Panic gripped the young mother when she found her 15-month-old daughter holding a half-empty bottle of baby aspirin.Frantically she tried to fathom how many of the brightly colored pills the child had swallowed -- counting those the toddler clutched in her tiny fist, those left in the bottle and others strewn on the carpet.

All the while, her mind wrestled with the vision of a comatose child -- the victim of an accidental poisoning.

The mother at last determined that the little girl, who weighed 23 pounds, had ingested about 11 pills -- not enough to poison her or require that her stomach be emptied, said Dr. Toby Litovitz of Georgetown University Hospital.

"It's every parent's nightmare," said Litovitz, who is director of the National Capital poison Center, which opened at the Georgetown hospital recently.

The center, one of 52 in the National Poison Center Network, will serve as headquarters for aid to poison victims in the metropolitan area. It is located in three rooms adjacent to the hospital's emergency room.

Litovitz advises parents to memorize the telephone number of the center -- 625-3333 -- and to keep on hand at home a bottle of syrup of Ipecac, a vomit-inducing agent sold without prescription for about $1.

Knowing what to do in the event of a poisoning is vital if serious complications, and perhaps even death, are to be prevented, Litovitz said.

"The faster we empty a child's stomach, the better, because less of the dangerous substance is absorbed into the body," she continued.

Litovitz suggests that parents call the center immediately if a poisoning is suspected, rather than follow guidelines for emergency treatment suggested in poison-prevention pamphlets distributed by some area stores.

"I'm not saying they are wrong, but I can't say they are right," she said.

Never administer Ipecac, the vomiting-inducing agent, expect on the advice of medical personnel, she explained, because using Ipecac is not advisable in some poisonings.

"Always call the poison center first," she repeated.

Toxic substances always should be kept in their original containers and out of children's reach. Dangerous plants -- in and out of doors -- should be so labeled and also kept out of reach, the doctor said.

Never mask poisonous substances, Litovitz warned. She mentioned, for example, that some city residents try to kill cockroaches with boric acid laced with sugar.

"It will not kill the bugs," Litovitz said, "but a teaspoon of boric acid can kill a child."

At the poison center, phones are answered around the clock by nurses with toxicology training. Litovitz, a physician who specializes in emergency medicine, is available to handle difficult cases, and a small army of nationally recognized poison specialists is accessible by telephone day and night.

It is 5 p.m. The poison center's six telephone lines ring in succession.

Nurse Barbara Fahey is calm and precise as she answers the phone. She quickly takes vital information from the caller.

"What has the child swallowed?" she asks. "How old is the child? When did this happen?"

Within 15 minutes she has reassured several frantic mothers whose children have gotten into a variety of undesirable substances.

The pre-dinner hour generates a rush of calls, Fahey says. It is a time of day when children often are not watched as closely as usual, because Mom is busy preparing dinner.

A 2-year-old has eaten "a couple of mouthfuls" of D-Con rat poison. Another has drunk some Wisk liquid detergent. One has licked Magic Markers, another has eaten kitty litter (neither is poisonous) and a 12-month-old boy has sprayed Pledge furniture polish into his eyes.

In the cases involving the rat poison and detergent, the amounts consumed were negligible and the children did not require emergency treatment. Fahey instructed the mother of the child with furniture polish in his eyes to wash the baby's eyes for 10 minutes. She later made a follow-up call and learned that the boy was fine.

Had a child eaten enough of a toxic substance to place him or her in danger, Fahey would have instructed the parent whether to induce vomiting, take the child to the nearest hospital emergency room, or both.

She then would have called ahead to the hospital to alert emergency room personnel that the poisoning victim was on the way.

At Fahey's fingertips is a file of microfiche cards that can be inserted into an electronic viewer to identify a poison by its brand name and its chemical composition.Each card gives specific symptoms the poison causes, and step-by-step treatment.

Known as Poisindex, the file enables Fahey to tell physicians what antidotes to administer. Litovitz said that more than 60,000 poisonings occur in the Washington area each year, 80 percent of them in children under 5 years old.

Most poisoning involving children can be treated safely at home, with followup provided by Poison Center personnel, the doctor said.

A survey by the center found that fewer than 8 percent of people in the Washington area would call a poison center in the event of a poisoning. Most would immediately go to a hospital emergency room. Litovitz said she hopes the opening of the new center will change this attitude.

"Without a poison center people would be filing into emergency rooms, paying large bills, waiting and getting upset, when so many of the poisonings do not require emergency room treatment," Litovitz said.

For the last 25 years, the area's only poison center was at Children's Hospital National Medical Center. Children's will now provide supportive services at the Georgetown poison center, as will many area hospitals.

Poison prevention is being emphasized at the new center, Litovitz said. She added that she hopes grant money soon will become available to begin prevention programs in the area's pre-school centers.

Green "Mr. Yuk" stickers placed on containers of toxic products can warn children, even those too young to read, to keep hands off, Litovitz said. The stickers are available by calling the Georgetown center.

Poison prevention measures such as the Mr. Yuk campaign and protective capping on medicine bottles have helped to reduce the number of poison-related deaths among children.

Since 1968, when poisoning statistics first were reported, the number of poison-related deaths in children under 5 has dropped steadily, according to Dr. Mark Fow, acting director of Federal Drug Administration division of poison control. The latest figures, from 1977, show 94 reported deaths, compared with 284 in 1968 nationwide. There are no statistics for the Washington area.

Still, children are poisoned. Litovitz blames "children's curiosity" and the fact that many parents do not realize how highly toxic some household substances and common items can be.

For example, two cigarette butts ingested by a child could prove fatal. Chewable multivitamins, which parents sometimes persuade children to eat by calling them candy, can cause liver failure if too many are ingested at one time.

Shady Grove Adventist Hospital in Rockville has its own poisindex system.The emergency room director there, Dr. Joseph Fortuna, said it is for the convenience of emergency room personnel and is not intended to duplicate the service offered at the Georgetown center.

The system at Shady Grove is getting a workout, Fortuna reports. It is used up to three times daily to aid in the treatment of poisonings, usually involving suicide attempts.