THE spinning electron of Uhlenbeck and l Goudsmit has brilliantly filled up a serious gap in atomic physics, but, while we cannot withhold our admiration from its successes, it is only fair to consider certain defects from which it suffers. When what is required is to double the number of states of the electron, it is at the least generous to introduce three extra degrees of freedom and then make an arbitrary (though not unnatural) assumption which cuts down the triple infinity to two. The electron is in fact given a complete outfit of Eulerian angles, even if it may not be necessary so to express the matter explicitly. Now we regard the electron as the most primitive thing in Nature, and it would therefore be much more satisfactory if the duality could be obtained without such great elaboration. The present communication is an attempt to do this; it is, I think, promising, though falling short of complete success, but as future stages would involve a very large amount of work, it seemed better to expose the theory to criticism at once, in case some serious objection can be made against the whole principle of it.