They ate snails and duck and clams casino, filet mignon and Dover sole. For some there was scotch, for others, just cola.

It was with food and drinks inthe ornate Hotel Washington dining room that a new round of negotiations began last night to end the 18-day strike by city teachers.

Mayor Marion Barry said the District government would pay for the food and drinks as well as meeting rooms and bedrooms inthe hotel at 15th Street and Pennsylvania Avenue NW. "If it brings a settlement, we think everyone inthe city will think this is worthwhile," one mayoral aide said.

The dining began about 9 p.m. with union negotiators gathered around a big table at one end of the Two Continents Dining Roon. Board negotiators sat in a nook at the other end of the roon, with members of the board majority and School Superintendent Vincent Reed sitting in a nook beside them.

Members of the board's minority faction, which usually has been more favorable to the teachers' union, sat at different tables around the room somewhat closer to where the union was gathered.

Barry, City Council Chairman Arrington Dexon and their aides ate in the middle of the room.

Finally, after 10 p.m., the diners began drifting off to check into their bedroons.

Not all of them made it to the mezzanine, where negotiations were being held, kuntil after 11 p.m.

As the negotiating sessions began near midnight several of the participants complanined that they already were tired. "Maybe this is just going to be a physical test of who can last the longest," one school negotiator remarked. But an aide to Barry said she thought having everyone tired might be a good thing.

"Maybe if thet gey real tired," she said, "it will bring them all together."