The fundamental principles involved in the theory of frequency multiplication by means of iron-core coupled circuits are briefly reviewed from the standpoint of Fourier analysis as well as that of recurring transients. Oscillograms and figures illustrating the effect of transformer inductance and shock duration upon wave form are given. Oscillations of the first and second kind are discussed in their relation to the analogous arc circuit problem. Efficiency and power output are considered in their dependence upon primary and secondary current amplitude, and the conditions for smoothest wave form and maximum efficiency are pointed out.