STRAIGHT UP OR ON THE ROCKS: A Cultural History of American Drink by William Grimes (Simon and Schuster: $18; 183 pp.). You can just hear the tipsy spirit of journalist H. L. Mencken in these pages, toasting the cocktail as "the greatest of all the contributions of the American way of life to the salvation of humanity." So in love was Mencken with this American invention, New York Times culture reporter William Grimes writes in this witty and elegant book, that he once hired a mathematician to compute how many cocktails could be made from the ingredients available at a respectable bar. The total was 17,864,392,788. "We tried 273 at random," he reported, "and found them all good." Perhaps in an effort to portray his humble subject as worthy of a serious history, Grimes reads too much significance into what is essentially a spoonful of sugar and a dollop of bitters to help the medicine go down: "Cold, clean and slightly astringent," he writes at one point, the cocktail "represents a decisive break with the pre-industrial past." This is not to say that cocktails lack a genuine and compelling history. Grimes argues persuasively that they first emerged in America because our "competitive and mobile" business culture required us to "develop social forms that promote quick and effortless acquaintance rather than strong, lasting ties." At the same time, cocktails also have long afforded Americans the ultimate escape from business, as we see in this poem Grimes quotes from the San Francisco News Letter of Dec. 12, 1904: "When the office clock is showing / That the time is half past four, / I feel I must be going / Where I've often gone before, / For I need no rough awakening, / And I want no whistle's hoot, / To say my thirst needs slaking / On the cocktail route."