Much has been written on the design of transformers to carry direct current in the primary winding in addition to alternating current, and the value of an air-gap in the magnetic circuit has also received considerable attention. In thepresent paper the subject is taken up a new, and a method is demonstrated by which graphs relating to different values of direct current and of a.c. swing are plotted on a single chart. It is shown how these charts enable the designer to obtain the nearest possible approximation to a condition of constant inductance in the face of any variations of direct current or of a.c. swing (δB). In these charts abscissae æ give the air-gap in cm and ordinates give ΔB/δ, wheregrepresents gilberts. Examples of the use of δB.Δ in the calculation of the inductance are given, and test results on transformers designed from the charts are included as illustrating the value of the procedure.Attention is drawn to the paucity or lack of data available and certain subsidiary questions relating to the use of transformers of the type in question are dealt with in conclusion.