The paper first deals with the general principles of, and the conditions to be fulfilled by, coil ignition apparatus for internal combustion engines.It then describes a simplified treatment of the induction coil, regarded as a closely-coupled system with damping due to secondary loading, an assumption which is found to give results agreeing fairly well with practice.From this theory is developed a basis of coil design, enabling optimum values to be chosen so as to meet given conditions and indicating the limits which are met under extreme conditions of operation, generally at high engine speeds and low battery voltages.Methods of extending the range of operation, when necessary, are then dealt with, and special designs are described which have been developed with a view to meeting extreme conditions of operation.A further section deals briefly with the constructional features of modern coil systems, and with the principal points embodied in the various details.