Like a doomed Ahab roaming the oceans in search of the great whale, the impoverished D.C. government is exploring untried regions of law and policy in its never-ending quest for cash.

City officials took the first steps yesterday toward implementing a new law giving the District the right to seize dormant bank accounts and other unclaimed property -- a law that could produce $50 million over the next 18 months.

The day before, Mayor Marion Barry asked the City Council for the authority to sell 27 parcels of city-owned property, including the old Georgetown incinerator and other choice sites in Georgetown and downtown.

Both measures are expected to provide one-time-only revenue infusions that the District must have to stave off budget deficits this year and next. No one really knows how much the real estate sales will bring in or how much money is in unclaimed bank accounts.In any event, the bank account funds are already earmarked to replace lost revenues from the repealed gasoline sales tax.

In a letter to Council Chairman Arrington Dixon, Barry said the property sales would being in "approximately $14.7 million in revenue" this year. The District's 1981 budget presumes that $9.3 million will be raised through property sales; the additional revenue would be used to partially offset anticipated overspending by city agencies.

As the city's population has declined over the past 20 years, many of the estimated 2,200 properties owned by the municipal government -- schools, firehouses, storage lots -- have been vacated or declared surplus. Sale of such properties would benefit the city government in three ways: it raises immediate revenue, cuts maintenance costs, and puts the properties back on the tax rolls.

A three-quarter-acre vacant lot at 28th and M streets, NW, on the eastern edge of Georgetown, adjacent to Rock Creek Park and across from the luxury Four Seasons Hotel, is probably the most desirable of the properties to be offered for sale. Now used as a parking lot for city repair trucks, it is zoned for mixed-use development, and real estate experts say it is worth more than $2 million.

The mayor also wants to sell the old Georgetown incinerator at 31st and Water streets NW, on the waterfront. Zoning on the 1.2-acre site would permit residential, commercial or hotel development. High interest costs and lagging sales in other waterfront projects have cooled the ardor of developers, but the site might be snapped up as a bargain for the future.

Also available in Georgetown are the old Engine Co. 5 firehouse at 3212 M St. NW, in the heart of the booming commercial strip, and a small vacant lot next to Addison school at 33rd and P streets NW.

On the fringes of downtown, Barry proposed to sell a parking lot at 13th and N streets NW, near Thomas Circle, and another at Third and E streets NW, near D.C. Superior Court. That site is within the "hotel incentive zone" created to promote hotel development in the area near the new Convention Center.

The property list is full of little ironies and bits of history that reflect how the city has changed, mostly since the 1968 riots. A vacant lot at 1200 Bladensburg Rd. NE is described as "adjacent to an old Eddie Leonard's Sandwich Shop (now Chan's Carryout)." The old 11th Precinct police station on Martin Luther King Jr. Avenue in Anacostia, long vacant, is for sale.

The surplus bank account measures that went into effect last month allows the D.C. government to seize bank accounts, uncashed checks, safe deposit boxes and other financial assets that have been abandoned or left by individuals who died or cannot be found. Similar laws exist in more than half the states.

Joseph Lund, of the Department of Finance and Revenue, told business executives at a meeting yesterday that they must notify the District by June 20 of all property that has been unclaimed for at least seven years as of Jan. 1. Until those notices are compiled, it is not possible to say how much money the District will get.