Section 1 .— The hypothesis that the electron has a magnetic moment was, as is well known, first introduced to account for the duplexity phenomena of atomic spectra. More recently, however, Dirac has succeeded in accounting for these same phenomena by the introduction of a modified wave equation, which conforms both to the principle of relativity and to the general transformation theory. Formally, at least, on the new theory also, the electron has a magnetic moment of εh/mc , but when the electron is in an atom we cannot observe this magnetic moment directly; we can only observe the foment of the whole atom, or, of course, the splitting of the spectral lines, which we may say is “caused” by this moment. The question arises, has the free electron "really” got a magnetic moment, a magnetic moment that we can by any conceivable experiment observe? The question is not so simple as it might seem, because a magnetic moment εh/mc can never be observed directly, e.g ., with a magnetometer; there is always an uncertainty in the eternal electromagnetic field, due to the uncertainty in the position and velocity of the electron, and this uncertainty is greater than the effect of the electron magnet which we are trying to observe.

The scattering of fast electrons by atomic nuclei. (1929). Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 124(794), 425–442.