At the present time there exist no established, non-destructive methods for the measurement of depth of hardness in surface-hardened steels which are independent of the effects of chemical composition and quench procedure.Electrical non-destructive methods are dependent upon changes in the electrical and magnetic properties of steel which occur when it is hardened.The electrical method investigated by the authors was an a.c. one, based upon the measurement of the complex impedance of a search coil magnetically coupled to the test surface. Distinctly favourable results were obtained, and the paper is concerned with the theoretical and practical aspects of the procedure.