belonged to the Ku Klux Klan and had killed blacks, according to testimony she gave police.

She said she remembered seeing a rifle in his room and his asking her to make him a list of black pimps in the town so that he could kill them, too.

Three days later, on the evening of Aug. 20, two black youths, Theodore Fields, 20, and his friend, David Martin, 18, were jogging through Salt Lake City's Liberty Park with Carma Ingersoll, a white girl Fields knew, and her friend, Terrys Elrod. They followed a path Fields and Ingersoll had run along the night before, and were jogging out of the park when the two young men fell in a hail of bullets fired from a high-powered rifle.

A neighbor nearby said he had seen a white man pull up earlier and park in a brown Camaro. The neighbor said he rushed outside again when he heard the shots and saw the same man, crouched and running, jump into the car and drive off.

Authorities see similarities in the circumstances of the murders they are investigating in the other cities.

Jesse E. Taylor, 42, a black man, and his companion and coworker at an Oklahoma City nursing home, Marion Bresette, 31, a white woman, were in a crowded supermarket parking lot putting groceries into their car on Oct. 21, 1979, when a volley of shots fired from a high-powered rifle burst from a clump of bushes on the state fairgrounds across the street.

Two bullets hit Taylor, wounding him fatally. As Bresette ran to his aid another bullet hit her in the torso, killing her. Bresette's three children by a former marriage, ages 9, 10 and 12, were in the car, but were not hurt. Oklahoma City police said the suspect is a white man witnesses saw in the area that afternoon.

Lawrence E. Reese, 22, a mildly retarded young black man who did odd jobs for a living, was standing at the counter of a Church's Fried Chicken carryout in the heavily black north side of Indianapolis late in the evening last New Year's Day when he was killed by a sniper who sprayed bullets through the plate glass window.

Two weeks later and about two miles away in north Indianapolis, Leo Thomas Watkins, 19, was killed in a nearly identical manner as he helped his father with a pest extermination job at a convenience store.

Late Sunday night, June 8, in Cincinnati, Darrell Lane, 14, and his cousin, Dante Brown, 13, who was visitng the Lane home in the integrated Paddock Hills neighborhood of Tudor homes, both decided to go out to buy soda pop. As they walked to a nearby store, they were fatally wounded by a sniper believed by authorities to have been perched on a railroad trestle over the street. Darrell's father was a paramedic in the first rescue squad that arrived on the scene.

A week later, in Johntown, Pa., Kathleen Mikula, 16, a white high school freshmen, and her black fiancee, Arthur Smothers, 22, a former high school athlete who once ran in the Boston Marathon, were walking from her parents' home on the west side of Johnstown across a bridge to his family's home on the east when they were both shot and killed.

He was shot in the back, in the groin and, after he fell, in the foot. The sniper, believed by local police to have been firing from wooded hills, shot her in the brest and, as she lay dying, squeezed off another bullet that went down her shoulder and torso, lodging in her hip.

A witness later reported to police seeing a dark Nova racing up hilly road from the scene of the shootings. CAPTION: Picture, Atlanta Mayor Maynard Jackson, surrounded by security men, shows a stack of $100,000 collected as a reward for information about the city's murdered and missing children. Ten youngsters have been killed and four are missing in the last 15 months. AP