Oh where, oh where have your leftovers gone? Oh where, oh where can they be? if you've had all you can possibly eat, Please bring the rest home to me! -- Jean Melster, Chicago (Wife of the former president of the Babcraft Corp. of America, a manufacturer of doggy bags)

WHEN LOUIS Szathmary, chef-owner of Chicago's Bakery Restaurant, got a phone call shortly after midnight, it wasn't a request for a reservation. g

The voice, agitated, asked, "Is there an extra raincoat there? This one I brought home isn't mine."

Louis replied, "No raincoat."

Hardly had he hung up the phone when the other phone rang. This caller, who was staying at a Michigan Avenue hotel, asked,"Did anybody leave a London Fog at the restaurant, or call to say he had taken home the worong one?"

Louis asked for a description. The caller hesitated, "It's kind of embarrassing, but I have a half portion of roast duck packed in aluminum foil in one pocket and one of your napkins with two slices of bread and butter in the other pocket. I planned to have them for breakfast."

Louis gave the first caller's number. He later learned that the coats and edibles had been exchanged within the hour.

Says Louis, "Ten years ago, nobody would think of asking for a doggy bag in our type of restaurant, but the 1970s brought a change and lately we have practically no night that somebody would not ask for a piece of beef, duck or pheasant to be packed."

Louis Szathmary sees it as a spinoff of our ever-tightening economy, but elsewhere across the country there are restaurants elevating the idea of toting home those culinary tidbits into the new chic.

At Boston's elegant Cafe Budapest, a matron looked at the Viennese sweets beckoning from the dessert tray. Her eyes said, "Yes!" Her tummy said, "No!" It was a moment of agony.Assistant maitre d'Brian Angelo, having been through this scenario many times before, graciously suggested he could wrap it up to be enjoyed later on. The pastry and doily were delivered to her table in a white box.

Says Angel, "We get two or three requests every evening from patrons who want to wrap up meat, chicken or a slice of cake. We've even wrapped up an open bottle of wine."

In Washington, at The Big Cheese in Georgetown, a woman laughed uproariously and her dinner companinon applauded loudly. It was neither a souffle nor a fried Norwegian cheese responsible but the presentation of one of waiter Peter White's aluminum foil doggy bags -- in the shape of a silvery swan.

Says owner Barbara Witt, "He does with foil what origami artists do with paper -- ducks, mice, swans, cats, pigs. Lots of our patrons ask and we love to do it for them. Peter White's doggy bags look like party favors. It's such fun. No one would ever know it's leftovers."

When it comes to taking home those tidbits, you might say that what one man considers edible extras, another sees as garbage. The lines are drawn between believers and non-believers.

Comedan Bob Hope is a believer: "No one should be embarrassed to ask for a doggy bag, especially if in-laws are coming for dinner the next night."

Lois Lindauer, international director Diet Workshop, is a believer: "Doggy bags are great for would-be skinnies. When your dinner arrives, eye-measure your serving portion and section off the excess to be toted home. It makes good diet sense, as well as good dollar sense."

Jeanne Volts is a believer. In fact, the contents of her bow-wow bags are even tastier the second time around in oriental skillet suppers, omelets and soups. But then you'd expect nothing less than this kitchen-time creativity from Voltz. She's food editor of Woaman's Day magazine.

For syndicated humorist Art Buchwald, it's irrelevant. "I never ask. The reason for this is that I eat everyting on my plate and also everything on everybody else's plate. If it's good enough for my dog, it's good enough for me."

Patrick Terrail owner of Los Angeles' exclusive Ma Maison, is a believer. "We serve up leftovers as swans of foil. There's no reason not to oblige. Our patrons have the right to take it."

But Paul Kovi, co-owner of New York City's Four Seasons, is staunchly against it. "This doesn't go in our restaurant. I find the idea offensive. I don't want to talk about it!"

Paul Kovi may not be aware of the cachet doggy bagging had as early as the 1800's.

Cookbook author Roy Andries de Groot relates from his research, "I believe it was the great Alexandre Dumas who invented the idea of the doggy bag. He was such a brilliant cook that, when any of his friends were unable to accept his invitation to dinner, they would send around a servant with a bag to collect their portion of the meal. Dumas wrote to his friend Jules Janin, 'I made a salad of foie gras which pleased my guests so well that when Ronconi could not come, he sent for his share of the salad which was taken to him in a dish covered by a bag under a great umbrella, so that the rain might not soak the bag and no foreign matter might spoil the dish.'"

Reports De Groot, who is a frequent world traveler, "I am an inveterate demander of doggy bags. Even if the food is bad, I often insist on taking it with me just to throw it away -- as a form of protest against restaurants that serve grossly over-large portions at grossly over-elevated prices.

"I am not alone. The doggy bag idea has even reached high society in London. Recently, dinning at the expensive, famous, very swanky Mirabelle in Mayfair, I insisted on carrying off the remains of a Carre de Veau a la Prince Orloff, complete with truffles and wild mushrooms. They were ready with a golden doggy bag with a royal crown on it and the printed message, "We are delighted that you like our food so much that you want to take it home and finish it. Please don't waste it on your dog. Enjoy it yourself with our compliments."

"Now that's a clever ploy," says marketing expert Lawrence H. Wortzel. "Given the price of food at restaurants and the large portions at some of them, there are a lot of people who would like to take doggy bags and it would be a good competitive move for the restaurant to make it easy for them to do so. I'm not suggesting bags on the table. That would be an open invitation to walk off with sugar bowls, ashtrays and silverware. Rather, train waiters and waitresses to offer them." a

Boston University marketing professor Wortzel foresees more bagging, especially at family-type restaurants, as America tightens its collective belts.

But Los Angeles Times restaurant reviewer Lois Dwan is no fan. She says, "Some restauratns make a point of saying they have doggy bags. It's gimmick and not quite honest." Dawn explains, "Customers think they are getting a free extra meal, but they are paying for those big portions. Choose a restaurant for the skill of the kitchen and not the fact you'll get a second meal out of them by packing up the leftovers."

Dr. Richard Gelles, chairman of the sociology department at the University of Rhode Island, explains the psycological motivations: "It depends on the social status of the patron and the perceived social status of the restaurant. If you feel superior to those who are serving you; if you don't care about their opinions, you will go ahead and ask that the leftovers be wrapped up. If you feel inferior, you will worry about losing face in which case you could leave an entire dinner on your plate." He mentions a colleague who takes home the extras from the neighborhood steak house but leaves them on the plate when at a fashionable Washington restaurant such as Sans Socuci.

Whether to ask for a doggy bag or not depends on the restaurant, according to Elizabeth Post, author of "The New Emily Post Etiquette." She says, "In the everyday family-type restaurant it is more proper than at your fine restaurant. We are all feeling the inflation, so why not? You've paid for it. Don't do it at someone's home," she adds, Alexandre Dumas to the contrary.

For anybody who doubts that doggy bags (poodle packs, bone bags, Fido bags, bow-wow bags, cat saks, undoggie bags, people bags) are here to stay, you should know that manufacturers such as Chicago's Bagcraft Corp. of America are turning out hundreds of millions -- waxed paper-lined, foil-lined, grease-resistant, double-tight tin-locked top, even a few with peek-through windows so no guessing the next day when you open wide the refrigerator door. They come resplendent with poetry, restaurant logos, art that will have you craving for another meal right now -- Chinese or fish and chips.

If your dog reads, this bag's warning would impress you: "Like hell it's yours Gigi -- these steak bones are from Tosi's Restaurant, Stevensville, Mich."

It even goes on at the White House although excetive chef Henry Haller says, "Never!" Obviously he doesn't see everthing that goes on outside his kitchens. Last June, Rosalynn Carter entertained 100 newspaper and magazine food editors at a late afternoon buffet. A few were seen wrapping up Chef Haller's goodies n those printed White House paper napkins to savor later.