existence of electromagnetic waves, which travel at the speed of light. In other words, light is but one kind of electromagnetic wave. Maxwell's theory predicted there ought to be other types, with different frequencies. After some ingenious experiments, Maxwell's prediction was confirmed by German physicist Heinrich Hertz. In the process, Hertz generated and detected what are now called radio waves and built crude radio antennas and the predecessors of satellite dishes. Dutch physicist Hendrik Lorentz derived, using suitable boundary conditions, Fresnel's equations for the reflection and transmission of light in different media from Maxwell's equations. He also showed that Maxwell's theory succeeded in illuminating the phenomenon of light dispersion where other models failed. John William Strutt (Lord Rayleigh) and the American Josiah Willard Gibbs then proved that the optical equations derived from Maxwell's theory are the only self-consistent description of the reflection, refraction, and dispersion of light consistent with experimental results. Optics thus found a new foundation in electromagnetism. But it was Oliver Heaviside, an enthusiastic supporter of Maxwell's electromagnetic theory, who deserves most of the credit for shaping how people understood and applied Maxwell's work for decades to come. Maxwell originally wrote down a grand total of 20 equations for the electromagnetic field, which he later reduced to eight. Heaviside rewrote them in the form commonly used today, just four expressions. In addition, Heaviside was responsible for considerable progress in electrical telegraphy, telephony, and the study of the propagation of electromagnetic waves. Independent of Gibbs, Heaviside assembled a set of mathematical tools known as vector calculus to replace the quaternions, which were in vogue at the time but which Heaviside dismissed as "antiphysical and unnatural." Faraday also investigated how electrical currents affected chemical solutions. His experiments led him to the two laws of electrochemistry. Together with Whewell, Faraday introduced the basic vocabulary for the subject, the words electrode, anode, cathode, electrolysis, electrolyte, ion, anion, and cation. They remain in standard usage. But Faraday's work was of value to more than just chemists. In his Faraday Memorial Lecture in 1881, the German Hermann von Helmholtz asserted that Faraday's laws of electrochemistry hinted at the atomic structure of matter. If the chemical elements were distinguishable from one another by simple ratios of mass, and if the same amounts of electricity deposited amounts of these elements upon the poles in ratios, then electricity must also come in as discrete units, later named