In the 1830s the Belgian astronomer Adolphe Quetelet applied the law of frequency of error to people. According to many histories of statistics, Quetelet's revelation that measurements of human bodies followed what we now call a normal distribution inspired the creation of modern statistical tools for studying society. It was not, however, until the work of figures such as Francis Galton some fifty years later that population statistics, in a highly mathematized form, developed into what historians of science recognize as a discipline proper. The question of what happened to population statistics in that intervening half-century is the concern of Libby Schweber's Disciplining Statistics. Contrasting the fortunes of two similar mid-nineteenth-century projects – vital statistics in England and demography in France – she traces ultimately unsuccessful disciplinary claims with the overall aim of explaining the factors that shape such activity. A sociologist by trade, Schweber argues that we must explain the emergence of disciplines without overemphasizing the role played by, for example, disciplinary gatekeepers or epistemological criteria. Instead we must recognize people, politics, epistemology and institutions as being interrelated in specific contexts that mould the development of scientific knowledge.

Schweber's account of early attempts to form disciplines around population statistics is divided into four parts, with her two largely separate narratives in chronologically comparative sections. We learn that in nineteenth-century England vital statisticians enjoyed a great deal of success in promoting their work. They not only gained a foothold in organizations such as the British Association for the Advancement of Science (BAAS), which created a statistical section in 1834, but also came to play an important role in political debate and legislation, particularly regarding public health, as William Farr's guidance of statistical practice at the General Register Office from the late 1830s until 1880 demonstrates. The parallel story of French demography, however, is one with fewer successes to speak of. Demographers were shut out not just from political debates in France, but from scientific ones as well, and their efforts battling these rejections amounted to little.

Why, Schweber asks, were seemingly identical projects greeted in such different ways? Her answer to this question lies in the institutional, political and epistemological consequences of a fundamental difference between France and England in their styles of reasoning about numbers. In France scientific knowledge was seen as providing an exact fit between reality and numbers. Demographers therefore struggled to convince their audiences that the homogeneous statistical population that formed the basis of their work was an accurate representation of society. For example, prominent critics asked what could be learnt from the demographer's figures, such as averages, which had no identifiable physical manifestation. By comparison, the vital statisticians in England were untroubled by these concerns. The English instead made instrumental use of vital statistics in political debates about social issues such as the public health campaigns of the sanitary movement in the 1840s. Consequently the disciplinary activity of vital statisticians was shaped by debates about whether their work was best understood as objective science or as politically motivated opinion.

Schweber's analysis provides many interesting insights into debates during a period when there were few strict boundaries between statistics, politics, political economy and a variety of projects that fell under the general term ‘social science’. Her comparative approach successfully highlights the differences between France and England, in terms of politics, institutional arrangements and attitudes towards statistics, and in a way that helps support her argument about the interaction of individual actors and general contexts in the development of disciplines. However, the narrow focus Schweber adopts undermines the flow and force of her argument at crucial points. The problem is most severe when she writes on aspects of nineteenth-century social science that have been the subject of important recent studies. Quite rightly recognizing work such as Lawrence Goldman's on the Social Science Association, Schweber frequently loses her thread as she attempts to explain how the vital statisticians dealt with accusations that their work was unscientific. Whilst accepting that the agenda for statistics was often set in other fields, as other scholars have shown was the case, Schweber fails to explore the significance of this point any further. This neglect becomes most apparent in Chapter Eight, where she addresses an attempt led by Galton in the late 1870s to disband the statistical section of the BAAS. Repeatedly informing us that the course of those events and the context of their outcomes was deeply coloured by political economy, Schweber at no point offers an in-depth analysis of the aspects of political economy to which she alludes. As a result, the sporadic and casual references to people such as W. S. Jevons are likely to be a mystery to everyone but the specialist.

Further to these oversights, Chapter Eight is also home to the most serious error to be found in Disciplining Statistics. Concentrating on events at the BAAS in the late 1870s, Schweber attempts to trace a protracted exchange of views between Galton and Farr and their supporters in the periodical press (pp. 182–9). However, one finds that few of the endnotes accurately cite the articles Schweber quotes from. As a result of a wayward use of ‘ibid.’, anyone wanting to return to the primary source material is faced with the challenge of first figuring out where the referenced passages are really to be found.

On finishing Disciplining Statistics one is left with the feeling that, at 225 pages of text, it is ultimately too short to deal comprehensively with its chosen subject matter. Yet overall it must also be recognized that Schweber succeeds in terms of many of the goals she sets out at the beginning of her study. With the aid of an excellent opening historiographical survey in particular, we are reminded of the issues that divide scholars when it comes to discipline formation. Indeed, Schweber's own argument about how best to approach such subject matter offers many important insights for historians of science to consider.