Southern Railway Co., whose trademark proclaims that it "serves the South," is planning an "Inauguration Special" from Atlanta to Washington and back to carry some of Jimmy Carter's fellow Georgians to the Jan. 20 inaugural.

The special will leave Atlanta on the evening of Jan. 18 and arrive here the next morning. Along with the regularly scheduled Southern Cresent, the two trains will carry about 650 passengers on 35 cars.

Amtrak, the national rail passenger corporation, is planning a separate "Peanut Special" from Plains to Washington, starting from the now famous Seaboard Coast Line station in Carter's home town.

Southern chairman W. Graham Claytor Jr. said yesterday the unusual passenger volume in January should swell his firm's normally low business in the first quarter. But the passenger operation will continue to operate at a loss of about $3.5 million a year, he said.

The Southern Crescent, which operates from Washington to Atlanta daily and from Atlanta to New Orleans three times a week, is Southern's only remaining passenger service.

Claytor said yesterday that there are no plans to cut out the Crescent in the foreseeable future. But, like other long-distance trains outside the dense Northeast corridor, "there is no way it can be run on a breakeven basis," he added.

The reason Southern wants to maintain its last passenger train in public and community relations, Claytor added. "It's the standard by which Amtrak is measured in many ways and has a tremendous impact on the public. Railroads lost a good deal of public respect by getting out of the passenger business."

The Crescent also attracts some freight business from shippers who are impressed with the passenger operation, Claytor added.