The House District Committee yesterday authorized $1.84 million in federal funds for Metro to study adding 77 miles to the planned 101-mile subway system.

Under the most optimistic construction schedule, Metro will not complete the 101 miles until 1990. If all of the 77 proposed miles were to be incorporated into the system, Metro's construction program, currently estimated to cost $8.2 billion, would extend well into the 21st century.

The study, first proposed by Rep. Herbert E. Harris II (D-Va.), would cost $2.3 million with the rest of the money coming from state or local governments. The study would be scheduled for completion 18 months after final congressional approval, but only six months would be allowed to complete the analysis of a proposed entension to Dulles International Airport.

That extension has long been considered the most logical for Metro. It would be 17 miles long, would run in the median of the Dulles Access Road from the planned Orange Line station at West Falls Church, and would probably include stops at Tysons Corner, Westpark (an office complex just outside the Beltway), Wolf Trap Farm Park, Reston and Herndon.

Other extensions to be studied are:

An 18-mile crosstown line in the District that would include a stop in Georgetown and probably run under H Street. Street Station west to Van Dorn Stret, then south into Fairfax County, terminating at the Springfield-Franconia station, near Springfield Mall. One extension would run 10 miles in an old railroad right-of-way from just south of the Beltway to Burke. The other would run six miles along the existing Richmond. Fredericksburg and Potomac Railroad tracks from the Springfield-Franconia station to Lorton, where it would connect with parking lots the Virginia Department of Highways and Transportation is planning for the Interstate 95 corridor, which the route would parallel.

A 14-mile extension to the Red Line, which will terminate at Shady Grove Road in Montgomery County under the current plan. The extension would include a stop at Germantown, then would continue to Clarksburg, which is close to the Frederick County line.

A 13-mile extension of the Blue Line in Prince George's County from the Addison Road station (scheduled to open this November) to Bowie, with a stop at the Capital centre.

A 9-mile extension of the planned Green Line from Rosecroft Raceway in southern Prince George's County south to Brandywine, near the Prince George's-Charles County line.

Harris had no trouble finding enthusiastic cosponsors from the Washington area congressional delegation and took unbrage at a reporter's suggestion the study was na election year boondoggle.

"I don't care how people interpret the motivation," Harris said. "The record shows that when I start these things I get them done."