Books: Not Fair RACHEL AND HER CHILDREN

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Jonathan Kozol does his best to keep cool while writing about homeless children. He tries to keep cool while reporting that there are some 500,000 of them in this wealthy land, a number slightly greater than the population of Atlanta, Denver or St. Louis. He tries to keep cool while reporting that federal support for low-income housing dropped from $28 billion to $9 billion between 1981 and 1986 and that legal evictions in New York City during one recent year totaled nearly half a million. He tries to keep cool while reporting that although New York owns more than 100,000 units of empty low- cost housing, it squanders $2,000 or more per family per month on squalid welfare hotels, and that the largest such hotel in New York is operated by (irony of ironies) South African "investors."

Kozol has greater trouble keeping cool when he actually goes into the Martinique Hotel, once a fashionable establishment on Manhattan's Herald Square, and starts talking with some of the 1,400 children (400 families) crammed in there. Like the girl he calls Angie, who is twelve and already skilled at fending off the men who want to buy her. "I may be little but I have a brain," she tells Kozol. He likes her. "She's alert and funny and . . . I enjoy her skipping moods," he writes. One day he learns that after her mother's welfare check failed to arrive, Angie was caught stealing food from the supermarket and was brought home in handcuffs. "When I came to this hotel I still believed in God," the mother tells Kozol. "I said: 'Maybe God can help us to survive.' I lost my faith. My hopes. And everything. Ain't nobody -- no God, no Jesus -- gonna help us in no way."

Perhaps the most terrible of all these terrible stories is that of Holly Peters, 24, who was raised in foster homes and worked for a time as a waitress, got married, went broke, lived on the dole. She was so run-down when her son Benjamin was born that he weighed only 4 1/2 lbs.; he survived in an oxygen tent, receiving blood injections. During that hospital stay, he contracted a viral infection that left him partly blind, deaf, hydrocephalic, brain damaged. After three months, the hospital released him and told Holly to give him phenobarbital when he had seizures. She took him to a welfare hotel near Times Square. Five weeks later she was evicted. She says it was because she wanted her husband to stay with her, which is against the rules. Holly and the baby slept several nights in the offices of the welfare bureaucrats.

The baby was having so many seizures by now that she took him back to the hospital. The doctors operated on him, inserting a shunt into his skull to relieve the pressure on his brain, then released him again. "It was evenin', like about four-thirty, five o'clock," Holly recalls, "and we was walkin' in the street. It was rainin', as a matter of fact. Not a warm night." Several ( days later Holly was still wandering around with her dying baby, being sent from hotel to hotel. "The place the shunt went in, his wound had gotten bad," she tells Kozol. "It was sunk in and you could see his skull. His eyes was sinkin' too."