_Electrodynamics._—Faraday’s representation of electric and magnetic fields by lines of force had been of great value in predicting the results of experiments in electromagnetism. But a more mathematical formulation of the laws governing these phenomena was needed in order to make possible quantitative development of the theory. This was supplied by Maxwell in his epoch-making treatise on “Electricity and Magnetism.” Starting with electrostatics and magnetism, he gives a complete account of the mathematical methods which had been devised for the solution of problems in these branches of the subject, and then turning to Ampère’s work he shows how the Lagrangian equations of motion lead to Faraday’s law if the single assumption is made that the magnetic energy of the field is kinetic. In the treatment of open circuits Maxwell’s intuition led to a great advance, the introduction of the displacement current. Consider a charged condenser, the plates of which are suddenly connected by a wire. A current will flow through the wire from the positively charged plate to the negative, but in the gap between the two plates the conduction current is missing. So convinced was Maxwell that currents must always flow in _closed_ circuits, that he postulated an electrical displacement in the medium between the plates of a charged condenser, which disappears when the condenser is short-circuited. Thus even in the so-called open circuit the current flows along a closed path. Maxwell’s theory of the electromagnetic field is based essentially on Faraday’s representation by lines of force of the strains and stresses of a universal medium. So it is not surprising that he was led to a consideration of the propagation of waves through this medium. The introduction of the displacement current made the form of the electrodynamic equations such as to yield a typical wave equation for space free from electrical charges and currents. Moreover, the disturbance was found to be transverse, and its velocity turned out to be _identical with that of light_. The conclusion was irresistible. That light could consist of anything but electromagnetic waves of extremely short length was inconceivable. In fact so certain was Maxwell of this deduction from theory that he felt it altogether unnecessary to resort to the test of experiment. For the electromagnetic theory explained so many of the details which had been revealed by experiments in light, that no doubt of its validity could be entertained. Even dispersion received ready elucidation on the assumption that the dispersing medium is made up of vibrators having a natural period comparable with that of the light passing through it. [Illustration: James Clerk Maxwell]