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The relationship of the circle to the ellipse in special relativity is investigated and the results used to derive a metric that can be applied to study rotating frames of reference. It is known that the form of Maxwell's electromagnetic equations in a gravitational field is produced by replacing ordinary differentiation by covariant differentiation of the electromagnetic field tensor. The Schwarzschild metric is usually used for covariant differentiation in the gravitational field. The metric used herein to give Maxwell's equations in a rotating system is derived from the properties of the Lorentz transformation. The electromagnetic field tensor proposed for the rotating system is symmetric with respect to the magnetic and the electric field. The electromagnetic equations that are produced for the rotating system yield solutions that give standing waves. These waves are finite, contained, and localized in a small region of space. It is suggested that particles of matter with the properties of billiard balls do not exist but packets of contained electromagnetic waves may have some of the properties of particles. One such property is inertia, because waves carry on in their existing state until they are changed by refraction, reflection, diffraction, or interference with other waves. Units are chosen so that the velocity of light is unity. The distance traveled by a light signal in an inertial frame of reference equals the time of travel. [ABSTRACT FROM AUTHOR]