In most of the European states during the first half of the nineteenth century, the use of numbers as a language to decode societies facing industrial und urban changes gave rise to the idea that statistics could be a powerful tool to construct and manage the social world. Libby Schweber introduces her book by reminding readers that despite this enthusiasm for numbers there were varied and competing conceptions of statistics. The two main ones had origins in the eighteenth century: political arithmetic and descriptive statistics. The first, rooted in the calculations of probability, was extended to estimation and came to be strongly distrusted, while the second became official through the creation of statistical bureaus.

Stimulated by the works of Quetelet, who merged both conceptions, social scientists defined a new approach to statistics that relied on a probabilistic or inductive mode of reasoning, and sought to identify laws and patterns of causality. When this scientific approach spread across Europe it met with different receptions, which scholars of styles of reasoning have analysed by stressing differences between liberal and authoritative political systems. Schweber's study contrasts sharply with that approach by comparing the two liberal states of England and France. This topic has been little studied for the period she investigates, from 1830 to 1880, and her sociological approach of focusing on the notion of discipline is also unusual in the history of statistics.

In the mid-nineteenth century new conceptions of statistics were promoted in both France and England, but with differing success. In France, Achille Guillard and Adolphe Bertillon introduced a new approach called “demography,” which saw statistics as an inductive science in search of causality. They submitted their method to two prominent institutions—the academy of political and moral sciences, and the medical sciences. But over several decades its claims were dismissed on the grounds that statistics was merely a descriptive science. In England during the same period, on the other hand, William Farr succeeded in imposing an official administrative statistics under the name “vital statistics,” which relied on induction and an experimental mode of reasoning. In France statistics was confined to a representative role, while in England the field became an instrument of social reform.

To highlight this striking divergence, Schweber takes from the sociology of science the notion of discipline, and with it she draws attention to the rules regarding which activities can qualify as scientific. Thus she explains the different functions of statistics in each state mainly in terms of institutional logics. For instance, in France the academies dominated, while within English scientific societies the scientific, political, and social elites were linked. In addition to this sociological frame, Schweber profitably employs the notion of disciplinarity to consider claims for recognition. In France, attempts were first made to integrate demography into instituted disciplines, and when these failed it was promoted as a separated discipline. By the end of the century, however, both demography and vital statistics had lost their specificity as disciplines, though they were acknowledged as statistical modes of reasoning within other disciplines, and as aspects of professional training. Schweber's book sheds new light on the history of national traditions of statistics, while at the same time presenting a model for understanding other historical episodes within a similar comparative frame.