The Arlington County Board has agreed to join residents of the Stonewall Jackson area of North Arlington in an effort to get the first mile of a 230,000-volt transmission line placed underground instead of overhead as proposed by the Virginia Electric and Power Co.

Vepco wants to erect a mile-long stretch of 14 overhead transmission lines averaging 90 feet high through a largely residential neighborhood as part of a two-mile project to meet future electrical demands in the Ballston and Clarendon areas. The proposed $4.3 million project also includes a new substation in Clarendon.

The second mile of transmission lines in the project will go underground in ducts built years ago during street renovations. Vepco spokesmen have said it would cost another $1.5 million to run the first mile underground.

The first mile is slated to run overhead from Vepco's Glen Carlyn substation at South Kensington Street and Four Mile Run Drive, along the old right-of-way of the defunct Washington and Old Dominion Railroad, to the Avon substation near Fairfax Drive and Buchanan Street. From there it would run underground for a mile to the new Clarendon substation near North Nelson and North Quincy streets.

Vepco has argued that it legally is obligated to choose the least expensive alternative for its customers in order to keep costs down state-wide, and has contended that placing the first mile underground at the request of a local government would set a bad precedent.

But the county board and the nearly 100 citizens who attended Saturday's board meeting to complain about the project disagreed with Vepco. Speaker after speaker cited aesthetics and possible safety hazards if the project were built as Vepco proposes.

Vepco has applied to the State Corporation Commission, which regulates utilities in Virginia, for approval to erect the transmission lines and substation. The SCC has set a July 27 hearing in Richmond, but county board members said they would try to get the hearing moved to Arlington.

Because state law now prohibits the county from blocking such projects by denying use permits--as a previous board did to block the same project in 1974--the board decided to intervene at the SCC hearing. Members said they would try to persuade the SCC to order Vepco to spread the additional cost of placing the first mile underground among customers state-wide, although they asked for a report from the county staff on the possibility of a surcharge on Arlington customers or a surcharge on only those who would directly benefit from the project.