In this detailed and challenging book, George Smith and Raghav Seth (hereafter referred to as “the authors”) explore the way in which Jean Perrin’s experiments on Brownian motion contributed to knowledge of molecules. Within philosophy of science those who wish to take a realist as opposed to an instrumentalist stance with respect to scientific knowledge frequently invoke Perrin’s experiments on Brownian motion as providing decisive evidence for the reality of molecules. The case developed here has relevance for the philosophical debate. However, the authors do not tackle it head on. Rather, they seek to clarify the nature of the relevant science itself and to pinpoint exactly how Perrin’s study of Brownian motion contributed to and changed it. When they investigate the state of development of the knowledge of molecules at some historical juncture the authors put themselves in the shoes of a senior scientist required to write a review article on the state of development of the science at the time. The significance of the findings reported in this way for the philosophical debate about realism is addressed only in a short postscript. Nevertheless, any philosopher hitherto who wishes to take a stand on the relevance of Perrin’s studies to the debate about realism will need to take heed of the findings here. All of the publications on the matter that preceded its publication will need to be reconsidered, my own included.

Research for Brownian Motion and Molecular Reality: A Study in Theory-Mediated Measurement was triggered by an article by Bas van Fraassen, “The perils of Perrin in the hands of philosophers.” Philosophical Studies, published in 2009. In it van Fraassen maintains that with his experiments on Brownian motion, Perrin offered empirical grounding for the kinetic theory by measuring its parameters, the mean kinetic energy of molecules and Avogadro’s number, but did not do more than that. Van Fraassen resists the conclusion that Perrin established knowledge of molecular reality. The authors follow van Fraassen in focusing on the way in which Perrin’s experiments provided evidence and what they provided evidence for. They develop an account of “theory-mediated measurement” that captures the way in which Perrin’s experiments, when taken in conjunction with work by others, much of it independent of Brownian motion and the kinetic theory, was sufficient to establish significant knowledge of molecules by around 1913. The authors pay particular attention to the details of the way in which values of Avogadro’s number by independent methods converged, and to such a degree that Perrin’s values for that number could be seen to be about 10 percent too high.

Their argument is enriched by the extent to which they draw on historical dimensions of the debate centred on Perrin’s work that have not been adequately recognised. For instance, they take a close look at the way in which the kinetic theory was assessed by leading scientists of the time, such as Oskar Meyer, Wilhelm Ostwald, and Walther Nernst, noting that they were well versed in the degree to which the kinetic theory had experimental support but were also mindful of its inadequacies, the latter stemming from the science itself rather than the imposition of some metaphysical or epistemological viewpoint. In the case of Perrin’s work the authors make the point that Perrin’s book Atoms is not a reliable source because of its polemical nature and because it was a “moving target” insofar as Perrin rewrote it a number of times after its first appearance, a fact that is not made clear in the widely used English translations. They focus rather on Perrin’s journal articles and especially on his contribution at the Solvay Conference of 1911, prepared for a highly select audience of distinguished scientists. The authors analyse the various methods of measuring Avogadro’s number in more discriminating detail than is in evidence in previous literature on the topic. This enables them to see those determinations as examples of confirmation of knowledge of atoms and molecules via theory-mediated measurement, which they construe as a prelude to the consolidation of quantum electrodynamics by reference to a web of mutually independent physical constants, the measurement of which converges on values agreeing up to 10 significant figures.

A very revealing way in which the authors assess the role of experiment as providing evidence for theoretical claims is to separate the question of the status of experimental knowledge of Brownian motion itself from the bearing of that knowledge on the molecular-kinetic theory. By way of his ingeniously designed experiments, Perrin was able to show that the motion of the granules exhibiting Brownian motion is random in a technical sense. Assuming that the changes in motion of the granules were perfectly elastic and governed by Newton’s laws of motion, he derived an equation that described the equilibrium of the concentration of granules in an emulsion as a function of height arising from the balance between the net buoyancy weight of the granules and a vertical force arising from the decrease in concentration of the randomly moving granules with height, confirming in a number of mutually reinforcing ways that the equation correctly described the measured concentrations. By feeding into the equation measurable parameters, such as the concentration of granules as a function of height and the radius of the granules, Perrin was able to calculate the mean kinetic energy of the molecules. His results implied that at a given temperature the mean kinetic energy is a constant, independent of the nature of the density of the material of the granules, their radius, their concentration, and the density of the liquid in which they were suspended. Following the lead of Einstein, Perrin was also able to avail himself of an equation linking the mean displacement of granules per unit of time to their mean kinetic energy on the assumption that the motion of the granules through the suspending liquid obeys Stokes’ law. This gave Perrin another way of calculating the mean kinetic energy of the granules, with results that meshed with those obtained from observations of sedimentary equilibrium. Yet another way of calculating that mean kinetic energy was available once the gross diffusion of granules through a liquid prior to the establishment of equilibrium was measured, and again this third measure was in agreement with the previous two. This identification of bulk diffusion as the statistical outcome of the random motions of individual granules was a novelty that was quite independent of the kinetic theory. The authors describe all this in great detail and to great effect.

While the consideration of knowledge of Brownian motion independent of kinetic theory is an instructive way of exploring the connection between theory and evidence, this is not the way in which Perrin and his contemporaries viewed the situation. They saw the experimental exploration of Brownian motion as a way of testing implications of the molecular-kinetic theory. For once the cause of the motion of the granules is attributed to collisions with the random motion of molecules of the suspending liquid, and the granules are treated as large molecules from a mechanical point of view, then the details of Brownian motion identified by Perrin’s experiments can indeed be seen to be consequences of the kinetic theory. In particular, the mean kinetic energy of granules measured by Perrin by mutually supporting methods is in fact a measure of the mean kinetic energy of molecules. And once Perrin knew the latter, he could calculate Avogadro’s number. Perrin supported the molecular-kinetic theory by experimentally confirming its predictions in a new area.

The authors have reservations about seeing things in this light. They liken the view that a theory can be established by confirming its predictions to “inference to the best explanation,” a position they do not hold in high regard, reminding us on more than one occasion that the inference to the identification of light as transverse vibrations in an elastic aether, widely accepted in the 19th century, proved to be erroneous. However, it should be recognised that before a theory can be said to successfully explain a phenomenon or be confirmed by the success of its predictions, stringent demands must be met. Within science, the explanation of a phenomenon by a theory should only be accepted if there is independent support for that theory whilst the auxiliary assumptions that need to be added to a theory to make predictions possible should also be supported by independent evidence. Perrin’s support for the molecular-kinetic theory by his experiments on Brownian motion lived up to strong demands of this sort. The molecular-kinetic theory that he adopted already had an impressive range of support and explanatory success, and, as Perrin himself stressed, his predictions followed by adding very little in the way of auxiliary assumptions to the basic tenets of the theory. Perrin added to the case for the molecular-kinetic theory by applying it in a new area in a number of mutually supporting ways. If this did not constitute significant support, then it is difficult to see how a theory can ever be supported by making successful predictions.

Even if the authors were to accept what is said in the previous paragraph, there is much that remains to be said on their behalf. For as they make clear, there was more to the case that was made for the molecular-kinetic theory around the time of Perrin’s experiments than the confirmation of its predictions with respect to Brownian motion. What made the case for the molecular-kinetic theory so strong by around 1913 was the way in which atomic and molecular theory—in a number of areas, Brownian motion being just one of them—were mutually supportive. Already in his address to the Solvay Conference in 1913, Perrin was making much of the fact that calculation of Avogadro’s number from electrolysis and measurement of the charge on the electron were in agreement with his own measurements from Brownian motion. By that time there were other reliable methods for measuring Avogadro’s number from other phenomena, such as radioactivity and blackbody radiation. One of the strengths of the book under review is the discriminating detail the authors bring to the various measures of Avogadro’s number. Not all of them lived up to high standards because they relied on assumptions lacking independent support. However, the authors are able to identify a few measures, some based on the charge of the electron and others on radioactivity, that could be judged to be particularly reliable and the results of which converged. Interestingly, from the point of view of the emerging consensus, Perrin’s own results were about 10 percent too high, although later measures involving Brownian motion by Harvey Fletcher in 1914 were more in keeping with it.

I found the most interesting theme to be the emphasis placed on the importance of converging measures of physical quantities, measures that can involve theory at a number of levels. A point not singled out for mention by the authors is Perrin’s insistence that basic measures of such quantities as the density of the material of the granules, the density of the suspending liquid, and the radius of the granules, which needed to be fed into his equations, be measured by at least two and sometimes three independent methods that yielded agreeing results. At a level involving a little more theory is the agreement of the various measures of the mean kinetic energy of the granules involving diverse aspects of Brownian motion. Finally, we have the agreement of measures of Avogadro’s number mentioned in the previous paragraph. A feature of the latter is that they presupposed only very general features of the various phenomena, such as the carrying of one, two, or three units of the electronic charge by ions; the chaotic motion of granules in Brownian motion; or the discreet nature of alpha particles collected in a receiver. The agreeing measures of Avogadro’s number strongly supported the existence of molecules presumed by the various theories while leaving their detailed application as a separate issue.

At the beginning of their study the authors mention how they were attracted by van Fraassen’s paper on Brownian motion and its emphasis on the nature and importance of evidence. By the end of their book they have in fact constructed a case that is a decisive rebuttal of van Fraassen’s scepticism with respect to the ability of science to gain knowledge of molecules. They do not make this crucial point as clearly as they might have.