In this rugged hardpan of north China known for poverty and coal, Zhang Yi had but two frail daughters to help scratch out a living. When his wife became pregnant again, he hoped for a son, brushing off official threats of penalties for an unauthorized third child.

But his wife bore another girl, and Zhang recalculated the cost. He packed the child in a cardboard box, left her for dead and informed authorities that she was stillborn, according to family planning officials here.

The baby girl became another victim of the ugliest side effect of China's war against overpopulation -- female infanticide.

Official population statistics indicate a loss of more than 230,000 baby girls in 1981, a casualty list that is said to have grown dramatically in more recent years as the Communist government tightened its nationwide policy limiting Chinese couples to one child. Authorities have refused to reveal sex ratios of newborns after 1981.

The one-child policy seeks to stop runaway population growth from derailing the nation's modernization effort: China's 1,038,000,000 people already make up 22 per cent of mankind living on just 7 per cent of the world's arable land. In their zeal to limit births, however, local officials often resort to coercion, encourage widespread abortion and intrude into the reproductive lives of most married couples.

As it runs up human costs, the policy has aroused a strong backlash among China's usually compliant citizenry. It has expressed itself in physical attacks against birth control authorities, acts of subterfuge and more serious criminal behavior.

Female infanticide is the most extreme form of resistance to the one-child controls, a desperate act by parents squeezed between official restrictions and the traditional preference for male offspring.

Many Chinese think that if they can have only one child, better to give away, abandon or even murder a baby girl and try again for a boy.

Sons traditionally are prized for passing on the family name, a Confucian legacy enshrined in the saying: "There is no behavior more unfilial than to have no male descendants."

In China's vast countryside of 800 million peasants, moreover, boys serve as social security for elderly parents. Without pensions or old-age homes, they have only their sons to work the fields and handle the beastly burdens of rural life -- hauling water, cutting firewood, feeding livestock and cleaning outhouses.

Daughters, by custom, move in with their husband's parents after marriage and are known colloquially as "goods on which one loses." Chinese society already has begun to reflect the tragic dimensions of this bias for males, with five boys born for every girl in some places and a nationwide ratio of male to female births that greatly exceeds world standards.

The frantic push for boys in a one-child society can be charted in official accounts of drowning, suffocation, poisoning and desertion of baby girls. It is seen in the popularity of scientific fetus tests and superstitious rites to forecast the gender of the unborn child -- with abortions following for women thought to be carrying a girl.

Couples try again and again for a son, enduring heavy fines, loss of jobs and official harassment.

Even though the male chromosomes determine the sex of a child, women absorb the blame if the baby is female. They often pay a price of beatings, scorn by their own family and divorce. The pressure reportedly has driven some wives to suicide, others into mental institutions.

The government in Peking decries female infanticide and propagates equality of the sexes, warning of the dangers to future generations of a lopsided sex ratio.

But few cases of baby killing or wife abuse are known to be prosecuted, and the central government appears to be stymied by negligent local authorities who often dismiss such offenses as "family conflicts."

Nor does Peking have a strategy for reconciling its one-child rule with the common yearning for boys. It insists on birth control for the good of posterity. But it offers no practical solution to China's millions who cannot secure their own futures without old-age benefits or sons.

Liu Chunsan, a farmer from east China, threw his four-year-old girl down a well two years ago, believing that his wife could be given another chance for a boy if the couple were childless. Sentenced to 15 years in jail, he told a Chinese reporter that he wanted a son as a hedge against the future.

"I loved my daughter," Liu said in a prison interview. "But sooner or later she would get married and leave me for a husband. I would have supported her for 20 years for nothing."

Female infanticide was known to China in the pre-Communist period, especially during times of famine. But it seemed to disappear until the one-child policy increased the cost of bearing a daughter. The Numbers on Female Infanticide

No statistics on female infanticide are published by China. But an analysis of national census data compiled in 1982 helps to quantify the problem. The census was the most comprehensive ever taken in China and only the third of the Communist era. The earlier surveys of 1953 and 1964 were separated by years of political turmoil.

To calculate the extent of female infanticide, western demographers base their analysis on a natural sex ratio at birth of 106 males for every 100 females, or 1.06, which is the internationally recognized norm.

China's earlier censuses show even lower ratios of boys -- 1.04 in 1964 and 1.05 in 1953 -- among babies under a year old.

The most recent census, however, recorded 1981 births of 10,765,292 boys and 9,924,412 girls, representing an unusually high sex ratio of 108.5 male to 100 female, or 1.085.

Comparing the actual number of female births to the world norm indicates a loss of 232,000 baby girls in 1981 alone.

An official Chinese survey revealing sex ratios by order of birth in 1981 points to a pattern of female infanticide. Sampling .01 percent of births, the study published last year found the proportion of male babies rising dramatically among unauthorized second-born, third-born, fourth-born and fifth-born children.

If parents had to be penalized for violating the one-child policy, they apparently wanted to make sure they got a son in return.

For first-born children, the sex ratio actually fell below the world norm of 1.06, according to the survey.

But it soared to 1.15 for second-born children in cities. In rural areas, where the ban on second children still was enforced laxly in 1981 and parents may have felt less pressure to have a son on the second try, the ratio for third or later births was 1.12.

Western demographers say that while males are statistically favored among first births, the odds of having a boy actually decrease for second and later children.

The authorities have refused requests for gender breakdowns of births in recent years. But Chinese population experts in Peking have revealed privately to western demographers that the national sex ratio of newborns rose to 1.09 In 1982 and 1.11 In 1983.

Applying those unofficial ratios to total births listed for those years indicates a loss of almost 300,000 baby girls in 1982 and 345,000 in 1983.

Chinese officials are contradictory in their analysis of female infanticide. While acknowledging that the problem is serious, they contend that the 1981 sex ratio does not necessarily reflect widespread killing of infant girls.

Propaganda chief Shen Guoxiang, of the state Family Planning Commission, said in an interview that Chinese studies show the 1.085 ratio to be "normal." When he was reminded of the international norm and of earlier Chinese censuses showing much lower proportions of male to female babies, he refused to respond and stalked out of the interview.

A partial explanation for the sexual imbalance may be under-reporting of girl babies. Fearful of losing their chance for a son, peasants in remote areas may not inform authorities of the birth of daughters. As a result, the true number of female births is not reflected in statistics.

But a more sinister explanation comes to light in official reports and scores of interviews over the past three years.

"At present, the phenomenon of butchering, drowning and leaving to die female infants is very serious," said the Communist Party newspaper, the People's Daily, in January 1983.

Last year investigators for a local women's federation visited rural counties of Anhui Province in east China. They reported a "serious disproportion" of sexes in some places, where baby boys outnumbered girls by five to one and female infanticide was rampant.

One place called Plum Village had eight births in the first quarter of 1982. Three were boys who were healthy. Of the girls, however, three were drowned and two were deserted.

In Guangdong Province, a reporter for the Southern Daily newspaper uncovered 210 cases of female infanticide in just two counties in 1982. Some peasants, he wrote, "place a bucket in front of the delivery bed, and if the newborn is a girl, she is immediately drowned in the bucket.

"Some people conspire with the midwife. If the baby is male, she is told to do a good job. If not, she must drown or choke it. Some suffocate girl babies with heaps of rags."

There are tales in the official press of baby girls who were forced to swallow insecticide or were bound in burlap sacks and thrown into the river. In the northeast industrial city of Tianjin, a man bit off part of his eight-month-old daughter's nose, planning to take advantage of a loophole allowing a second child if the first one is born deformed. Other baby girls reportedly are left to die in forests, in caves, on railway tracks or dumped into garbage cans and public toilets.

In the dreary coal city of Datong where Zhang Yi deserted his daughter, 26 of his neighbors in North Village Township also had unauthorized third children in 1981 -- half boys and half girls, according to Communist Party Secretary Chen Purong. All of the boys thrived, but four of the girls met the same fate as Zhang's daughter -- listed as stillborn and abandoned, said Chen.

"No one wants to pay a fine for a girl," explained township director Zheng Fen.

Many baby girls never make it to birth. In the countryside, superstitious peasants pay self-styled sorceresses to divine the sex of a fetus. Pregnant women with unusally big bellies and a craving for sour foods are thought to be carrying girls. Without the aid of more modern tests to determine the gender of their babies, they simply have abortions.

Women who have access to China's few well-equipped hospitals resort to amniocentesis, a test to determine the health of a fetus that can also predict gender. According to a magazine in the northwest province of Gansu, fetus tests are so commonly abused that "the male baby population is rapidly increasing."

Some women have several abortions until they successfully bear a son; some just keep having babies -- up to nine girls in the case of unfulfilled mothers from Anhui Province.

"Why do we keep having babies and risking our health?" asked 15 Anhui women in a 1983 petition published in the People's Daily to explain why they had so many children. "Because there is no place in this world for those without sons. Even if it means death, we will keep trying for a son so that we may hold our heads high."

Failure to have sons can ruin a woman's life. While this dilemma for Chinese women is as old as China, it is intensified by the one-child policy. In the old days, women kept trying until they had a son. Now they have one chance. Unsuccessful wives have been poisoned, strangled, bludgeoned and socially ostracized, according to official reports.

A transportation worker in Shenyang named Jiang Yujie, 28, whose husband beat her for having a girl, reportedly attemped suicide in April 1983 by lying on a railroad track. When she was pulled off the tracks in time, her mother-in-law taunted her: "If you want to die, go drink DDT," the old woman was quoted as saying. "For every one like you who dies, there is one less to worry about."

Jiang took her life a few days later by drinking seven bottles of the insecticide. Weeping Over the Birth of a Girl

The presure on women is so great that many openly weep on learning they have borne a girl. Doctors say they often see families rejoicing over the birth of a son but dejected if the child is female. Some refuse to visit mothers in the hospital if they have delivered a girl.

Wang Yanjuan, 28, of Shanghai, was so distraught after giving birth to a girl that she threw her from the hospital window in July 1982, yelling to would-be rescuers, "Don't save her. Just let her die," according to the official journal Society.

"All of the other mothers in my hospital room had boys," Wang later told a judge. "Every time their families came to visit, they whispered about me. I really couldn't stand it anymore."

In Peking, a 37-year-old woman died in a mental hospital last October, having refused to eat or speak since her husband strangled their newly born daughter last June, according to her friends.

After years of silence, China's government has finally come to the defense of baby girls and their mothers. The state-run press reports cases of female infanticide along with the message that "boys and girls are equal." Billboards promoting the one-child ethic feature a pigtailed girl, striding hand-in-hand with prosperous-looking parents.

In a few areas, small monetary incentives are given to young couples who live with the wife's parents, and monthly bonuses are awarded to couples with an only daughter. Daughters have been given the same constitutional responsibility as sons to support elderly parents.

Officials even bend the one-child rule in special cases to accommodate male preference. In sparsely populated areas, couples with an only daughter are permitted to try again for a son. Some provinces quietly have begun allowing a second child if the wife's family has no male heirs, if the wife or husband is an only child or if either is disabled.

When it comes to punishing female infanticide, however, the government shows far less commitment. Despite a few well-publicized cases, the vast majority of baby killings and desertions are not prosecuted, officials say.

Although the Women's Federation of Anhui disclosed numerous drownings and abandonments in 1983, federation vice chief Li Mengliu said none of the findings was pursued by law enforcement authorities.

In the southern port of Zhanjiang, 12 baby girls were killed and 17 abandoned in 1982, according to Deputy Family Planning Director Wang Lianzhang. He said offending parents were criticized, but no one was prosecuted.

"We couldn't find convincing evidence," Wang said. "These cases are difficult to investigate."

At least part of the difficulty, however, appears to be official negligence at the local level. According the People's Daily, local authorities routinely regard female infanticide and wife abuse as a "family conflict," falling back on an old saying: "Even an upright official finds it hard to settle a family quarrel." These officials earn bonuses for assuring low birth rates in their factory or farm. If female infanticide means one less child, they have little incentive to stop it.

The Southern Daily reporter who uncovered widespread female infanticide in Guangdong Province said very few of the 210 murders were investigated. He reported that local officials were "insufficiently forceful in attacking those cases."

"What is even more shocking," he asserted, "is that some officials are sympathetic and supportive of this kind of criminal act. "They say, 'with the one-child policy, it is natural that people want a boy.' ".