Trinity's Child, by William Prochnau (Berkley, $3.95). A Russian missile lands in Northwest Washington and a dazed president in the ruins of the White House does battle for the survival of the human race. The weapons jargon is just right in this Doomsday thriller, which tours the American military commands as they fight a nuclear war. In case you didn't know, the title stems from the name of the first atomic weapon, that of the test device detonated at Alamogordo, N.M., in 1945.

The Tin Angel, by Paul Pines (Charter, $3.50). Pablo Waitz, proprietor of the Tin Angel jazz club, is in trouble. His partner has been shot to death. His club has been the target of arsonists and robbers. His mother is dying of cancer, and his lady friend is unhappy. Yet he can't seem to cut his losses. Despite ominous warnings from certain cocaine dealers, he is obsessed with finding the murderer and retrieving a missing $35,000. This is a tough, plausible thriller, short on gore, long on street smarts.

The Survivor, by Thomas Keneally (Penguin, $5.95). Forty years before this novel opens, Alec Ramsey went on a fateful Antarctic expedition. He returned, but the trek's leader -- and his great friend -- did not. Ever since Ramsey has been plagued by doubts as to whether he did all he could before abandoning his friend. Now another expedition -- to exhume and retrieve his friend's body -- is being mounted. In addition to prize-winning Australian writer Thomas Keneally's surefire plot, this 1969 novel features his keen sense of human psychology. Example: "The question again angered and harrowed him as would any preposterous accusation that happens to be a fraction of an inch wide of the preposterous truth."

Where the Rivers Flow North, by Howard Frank Mosher (Penguin, $5.95). Northern Vermont is where. These five short stories and a novella feature country people whose occupations center on the logging industry and whose lives tend to cluster at the unfortunate end of the spectrum. But the characters have dignity nonetheless, and Mosher writes about their lives, customs and environs in loving detail. One story begins with this evocative sentence: "Banked up snug against the stone foundation of a farmhouse, spruce boughs will catch and cradle the first hard snow of the year and hold it all winter, turning a cold wind and keeping in stove warmth better than any expensive sixing you can name." NONFICTION

Sports Illustrated Pitching, by Pat Jordan (Harper & Row, $6.95). This dissection of the classical style of baseball's highest art form discusses such esoterica as fastballs, curveballs, sliders, change-ups, screwballs, forkballs and knuckleballs. Other aspects of the duel between pitcher and batter, such as the catcher's signs and the pitcher's "blind spot," are included. Much light is thereby shed for the reader on the strategy and tactics of the national pastime.

The Neighborhood of Baseball: A Personal History of the Chicago Cubs, by Barry Gifford (Creative Arts, $7.95). It was the best of teams, it was the worst of teams, but it was Barry Gifford's team and why not? He was born in 1946, one year after the Cubs last won the National League pennant. This affectionate memoir of the Cubs remembers many sunny afternoons at Wrigley Field from the early 1950s to mid-1960s.

Asquith, by Stephen Koss (Columbia University Press, $10). Herbert Henry Asquith, the last Liberal prime minister of Great Britain, presided over the most brilliant cabinet of this century: Lloyd George at the Exchequer, Grey at the Foreign Office, Haldane at the War Office, Churchill at the Admiralty. Yet in 1916 Asquith was hounded out of Downing Street and his party never held power again. Was Asquith the victim or the agent of the Liberals' decline? The question has never ceased to fascinate historians. This life by a young American historian (whose untimely death shocked the profession) is widely regarded as the best in a long line of political biographies.

Mirror Makers: A History of American Advertising and Its Creators, by Stephen Fox (Vintage, $4.95). An exuberant history of that quintessentially American industry, advertising, from its founding in the early years of this century by such pioneers as J. Walter Thompson and Albert Lasker to its enshrinement on Madison Avenue, under such mogul hucksters as Raymond Rubicam, David Ogilvy, Jerry Della Femina and Shirley Polykoff.

Washington Embassies: A Guide for the Private Sector, by Carl Bartz (Washington Association Research Foundation, 1133 15th St. NW, Washington, D.C. 20005, $15). What do the 133 foreign embassies in Washington do, anyway? This guide to their activities for American businessmen spreads a wide net and catches a great dal of information, e.g. which embassies publish trade newsletters. The guide's aim is to help U.S. business sell abroad. And it shows how a nation's ambassador is, in a manner of speaking, a master salesman himself.

American Fictions 1940-1980: A Comprehensive History and Critical Evaluation, by Frederick R. Karl (Harper & Row/Colophon, $19.95). One way to assess what Karl is up to in this survey of contemporary fiction is to consider what he does to Gore Vidal. The witty essayist and best-selling novelist is mentioned only twice, both times in footnotes. The first note explains why Vidal did not make it into the main body of the text -- because his novels look to the past in subject matter and technique and because he has "repeatedly disparaged" most of the novelists considered in the book for "running with the academic pack." The second note points out that when he wants to, Vidal can write brilliantly about avant- garde fellow-novelists, as witness his fine essay on Italo Calvino. Karl himseldeeply in sympathy with the experimental novel, and his book is a lucid and painless introduction to its recent triumphs and "sensational failures."