Nine Men Who Ran New York"" is the subtitle of this affable history of the birth of machine politics in the United States and how the toddler grew. Its most provident feature, aside from an easy style and good documentation, is the assumption that political machines are made of men. From that eternal battle between the bosses and Reform, it is the former, like Milton's Satan, who emerges more human in their admitted vice. Tammany was born as a patriotic society in the struggle against the British, the authors point out, and as it grew into a political organization under the tutelage of the dashing Aaron Burr, its hold on the people in the wards, districts, city and state was that it worked for them and their interests. The tale of Boss Tweed and his bookkeeper's $200,000,000 ""error"" has been told before, but the authors introduce great rogues such as Fernando Wood and Richard Croker who will be unfamiliar to the general public. Their sympathetic portrait of Carmine De Sapio is bound to make reformers' hair stand on end, but it caps a book that is popularly edifying entertainment.