The history---the bitter defeats and final successes---of Project Vanguard is here recounted by a scientist-writer attached to the project from its early days in 1955. Using what is becoming a standardized technique for books of this sort, he starts with a major event--the failure of the Dec. 6 firing---and works backward to the beginning of the project. The story is a fascinating one. It includes inter- service rivalries, then government-private enterprise conflicts over who should do what in getting a device in orbit. It points up the results of newspaper attacks on the way the project was handled, especially spurred by Russia's successful Sputnik efforts. And it ends with a reasonable note of triumph on the successful St. Patrick's Day firing- 1958. Although semi-technical in language, the book is happily filled with anecdotes which will make it readable to a fairly wide audience.