The death Wednesday of Rep. Goodle E. Byron (D-Md.), a marathon runner who died of an apparent heart attack while running along the Chesapeake and Ohio Canal, has caused consternation in what can - without exaggeration - be called the runner's world of America.

Byron was no overweight weekend enthusiast. He had run in six Boston marathons, his best time being 3:28:40 in 1974, when he was 44. He had run in seven John F. Kennedy 50-mile races.

He had not smoked for at least 25 years.

Byron ran almost every day for at least half an hour, longer if his schedule permitted. He was scheduled to run here Saturday, National Jogging Day, in a 13-mile "minimarathon."

Byron seemed the perfect running specimen. And that is exactly what has caused alarm among runners, many of whom regard running as a protective panacea against heart attacks and a variety of other ailments. Estimates of the number of Americans who jog or run range from 10 million to 26 million.

Dr. Richard L. Bohannon, a cardiologist who is president of the National Jogging Association, issued a terse, guarded statement concerning Byron's death.

"We don't know the details of Goodle Byron's last physical examination," Bohannon said. "He has done so much jogging in the past that it seems doubtful that jogging caused his death. We are awaiting details of his autopsy."

The claim has been made - and was made again yesterday by California pathologist Dr. Thomas Bassler - that "completion of a marathon in under four hours is permanent immunity against a heart attack due to arteriosclerosis (hardening and clogging of the arteries)."

Bassler, reached at the Inglewood, Calif., hospital where he works, is an admittedly controversial figure in running circles, where his positions are well known. "The big question we're all wondering about," Bassler said yesterday, "is can marathon runners age? Can they die from old age?"

Bassler, who had already had three calls concerning Byron's death when a reporter called him yesterday, said that he will need to see microscopic slides or read a complete autopsy report before knowing whether Byron is the first marathon winner known to have died of a heart attack caused by arteriosclerosis.

Bassler's theory - that the arteries of marathon runners do not age - is based on a finding by an English physician named C. W. Adams that the Achilles' tendon and the coronary artery are made of "exactly" the same substance. "If the integrity of the Achilles' tendon can withstand 26.2 miles," Bassler said, "then the integrity of the coronary artery should protect you from whatever you're eating or any other activity."

Paul Milvy, editor of a New York Academy of Sciences symposium on the medical implications of the marathon, dismisses Bassler's theory as a "myth," resulting from the relative youth of marathon runners and the relatively small numbers - fewer than .02 percent, or 40,000 out of 220 million Americans - who have run a marathon. "You would hardly expect a sample of young runners," Milvy wrote, "especially since very few of them smoke."

Dr. George Sheehan, the New Jersey cardiologist who writes for Runner's World magazine, is the author of "Running and Being" and is recognized as a leading authority on running, said yesterday that he does not believe "that running is going to protect you from coronary disease."

Running and jogging, Sheehan said, "have to do with function. You get 40 percent more function out of your body if you run . . . jogging has to do with the physiology of the body, not disease, with the function of the body, not with heart attacks.

"I don't think there's anybody who will say that once you start jogging you don't get better physiologically, that you don't increase cardiovascular pulmonary function," Sheehan said.

"We will never know," Sheehan said, "what Byron was going through and what his symptoms were. Nature never drops you over without a warning."

Cardiac stress tests and other analytical technology will be no help Sheehan said, "if you don't listen to your body." A moment later, however, Sheehan allowed that "If I had chest pains I'd probably ignore it . . . Running has become more important to me. It's become part of my life. I try to listen, but I can understand people not listening."

Bill Rodgers, two-time winner of the Boston Marathon and holder of the American marathon record of 2:09:55, expressed concern that the wrong conclusion would be drawn from Byron's death.

"More people die because they don't exercise than because they do," Rodgers said. "I like to think when I run that my heart's not going to give out on me. But who can say? Nothing's certain in this world."