According to Albert Einstein, work of J.C. Maxwell in the fields of electricity, the magnetism and the kinetic theory of gases provided the executives necessary to the passage of Newtonian physics to contemporary physics. Its work constitutes an essential stake in the development of modern science, one decisive moment to understand the stakes of the debates which will animate the intellectual life of the end of the XIX E century and the beginning of the XXe century.

Very quickly, it shows brilliant provisions for the geometry (in 1846, it publishes its first article on the geometrical layout of the ovals) and for construction of mechanical models. At the sixteen years age, in 1847, it enters to the university of Edinburgh, where it is subject to mainly the influence of the physicist and experimentative brilliance David C. Forbes, and that of the metaphysician William R. Hamilton.

Entered in 1850 at the university of Cambridge, it obtains, after the success of its examination of exit in 1854, the pulpit of natural philosophy in Aberdeen. From 1860 to 1865, he teaches in King' S College of London and develops his scientific work; he resigns in 1865 for health reasons and withdraws himself in Glenlair. As from 1871, it is charged to create in Cambridge, thanks to funds granted by the duke of Devonshire, which was related to Henry Cavendish, the Cavendish laboratory. He dies of a cancer on on November 5th, 1879.

The first photography in three-color process

If the reputation of Maxwell is founded on his investigations in electromagnetism and kinetic theory of gases, it was also devoted, inter alia, with the vision of the colors, the Saturn's rings, geometrical optics, thermodynamics and mechanics.  

This multiplicity of the poles of interest should not eclipse the specificity of the Maxwellian thought. Between its hands, the electricity and the other disciplines of physics could acquire their fertile mathematical structures only insofar as its great control of the mathematical technique always remained under the control of an acute sense of physical reality. This exceptional association of a remarkable intuition in physics and facilities in mathematics, which points out Newton, founds at the same time the unit of the thought of Maxwell and the capacity of the scientist to reformulate the problems of physics.  

A pioneer of colorimetry
Maxwell, by prolonging the work of Thomas Young, set up the bases of quantitative colorimetry. Young had noticed that the colors were not given in a univocal way by the composition of the beam of light, but, quite to the contrary, that the same color could be perceived while sending on the eye of the beams of various compositions; thus, he had arrived at the fundamental concept of three-color process. He had thus proposed the assumption whereby there exists in the retina three types of receivers likely to answer each one the one of the three selected primary colors (according to Young, red, green and the purple one). Maxwell made his first experiments on the mixture of the colors in Edinburgh, in the laboratory of Forbes, since 1849. He carried out various combinations of colors by the fast rotation of coloured discs, divided into variable sectors. Then, by comparison of the effect on the sight of various associations, Maxwell and Forbes were led to the quantitative equations of the color and chose the red, blue and the green like primitive or fundamental colors.  

Thereafter, Maxwell discovered that daltonism resulted from a bad perception of the one of these three colors which left intact the mechanism of appreciation of both others. In its last reports on the color, published in Philosophical Transactions, he invented a “color box” in which the beams of light of various colors could be mixed according to various reports in order to be compared.  

The whole of this work leads to photography colors: Besides Maxwell carried out the first photography in three-color process by recombining by projection the images of an object photographed through three filters. The development of the rules defining colorimetry became possible.  

Saturn's rings

In 1855, whereas Maxwell finishes his studies in Cambridge and is on the point of leaving for Aberdeen, the subject of the fourth Adams price of the university of Cambridge is devoted to the investigation of the movement and the stability of the Saturn's rings. This problem, which had already been deepened by the French physicist Laplace in 1787, still raised very many difficulties. In fact, three assumptions were proposed: the rings either solid, or fluid (liquids or gas), or make up by independent material particles.  

Maxwell concludes, at the conclusion of delicate calculations, that only the third assumption was compatible with the stability of the rings, and thus that those consisted of a multiplicity of satellites of small mass. This work announces, of the opinion even of George Airy, by the method which it implements and the control of the mathematical language of which it is the sign, the richness of future work, and poses already the bases of the Maxwellian reflection on the kinetic theory of gases and the discontinuous structures.  

The kinetic theory of gases

The problem concerning the analysis of the movements of a large number of bodies which could enter in collision came to mind from Maxwell, on the one hand, under the impulse of its research devoted to the stability of the Saturn's rings and, on the other hand, because of its reading, in 1859, of the memories of 1857 and 1858 of Rudolf Clausius on the kinetic theory of gases. Clausius, by introducing the concept of the mean free path, could justify that a molecule moves during a short amount of time between two collisions.  

The “Maxwellian one”, function of distribution speeds
Clausius, like the whole of its contemporaries except for John J. Waterston, whose work passed unperceived, based his work on the simplifying assumption whereby all the molecules, whatever their nature, were driven in an enclosure at the same speed, dependant on the temperature. However, obviously, even by supposing equal initial speeds, appreciable differences appeared after some shocks, generating a whole range of values. It was thus necessary to find the means mathematically of expressing the speed of an unspecified particle at one moment given on its trajectory. Maxwell, in 1860, in “Illustrations off the Dynamical Theory off Gases”, published in Philosophical Magazine, then, on the basis of more rigorous method other, in 1867, in “One the Dynamical Theory off Gases”, published in Philosophical Transactions, establishes a statistical formula of the distribution speeds in a gas in balance (distribution of Maxwell).  

This result, which makes it possible to describe a real physical process by a statistical function, constitutes an innovation of decisive importance. In connection with work of Ludwig the Boltzmann relating to the problems of evolution of the systems, it will cause a reflection on the statute of the basic principles.  

Maxwell will apply then his function of distribution to the evaluation of the diffusion and viscosity coefficients, with thermal conduction like with other properties ignored at the time by Clausius. He showed inter alia, in experiments and theoretically, in 1866, in “One the Viscosity off Internal Friction off Air and Other Gases”, that the viscosity of a gas is independent of its pressure.  

In his last important article, published in Philosophical Transactions of 1879, Maxwell, in keeping with the experiments of William Crookes, poses the bases of the theory of the dynamic properties of gases under low pressure.  

Maxwell's equations

History
It is on on December 11th, 1855 that is read, in front of Cambridge Philosophical Society, the first work of Maxwell devoted to electricity: “One Faraday' S Lines off Force”. Maxwell is inspired there primarily by the articles published previously, in 1845 and 1847, by William Thomson, alias Lord Kelvin, as well as searchs for Michael Faraday, of which it will preserve the model of the tension fields understood like very fine tubes of force. This text, whose genesis can be recalled thanks to the correspondence exchanged between Maxwell and Thomson, is characteristic of Maxwellian methodology insofar as this last develops in the first part a series of hydrodynamic images which will then enable him to express the laws of electromagnetism in a mainly renewed mathematical language; the essential point consisting in deducing the known results from electricity and magnetism either on the basis of law of remote action of Newtonian type, but on that of a transmission of the electrical energy and displacement of an incompressible fluid in space.  

After a few years of reflection, Maxwell presents in 1861-1862, in Philosophical Magazine, the second work entitled “One Physical Lines off Force”, in which he proposes to build a coherent mechanical set theory of electromagnetism, i.e. “to examine the magnetic phenomena from the point of view of mechanics and to determine which kinds of tensions or movements in a given medium would be able to produce the mechanical effects observed”. The basic diagram is that of medium of a swirling type consisted a multiplicity of cells which, in a magnetic field, turn all in the same direction around axes parallel with the tension fields and whose training is carried out by a kind of roll of the dice. On this basis, Maxwell shows that, when the field acting on the dielectric medium (insulating matter or vacuum) varies with time, the position of the small balls of electricity changes and that, consequently, it results a true displacement current from it producing around him the same effects as a current of conduction in a metal (in both cases, the movement of the balls involves the rotation of the cells). That being, Maxwell gives to the law of the induction of Faraday his expression in differential form (second Maxwell's equation) and generalizes with the sizes quickly variable the laws of electromagnetism.  

Consequently, in the case of a variable electromagnetic signal, the dielectric medium can be the seat of transverse waves of which the propagation velocity is similar to that of the light; Maxwell observes, in a a little pathetic way, that “it is difficult for us not to conclude that the light is consisted the transverse waves of the same medium which produces the electric and magnetic phenomena”. Thus were brought luminous ether to Augustin Fresnel and ether closer to the electromagnetic actions. This integration of the light in the electromagnetic phenomena directs Maxwell towards the problem of the relative movement of the Earth and the ether, which will find its conclusion in the famous experiment of Albert A. Michelson and Edward W. Morley on speed of light.  

It is finally in the report entitled “with Dynamical Theory off the Electromagnetic Fields”, presented on on October 27th, 1864 in front of Royal Society, that Maxwell gives to his ideas their final form, forms that they will preserve in his Treaty of electricity and magnetism (1873). In the report of 1864, Maxwell leaves side, essentially, his model and described the mechanical properties of the electric field using the famous series of the four equations, called of Maxwell. The electromagnetic theory of the light rises directly from this whole of equations. In fact work of Heinrich Hertz, in 1887 will make it possible to obtain a direct experimental confirmation of the undulatory nature of the electromagnetic disturbances.  

The disappearance of the mechanical model in the report of 1864 makes it possible to better seize the range of this kind of model in Maxwellian methodology.  

Mathematical analogies and relationships
As of the first pages of its report “One Faraday' S Lines off Force”, written Maxwell: “To obtain physical concepts without adopting a physical theory, we must familiarize ourselves with the existence of physical analogies. I understand by there this partial similarity that we note between the laws of a given science and those of another which makes that one can be used to clarify the other. Thus all mathematical sciences rest on the relations between the physical laws and the numerical laws, so that the goal of any exact science consists in reducing the problems of nature to the determination of quantities while proceeding by operations on the numbers.”  

This Maxwellian methodology, centered on the idea of analogy and referring primarily to the mathematical relationships making it possible to bring closer various systems to laws (“a similarity between the relations, not between the things connected”), constitutes a constant topic of its thought, which it develops besides in an entitled conference “Analogy in Nature”, in front of the famous one and closed Apostles Club, in Cambridge, in February 1856.  

Mechanical, model models descriptive
It is also advisable to underline, if one wants to appreciate the whole of the Maxwellian thought, the role and the contribution of the mechanical models. But it is necessary well to be kept, as besides it suggests Maxwell himself, by his rejection in 1864 of the model advanced previously, to see in this one another thing that an imagined representation built on the basis of mechanical rules; from this point of view, to bring back all the phenomena to figures and movement carries out the Cartesian ideal well, but only in a methodological way, i.e. released of perspective metaphysics associated with the thought with Descartes. Maxwell, by his models, does not aim reality, it works out various supports being able to clarify the direction of the concepts.  

While not taking really with serious, from the point of view besides for Hamilton, its own mechanical engineering, Maxwell shows clearly that, for him, the whole of its differential equations constitutes its significant result. The field becomes gradually an irreducible entity, transforming the universe of physics and not awaiting more its justification of mechanical models. Consequently, a new perception of reality takes shape.  

By the diversity of his discoveries and the richness of the problems which it raised, Maxwell posed the bases in new manners of thinking. By drawing the attention to the concept of field, it opened the way with the contemporary physics, whose conceptual transformations of the beginning of the XX E century can be understood only from the point of view of its work.