We found the feathers first. They were black and white and not long separated from a downy woodpecker. Now they were scattered across a rotting log between the C&O Canal and the Potomac River. The rest of the bird had disappeared. But 150 yards away, in the crease of a sycamore tree, sat a barred owl looking very well-fed.

"It was either the owl or a hawk," said Dick Gauthey, a tall, dark-haired man who has been watching the birds that live on Cabin John Island in the Potomac so long he can tell you which ones sing off-key.

While most civilized citizens of this town were getting ready to watch the Redskins beat the Lions a week ago, Gauthey was searching the treetops of this 45-acre island, just a few hundred yards above Glen Echo, looking for birds of assorted feathers.

With a clipboard in one hand and binoculars around his neck, Gauthey was conducting a bird count. And never was a census-taker challenged by such a flighty population.

The winter count is one of three major ones made of this area's bird population each year. The others, a spring nesting count and a Christmas survey, are conducted by hundreds of ornithologists and amateur bird watchers. The stated goal of these counts is scientific. But much of the attraction, admit volunteers, is pure sport.

"This is a sport, just like tennis," said Gauthey, a 50-year-old Navy officer who has been spying on birds since he was a 12-year-old Boy Scout in Connecticut. "I like to think that something good comes out of this in the scientific sense. But it also is a very challenging game, to see how many species you can identify."

Bird watchers have sprouted some colorful feathers in the last decade. The old stereotype of the bespectacled bird watcher, who wore tweed knickers and was likely to get lost in the woods while following the flight of a yellow-bellied sapsucker, has disappeared with Doonesbury.

"Twenty years ago, people really thought you were a weirdo. They wondered why anybody would want to go out and look at birds," said Gauthey, who knows as much about the social and mating habits of his subjects as soap opera addicts know about theirs.

The contemporary birder is likely to be woods-smart and competitive. An extreme example of the breed is Roger Tory Peterson, America's most famous birder and the author of the best-known field guide to birds.

In April of last year, Peterson and two other birders conducted a birdathon in Texas, using a plane and a fast-moving van, in an attempt to set a record for the number of bird species heard or seen in the United States in one 24-hour period. The team identified 235 species, breaking the record of 231 set in 1978.

Another flamboyant birder, Jim Vardaman of Louisiana, traveled 161,000 miles by car, boat, plane and bicycle and spent almost $50,000 in 1979 in an attempt to identify 700 species of birds in one year. He fell one species short.

The best of the new breed of birders are conscientious types who have brought more attention to the sport, and consequently more interest and financial support for protecting our native and migratory birds. But the new competitiveness also has created a birder who is as bad as the worst hunter. In his pursuit of airborne achievement, he trespasses, destroys fences and intentionally harasses birds to make them fly.

Gauthey is perched with the good guys. He is a quiet, thoughtful man with eyes that seem to change color from brown to green as he looks from the ground to the sky.

Gauthey's career in the Navy has taken him to Hawaii, Virginia, South Carolina and California. He has taken advantage of those assignments to study the local birds.

Now he is the officer in charge at the David Taylor Naval Ship Research and Development Center at Carderock, and the self-appointed chief bird watcher for Cabin John Island. That island has been subject to a winter bird count since 1948, making it the oldest continuous winter survey site in the United States.

Last winter Gauthey, with help from a few other birders, took six counts of birds at Cabin John in January and February. There were an average of 199 birds counted there, representing 28 species including Carolina chickadees (23), starlings (20), American goldfinches (14), hairy woodpeckers, Cooper's hawks, barred owls and black vultures. In the summer more species nest there, including some that make the trip from South America.

You wouldn't think that people still ask Gauthey what he finds so appealing about his birds, but they do. In that group, concedes Gauthey, is one of his own family.

"My wife and daughter are interested in birding," he says. "But my son still thinks I'm weird."