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The history of linear motors is a history of shape. Once having departed from the cylindrical geometry of rotating machines, a wider world of three-dimensional design becomes possible. Linear induction motors dominate the field of linear drives to the same extent as does the rotary induction machine in relation to more complicated adjustable-speed motors. It is therefore thought appropriate to devote only one section to linear motors other than induction. A fairly full treatment of electromagnetic levitation is also included together with a treatment of oscillating machines. Perhaps the most important features are the division of electrical machines into two classes which are termed "magnetic" and "electromagnetic" and the "topological explosion" which is at present taking place in linear motor design. Some linear machines are already well established on a commercial basis but the vast bulk of recent inventions still remain to be exploited.