Maxwell succeeded in stating with precision certain points of Faraday’s ideas, and he gave them the mathematical form which, often wrongly, impresses physicists, but which when it exactly encloses a theory, is a certain proof that this theory is at least coherent and logical.[23]

[Footnote 23:  It will no doubt be a shock to those whom Professor Henry Armstrong has lately called the “mathematically-minded” to find a member of the Poincare family speaking disrespectfully of the science they have done so much to illustrate.  One may perhaps compare the expression in the text with M. Henri Poincare’s remark in his last allocution to the Academie des Sciences, that “Mathematics are sometimes a nuisance, and even a danger, when they induce us to affirm more than we know” (Comptes-rendus, 17th December 1906).]

The work of Maxwell is over-elaborated, complex, difficult to read, and often ill-understood, even at the present day.  Maxwell is more concerned in discovering whether it is possible to give an explanation of electrical and magnetic phenomena which shall be founded on the mechanical properties of a single medium, than in stating this explanation in precise terms.  He is aware that if we could succeed in constructing such an interpretation, it would be easy to propose an infinity of others, entirely equivalent from the point of view of the experimentally verifiable consequences; and his especial ambition is therefore to extract from the premises a general view, and to place in evidence something which would remain the common property of all the theories.

He succeeded in showing that if the electrostatic energy of an electromagnetic field be considered to represent potential energy, and its electrodynamic the kinetic energy, it becomes possible to satisfy both the principle of least action and that of the conservation of energy; from that moment—­if we eliminate a few difficulties which exist regarding the stability of the solutions—­the possibility of finding mechanical explanations of electromagnetic phenomena must be considered as demonstrated.  He thus succeeded, moreover, in stating precisely the notion of two electric and magnetic fields which are produced in all points of space, and which are strictly inter-connected, since the variation of the one immediately and compulsorily gives birth to the other.

From this hypothesis he deduced that, in the medium where this energy is localized, an electromagnetic wave is propagated with a velocity equal to the relation of the units of electric mass in the electromagnetic and electrostatic systems.  Now, experiments made known since his time have proved that this relation is numerically equal to the speed of light, and the more precise experiments made in consequence—­among which should be cited the particularly careful ones of M. Max Abraham—­have only rendered the coincidence still more complete.