Fairfax County chipped another notch yesterday in its belt of business acquisitions as Boeing Computer Services dedicated its new $35 million facility near Tysons Corner.

The expansion of Boeing, best known for its parent company that manufactures aircraft, represents the second phase of the Virginia county's drive to draw more business in, said Robert Torgerson of the county's economic development authority. The second phase is to nurture them and urge them to expand in the county.

Boeing's move from leased office space in Mclean to its own tinted-glass and steel buildings is "one of the more notable expansions," Torgerson said.

During the past few months, 17 small and medium-sized firms in the county have either relocated or expanded their operations in the county, Torgerson said. They included McDonald's fast food chain, which will move its regional offices from Tyson's Corner to Merrifield; the BDM Corp., a diversified professional services company which is expanding its national headquarters building in Tysons Corner facility; and Computer Sciences Corp., a nationally known computer system firm that leased new office space in Merrifield last February.

During a press conference yesterday at Boeing's Tysons Corner building, Robert W. Tharrington, a Boeing vice president, said the company constructed its own buildings because "with growth we wanted to have greater control of our destiny." The company decided to stay in Fairfax County because Boeing's employes were already living in the area and the proximity of the nation's capital.

At its new facility, Boeing eventually can triple the number of workers it currently employs, which is 500, Tharrington said.

The Being computer service supplies data processing services to business, industry and federal, state andlocal governments. It offers financial planning systems used in budgeting, computing services for engineers and other computer services.

The $15 million, two-building facility, which houses $20 million in computer equipment, consists of services to commercial users east of the Mississippi River, time-sharing services to the federal government and commercial users, software development, and management services. CAPTION: Picture, Sylvia Benavides picks a computer tape from the huge bank of billions of information bits at Boeing Computer Services. By Douglas Chevalier - The Washington Post