Transportation Secretary Brock Adams approved yesterday a $199 million federal grant that will permit completion of 60 miles of the Metro subway, but withheld part of the grant until the latest crisis in Metro's Perils of Pauline financial history is resolved.

The money will be used to bring to full operation the 60 miles of Metro that both local and federal governments have committed themselves to build. Those lines, and the projected completion dates, are:

The Red Line extension from Van Ness Center at Connecticut Avenue NW and Van Ness Street to Shady Grove, north of Rockville, scheduled for completion in early 1983. (An intervening section between Dupont Circle and Van Ness Center is due to open early in 1981.)

The Blue extension from National Airport to Huntington, just south of the Beltway and west of U.S. south of the Beltway and west of U.S. Rte. 1 in Fairfax County, scheduled for completion in early 1982.

The Blue Line extension from Stadium-Armony east to the Addison Road station, near AddisonRoad and Central Avenue in Prince George's County, scheduled for completion in late 1980.

Work has already started on all of those segments. The grant will be used for final construction work and to but electronic equipment and other items needed for operation.

The bad news is that some of that work cannot be started until the latest financial crisis is resolved. The crisis arises because of a new finding from teh General Accounting Office (GAO) that has the potential of costing local governments as much as $134 million.

GAO recommended in a Sept. 1 letter to Adams that Metro be required to use some of its investment income to pay interest on $1 billion in federal guaranteed revenue bonds.

Metro, with the full knowledge and agreement of the Department of Transportation, has already used $38 million of that money as the local-government share for $190 million in construction projects, with the rest of the money coming from federal sources.

Furthermore, Metro has firm plans for the rest of that money. They transit authority had programmed $17.3 million of investment income as a local share for $69.2 million of the federal grant Adams approved yesterday. Thus, Adams withheld the $69.2 million until the question is resolved. Local funds must be approved and in place before federal grants can be released.

Just last week Metro applied for a $68 million federal grant to hlep in purchasing badly needed new subway cars. The local share, $17 million, was to come from investment income. Some of that proposed local share - it could not be determined how much yesterday - could not be used for that purpose if the GAO recommendation holds.

Metro earns investment income from two sources. One is from local construction funds that are prepaid to the transity authority. The other is from investing upspent proceeds from the $1 billion in revenue bonds sold to construct Metro. It is the money earned on bond proceeds that is under debate.

If the GAO recommendation is adopted, then Metro would have to raise the $17.3 million some other way, a difficult proposition at best. Furthermore, the only recommendation from GAO on what to do about the $38 million already spent by Metro is that Adams "consider what action should be taken."

There was no mention of this substantial problem yesterday morning during an all-smiles session in the Longworth House Office Building that was called Rep. Herbert E. Harris II (D-Va), chairman of the House District subcommittee on Economic Development and Regional Affairs.

Harris had convened a meeting with Adams, his top lieutenants, Metro board chairman Joseph S. Wholey and Metro general manager Theodore C. Lutz Rep. Joseph L. Fisher (D-Va), the other Northern Virginia congressman who just happens to be running for re-election, dropped, in.

Adams spoke informally, urging the necessity for resolving quickly several key items in Metro's clouded financial picture. The Metro board has presented a plan to complete construction of the 100-mile system, but the plan needs action.

The key points that must be resolved, Adams said, are a permanent solution to paying interest on the revenue bonds and identification of sources for completing construction and for paying operating deficits of the subway.

Adams also said he would be willing to help lobby the state legislatures of Maryland and Virgures of Maryland and Virginia to receive support for Metro.

Harris' meeting was originally scheduled as a hearingtwo weeks earlier, but Adams cancelled out at the last minute in a disagreement with OMB over how he should state the administration's support for Metro.

Richard S. Page, chief of the Urban Mass Transportation Administration (UMTA) and a key Adams Lieutenant, said after the meeting yesterday that if Adams had been asked (he was not) he would have reiterated that the federal government "supports the goal of completing the 100-mile system."