James Clerk Maxwell was born on 13 June 1831 in Edinburgh, Scotland, into a family of high intellectual and cultural standing [1]. He showed interest in natural sciences from an early age, studying the nature of his garden as a child and starting scientific studies at the University of Edinburgh in 1847. Aged only 14, he wrote his first paper “On the description of oval curves…”, which appeared in 1846 in the Proceedings of the Royal Society of Edinburgh [2] (pp. 1–3). In 1850, he moved to Cambridge (first Peterhouse, then Trinity College), but in the meanwhile, he continued preparing scientific works on geometry, algebra, and elasticity. One very interesting instance is “On the equilibrium of elastic solids” [2] (pp. 30–73), read in 1850 and published in 1853 in the Transactions of the Royal Society of Edinburgh. In this paper, he entered the much debated question on the exact number of constants for (isotropic linear elastic) solid bodies (see, e.g., ^[3][4][3,4] for some details) with astonishing maturity for a young man aged 18 or so.

While in Cambridge, Maxwell greatly improved his knowledge of calculus, algebra, geometry, and natural phenomena, merging them into what we now would label as mathematical physics, that is, strong mathematical models for interpreting and predicting physical phenomena. In addition to continuing publishing while still a student (one instance is [1] (pp. 115–118)), this led him to become second best at the Mathematical Tripos of 1854, to be appointed Professor of Natural Philosophy (this was the name given in 19th century to physics in British educational institutions) at Marischal College in Aberdeen and elected Fellow of the Royal Society of Edinburgh in 1856, aged just 24 [1].

Maxwell’s following astonishing career in research, plus its undoubtable legacy in many fields of modern and contemporary physics and technics, are well known. One can read details in the site of the foundation devoted to him [1], in the preface to his collected works [2] (pp. ix–xxix), and in some biographies ^{[5][6][7][8][9][10][11][12][13]}[5,6,7,8,9,10,11,12,13], even though some of them were criticised by historians of science and epistemologists for being a bit naïve. In these documents (some of which are rather extended: for instance, ref. [5] counts about 600 pages!), we can also appreciate some descriptions of how Maxwell felt the influence of the Scottish culture of his time and the legacies of his families (his double surname actually comes from two influential Scottish families). Thus, this entry will not devote any space to these incredibly vast subjects, which would require a whole monograph to say the least, and will be limited to analysing in some detail the first paper where Maxwell dealt with electricity and magnetism.

In particular, it will focus on Maxwell’s unitary view of electrical and magnetic phenomena with those of another well-known branch of Natural Philosophy of his time, i.e., fluid motion. Indeed, in an entry work as the present one is, we believe that one should concentrate on a particular theme that can be of interest from both the epistemological and historical points of view. This entry then focuses on the apparent attempt by young Maxwell to reconcile ‘new’ branches of physics—i.e., electricity and magnetism—with the ‘mechanistic’ approach that was common in the epistemology of his time (see ^[3][4][3,4]), that is, the will to reduce all actions among bodies of whichever nature to those that could be seen as tractions or pressures.

Maxwell’s resorting to fluid mechanics came from his mastery in continuum mechanics; indeed, we should remember that he published several works in this field, e.g., [2] (pp. 80–114; pp. 246–247; pp. 248–262; pp. 377–409; pp. 514–525; pp. 598–604). In particular, the last two papers among the ones just quoted are known as original contributions in the theories of truss structures and of elasticity (a reciprocity theorem is formulated, which can serve as a means to solve redundant structures, see also [4]); to these, we should add [14] (pp. 102–104; pp. 161–207; pp. 492–497).

In the following, this entry will thus present Maxwell’s analogy between fluid flows and electric and magnetic flows, already highlighted in ^[15][16][17][15,16,17], on the basis of his first paper “On Faraday’s lines of force”, and thoroughly comment on its meaning and following developments. It will then also very briefly sketch some of the contents of the following papers, in order to highlight the above quoted developments. In technical publications it is not customary to quote original works massively; however, this entry will present a large number of excerpts from Maxwell’s “On Faraday’s lines of force”, sometimes in an extensive form. Indeed, far from being unwilling to provide our interpretation of Maxwell’s work, we firmly believe that any comment on the actual meaning and deep influence of scientific and technical contributions of the past cannot be thoroughly grasped if the original words of the author are filtered by the comments of the investigators. This is true not only for works on philology or philosophy, but it is well customary in history and philosophy of science and technology, in order to catch also the influence of culture, religion, and society of the time on the scientist’s thought and work. In this regard, it is worth recalling the second paragraph of [18], where we read that ‘science does not exist in a vacuum, and studies in the sociology, history, and philosophy of science often emphasize how scientists’ broader beliefs and practices influence their work, and thus the way that science develop’. Then, reporting Maxwell’s original words repeatedly and in full is not a mere action of bibliographic recovery, but a means of regaining the actual root of his thoughts. In addition, to the best of our knowledge, while in other monographs (e.g., ^[5][6][5,6]) attention is focussed on the most mature Maxwell’s treatise of 1873 (which will be only sketched below in this entry), little attention has been devoted to a detailed analysis of the origins of Maxwell’s investigations on electrical phenomena, basing on Faraday’s ideas of lines of force, apart from some hints in ref. [19] and a slightly more extensive discussion, completed by a French translation of the paper, in ref. [17]; thus, this will be the core of the entry’s contribution.