This is an outstanding book, an uncommonly well-written examination of the whole chain of events that led to the atomic bombing of Japan and the nuclear arms race. It is balanced, well-researched and complete. Mr. Batchelder is both a mathematician and a minister, and he has examined the ""Irreversible Decision"" with the cold logic of the former and the ethical considerations of the latter. For those Americans who may doubt it, the author proves that more than twice the 110,000 Japanese who died under the two A-Bombs would have been killed in conventional air raids and other action had the war continued for another three months and, as he believes, had the country capitulated without an invasion. This does not take into account the other countries involved. The author believes the atomic bomb was not a significant factor in Japan's defeat (since the country was really beaten) but it was the decisive factor in enabling the moderates to force a surrender. Turning to the question of whether the bombs could not have been used in some less destructive way, Mr. Batchelder finds that the second bomb was unnecessary and he concludes the first might have been dropped on a more purely military target than Hiroshima. Reviewing the matter on broad, ethical grounds, the author concludes that military thinking dominated the whole series of decisions that ended in the bombings. Had political (and ethical) thinking been introduced early enough, another course might have been possible. However, it is difficult to see, as the author unfolds the drama, how the participants could have acted any other way than they did. He suggests that for the future we might well have our ethical position more clearly in order before the press of events brings us face to face with such monumental decisions again.