The first section of the paper contains a brief review of the general theory underlying the determination of extra copper losses in armature windings carrying alternating current. Simplified methods of calculation are then described. The second part extends the study of the inverted turn transposition to the special case of three-phase windings, with two phases connected in series to form a single-phase winding and the third phase left idle. Formulas and tables are presented to show what reductions in copper losses may be expected for this connection, and to aid in deciding what type of transposition is best for a given winding. The final section of the paper deals with the twisted lead transposition, and presents formulas and tables showing reductions in extra losses to be gained from this method of inversion and connection. Details of the derivations of the formulas and examples of the use of the twisted lead transposition are contained in appendixes at the end of the paper.