WASHING ONE'S dirty linen in public can be a public service. And even the White House has obliged.

The secret of the care of fine linen and lace table cloths was given away by the late Marjorie Merriweather Post, the multimillionaire cereal heiress. Twelve years ago Post, who had some of the world's finest and most expensive table linens, had a leaflet printed up for her friends telling how to take care of heirloom pieces. She even took a hand herself with priceless cloths on which she had fed presidents and prime ministers, kings and queens and first ladies at her series of homes for all seasons.

Rex. W. Scouten, head usher at the White House under several presidents, turned our inquiries over to Shirley Bender, executive housekeeper for nine years.

There was a time when all the fine laundry was sent out to the Louise Hand Laundry. Spots were carefully removed immediately after a social function under the direction of Viola Wise, who has been treatng spots at the White House for 30 years.

The Louise Hand Laundry has gone out of business, so now all the small table items are done at the White House under the direction of Wise. Larger things are sent to Bergmann's Laundry.

The spotting is a very careful operation. The spot is placed over a folded Turkish towel and then treated with brown soap, lemon juice or a mild bleach such as diluted Clorox - usually in cold water for wine or coffee stains, but warm water for grease.

Heirloom pieces, which have come to the White House from several large estates, are spotted after use and folded and put away if not otherwise soiled.

"Every effort is made to preserve these fine pieces," says Bender. "After they have been spotted, they are carefully laid away so that they will not be worn out from too much handling, washing and ironing."

Mrs. George Maurice Morris, the grand dame of Washington's 18th-century hospitality, turns over her linen and lace problems to LeRoy Humphrey, her butler. Humphrey has handled such things at her Kalorama Road home, The Lindens, for the past 14 years. Morris serves most dinners on 18th-century lace doilies.

Humphrey has problem spots soaked by the Morris maids, usually in Clorox, after which the items are washed, ironed and put away carefully.

Friends have watched Post pore over an heirloom piece as it soaked in a basin on her dining room table at Hillwood, her 26-acre Washington estate.

The 1966 Marjorie Merriweather Post memo to friends suggested that the stained cloth be laid flat on a table and then to proceed as follows:

WINE SPOTS

"Take a shallow plate or dish and fill it with cold water. Place it under the spot area and soak, adding salt on top of the spot. If this is done without delay the spot should disappear quickly. If the spot is permitted to remain for any length of time, it will probably be necessary to soak it longer, possibly half a day or so.

"If the spot is stubborn, take the spot area out of the water. Put it on a dry towel and add lemon juice on the spot. This should bleach out the spot, and the spot area should then be rinsed in cold water."

COFFEE STAINS

"Take a shallow plate or dish filled with cold water and placed it under the spot area and soak. For coffee stains on either linen or lace, the spot should be rubbed gently with a little Ivory soap, then rinsed in cold water."

GREASE SPOTS

"Take a shallow plate or dish and place under the spot area. Pour hot water (not boiling) over the spot and soak. It should be rubbed gently with a little Ivory soap. Then rinse the spot in hot water and dry the spotted area by placing a towel underneath.

"Don't leave lace soaking too long in hot water as this would cause it to shrink."