This paper explores the relationship between operations research (OR) as practised during the Second World War and the claims of many of its proponents that it constituted an application of scientific method. It begins with an examination of the pre-war work of two of the most notable leaders in wartime OR, the British experimental physicist Patrick Blackett and the American theoretical physicist Philip Morse. Despite differences in their scientific work, each saw science as an essentially creative act relying on the skill and judgement of the individual scientist in the deployment of rational methods for the development of legitimate conclusions. When scientists began to study military operations, their investigations were defined by the technically sophisticated heuristic practices already surrounding military planning. They did not seek to replace these practices with their own rational methods. Rather, they became scholars of the military's methods and adapted their pre-war experience by shifting their self-disciplined attitude to their own work to bodies of military knowledge. Thus scientists learned so well to navigate an alien heuristic system that investigations they conducted within it took on the characteristics that they judged defined scientific work.

In 1823 the astronomer Friedrich Wilhelm Bessel gave notice of an observational error which is now known as the personal equation. Bessel, however, never used this phrase to characterize the finding that when noting the time of a certain event observers show a considerable ‘involuntary constant difference’. From this starting point the paper develops two arguments. First, these involuntary differences subverted the concept of the ‘observing observer’. What had previously been defined as a reference point of trust and precision turned into a source of an error that resisted any wilful intervention. Second, and contrary to later suggestions, Bessel's findings did not initially lead to discussions and measures of permanent control. In everyday astronomical work the influence of such differences could be avoided by comparatively simple means. Taking this into account offers a new perspective both on the history of the personal equation and on the significance of Bessel's findings. Whereas the former has to be read as the history of a rather particular reaction to the phenomenon of constant differences, the latter is connected with a rather fundamental transition in the epistemology of the observer.

This paper documents an important development in Robert Boyle's natural-philosophical method – his use from the 1660s onwards of ‘heads’ and ‘inquiries’ as a means of organizing his data, setting himself an agenda when studying a subject and soliciting information from others. Boyle acknowledged that he derived this approach from Francis Bacon, but he had not previously used it in his work, and the reason why it came to the fore when it did is not apparent from his printed and manuscript corpus. It is necessary to look beyond Boyle to his milieu for the cause, in this case to the influence on him of the Royal Society. Whereas the Royal Society in its early years is often seen as putting into practice a programme pioneered by Boyle, this crucial methodological change on his part seems rather to have been stimulated by the society's early concern for systematic data-collecting. In this connection, it is here shown that a key text, Boyle's influential ‘General Heads for a Natural History of a Country, Great or small’, published in Philosophical Transactions in 1666, represents more of a shared initiative between him and the society than has hitherto been appreciated.

The focus of Newtonian scholarship has shifted over the last couple of decades. Compare any relevant collection of studies from the third quarter of the twentieth century with a recent one such as Newton and Newtonianism: New Studies (2004), edited by James Force and Sarah Hutton, and the changes leap to the eye. Newtonian studies have been traditionally concerned with Newton's writings and achievements in the fields of mechanics, optics and mathematics, and with his influence on the subsequent development of these disciplines – a line of enquiry that was nourished by the systematic study of unpublished materials in the post-war period and has reached a high degree of technical sophistication. In this perspective, the priority attributed to Newton's natural philosophy and mathematics reflects the assumption that Newtonian ‘science’ should be granted an unquestioned pre-eminence over the rest of his much varied production, as the latter contributed ‘little or nothing to our twentieth-century world’. The landmarks of post-war Newtonian scholarship thus aimed at the identification, analysis and interpretation of Newton's ‘scientific’ manuscripts, carefully separated from the rest of his densely written and sometimes enigmatic paperwork. Establishing such a demarcation certainly made sense within a historiographical practice directed primarily at the reconstruction of Newton's contribution to the making of modern science, and was sustained by the perception of an essential continuity between Newton's alleged main concerns and the practices of twentieth-century physics and mathematics.

This paper takes up the concept of ‘crisis’ at both historical and historiographical levels. It proceeds through two examples of periods that have been described by historians of physics using a language of crisis. The first examines an incipient German theoretical-physics community around 1900 and the debates that concerned the so-called ‘failure’ of the mechanical world view. It is argued, largely on the basis of what is now an extensive body of secondary literature, that there is little evidence for a widespread crisis in this period. Abandoning the term as both description and explanation, one comes to the far more intriguing suggestion that the conflict over foundations was not evidence of a divisive dissonance but rather of collective construction. What has been termed crisis was, in fact, the practice of theoretical physics in the fin de siècle. The second example is the period either side of the advent of quantum mechanics around 1925. Different subgroups within the theoretical-physics community viewed the state of the field in dramatically different ways. Those, such as members of the Sommerfeld school in Munich, who saw the task of the physicist as lying in the solution of particular problems, neither saw a crisis nor acknowledged its resolution. On the other hand those, such as several researchers associated with Niels Bohr's institute in Copenhagen, who focused on the creation and adaptation of new principles, openly advocated a crisis even before decisive anomalies arose. They then sought to conceptualize the development of quantum mechanics in terms of crises and the revolutions that followed. Thomas Kuhn's language of crisis, revolution and anomaly, it is concluded, arises from his focus on only one set of theoretical physicists. A closer look at intra-communal differences opens a new vista onto what he termed ‘normal’ and ‘revolutionary’ science.