An earlier paper has described a very successful pole-changing winding for 3:1 speed ratio; which, however, had the disadvantage of needing eleven control leads and a slightly complicated controller. A new winding is here described¹ which needs only six control leads and a very simple controller, and which gives greater flexibility in the relative ratings at the two speeds. In addition, this winding can be made to operate efficiently at a third speed, using only nine control leads altogether, giving three speeds in the ratio 6:3:1, and at a fourth speed using thirteen control leads, giving four speeds in the ratios 6:3:2:1. The methods of obtaining the third and fourth speeds are described in the latter part of the paper.Besides being very successful in operation, this asymmetrical winding has a number of unusual theoretical features of very great interest. It is a working testimony to the possibility of permitting various forms of asymmetry and unbalance in electrical machinery without detriment to its operation.